Relevant bibliographies by topics / Numerical simulation of solutions

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Academic literature on the topic 'Numerical simulation of solutions'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

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Journal articles on the topic "Numerical simulation of solutions"

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Debrie, Ayalew. "Simulation of Harmonic motion." J. of Physical and Chemical Sciences 6, no. 3 (2018): 02. https://doi.org/10.5281/zenodo.1254645.

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            In this work, we study   the characteristics of simple harmonic motion and to solve physical problems related to simple harmonic motion (SHM) using MATLAB computer program. To achieve the objectives, the necessary techniques had been done using both analytical and numerical mathematical computations. Among the numerical methods, we had concentrate Runge Kutta forth order method. The solutions would be given by figures. For the undamped and damped SHM we solve numerically using the above numerical methods with applying the differential algorithm. With this respect, by adjusting the set of equidistant points (the step size) the numerical solution is comparable with the analytical one. For both cases, the undamped and damped SHM the numerical solution obtained using Runge-kutta is almost the same as to the solution obtained using analytical method.
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Skinner, J. W., and J. Y.-K. Cho. "Numerical convergence of hot-Jupiter atmospheric flow solutions." Monthly Notices of the Royal Astronomical Society 504, no. 4 (2021): 5172–87. http://dx.doi.org/10.1093/mnras/stab971.

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ABSTRACT We perform an extensive study of numerical convergence for hot-Jupiter atmospheric flow solutions in simulations employing a setup commonly used in extrasolar planet studies – a resting state thermally forced to a prescribed temperature distribution on a short time-scale at high altitudes. Convergence is assessed rigorously with (i) a highly accurate pseudospectral model that has been explicitly verified to perform well under hot-Jupiter flow conditions and (ii) comparisons of the kinetic energy spectra, instantaneous (unaveraged) vorticity fields and temporal evolutions of the vorticity field from simulations that are numerically equatable. In the simulations, the (horizontal as well as vertical) resolution, dissipation operator order, and viscosity coefficient are varied with identical physical and initial setups. All of the simulations are compared against a fiducial reference simulation at high horizontal resolution and dissipation order (T682 and ∇ 16, respectively) – as well as against each other. Broadly, the reference solution features a dynamic, zonally (east–west) asymmetric jet with a copious amount of small-scale vortices and gravity waves. Here, we show that simulations converge to the reference simulation only at T341 resolution and with ∇ 16 dissipation order. Below this resolution and order, simulations either do not converge or converge to unphysical solutions. The general convergence behaviour is independent of the vertical range of the atmosphere modelled, from $\sim 2 \times 10^{-3}$MPa to $\sim 2 \times 10^1$ MPa. Ramifications for current extrasolar planet atmosphere modelling and observations are discussed.
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Zhang, Cheng Li, and Yun Zeng. "A Simple Numerical Simulation Method for Lorenz System Families." Applied Mechanics and Materials 444-445 (October 2013): 786–90. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.786.

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Lorenz system families contain Lorenz system, Chen system and Lu system, their accurate analytical solutions are not yet obtained now. The segmenting recursion method was put forward in this paper, the equations of Lorenz system families were reasonably linearized within small segment, the recursion formulas were obtained by solving the approximate analytical solutions within small segment, and all numerical solutions were got by the recursion formulas. The chaotic motion of Lorenz system families were numerically simulated by means of the segmenting recursion method, the simulation results were compared with Runge-Kutta method. The comparative results show that the segmenting recursion method is very effective to numerically simulate Lorenz system families, not only method is simple, programming is easy, but result is accurate. this method is a universal new method to numerically simulate similar system.
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Mamman, Ali Bulama, Haruna Usman Idriss, and Bashir Mai Umar. "Numerical Solution of linear Second Order Partial Differential Equation." International Journal of Research and Innovation in Applied Science X, no. IV (2025): 951–65. https://doi.org/10.51584/ijrias.2025.10040081.

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This study explores the analytical and numerical solutions of partial differential equations (PDEs), focusing on parabolic (heat). The first part presents their analytical solutions using initial and boundary conditions and delves into the finite difference method (FDM), discussing forward, backward, and central difference schemes. These methods are applied to numerically solve one- and two-dimensional heat. The Crank-Nicolson method, recognized for its unconditional stability, is employed to improve the accuracy of heat equation solutions, overcoming limitations of explicit and implicit schemes. We then analyze the performance, strengths, and weaknesses of FDM through numerical simulations of one-dimensional heat. Due to computational constraints, Crank-Nicolson for 1D simulation, was not executed. Results indicate that the implicit backward difference method demonstrates superior stability by allowing unrestricted step sizes compared to the explicit forward difference method. These findings contribute to a deeper understanding of numerical PDE solutions and stability considerations in computational mathematics.
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Yokuş, Asıf, and Doğan Kaya. "Comparison exact and numerical simulation of the traveling wave solution in nonlinear dynamics." International Journal of Modern Physics B 34, no. 29 (2020): 2050282. http://dx.doi.org/10.1142/s0217979220502823.

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The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.
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Tai, Irfan, Marie Ann Giddins, and Ann Muggeridge. "Improved Calculation of Wellblock Pressures for Numerical Simulation of Non-Newtonian Polymer Injection." SPE Journal 26, no. 04 (2021): 2352–63. http://dx.doi.org/10.2118/205339-pa.

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Summary The viability of any enhanced-oil-recovery project depends on the ability to inject the displacing fluid at an economic rate. This is typically evaluated using finite-volume numerical simulation. These simulators calculate injectivity using the Peaceman method (Peaceman 1978), which assumes that flow is Newtonian. Most polymer solutions exhibit some degree of non-Newtonian behavior resulting in a changing polymer viscosity with distance from the injection well. For shear-thinning polymer solutions, conventional simulations can overpredict injection-well bottomhole pressure (BHP) by several hundred psi, unless a computationally costly local grid refinement is used in the near-wellbore region. We show theoretically and numerically that the Peaceman pressure-equivalent radius, based on Darcy flow, is not correct when fluids are shear thinning, and derive an analytical expression for calculating the correct radius. The expression does not depend on any particular functional relationship between polymer-solution viscosity and velocity. We test it using the relationship described by the Meter equation (Meter and Bird 1964) and the Cannella et al. (1988) correlation. Numerical tests indicate that the solution provides a significant improvement in the accuracy of BHP calculations for conventional numerical simulation, reducing or removing the need for expensive local grid refinement around the well when simulating the injection of fluids with shear-thinning non-Newtonian rheology.
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Pérez-Benítez, J. A., P. Martínez-Ortiz, and J. Aguila-Muñoz. "A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields." Brain Sciences 13, no. 8 (2023): 1142. http://dx.doi.org/10.3390/brainsci13081142.

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Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.
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Noshad, Mahlagha, Amir Pishkoo, and Maslina Darus. "Solving Conformable Fractional Differential Equations with ``EJS Software and Visualization of Sub-diffusion Process." European Journal of Pure and Applied Mathematics 15, no. 4 (2022): 1738–49. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4547.

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In this work, we numerically solve ordinary and conformable fractional differential equations using Easy Java Simulations software. Their solutions, including homogeneous and non-homogeneous parts, are compared in various time intervals. Using software’s visualization andsimulation features, we may better examine, compare, and evaluate solutions of analytical and numerical fractional differential equations. A kind of oscillatory behavior is seen in long enough times. In simulation of diffusion and sub-diffusion processes, two intriguing events have been observed.
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Risher, D. W., L. M. Schutte, and C. F. Runge. "The Use of Inverse Dynamics Solutions in Direct Dynamics Simulations." Journal of Biomechanical Engineering 119, no. 4 (1997): 417–22. http://dx.doi.org/10.1115/1.2798288.

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Previous attempts to use inverse dynamics solutions in direct dynamics simulations have failed to replicate the input data of the inverse dynamics problem. Measurement and derivative estimation error, different inverse dynamics and direct dynamics models, and numerical integration error have all been suggested as possible causes of inverse dynamics simulation failure. However, using a biomechanical model of the type typically used in gait analysis applications for inverse dynamics calculations of joint moments, we produce a direct dynamics simulation that exactly matches the measured movement pattern used as input to the inverse dynamic problem. This example of successful inverse dynamics simulation demonstrates that although different inverse dynamics and direct dynamics models may lead to inverse dynamics simulation failure, measurement and derivative estimation error do not. In addition, inverse dynamics simulation failure due to numerical integration errors can be avoided. Further, we demonstrate that insufficient control signal dimensionality (i.e., freedom of the control signals to take on different “shapes”), a previously unrecognized cause of inverse dynamics simulation failure, will cause inverse dynamics simulation failure even with a perfect model and perfect data, regardless of sampling frequency.
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Bretti, Gabriella. "Differential Models, Numerical Simulations and Applications." Axioms 10, no. 4 (2021): 260. http://dx.doi.org/10.3390/axioms10040260.

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Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, the development of numerical methods and efficient simulation algorithms play a key role in the computation of the solutions to many relevant problems. Moreover, since the model parameters in mathematical models have interesting scientific interpretations and their values are often unknown, estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In this respect, this Special Issue collects some important developments in different areas of application.
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Dissertations / Theses on the topic "Numerical simulation of solutions"

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Votapka, Lane William. "Numerical and Computational Solutions for Biochemical Kinetics, Druggability, and Simulation." Thesis, University of California, San Diego, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10062341.

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<p> Computational tools provide the automation and power that enable detailed modeling and analysis of many biomolecular phenomena of interest. Open source programs and automated tools empower researchers and provide opportunities for improvement to existing software. In the past few years, I have developed several open-source scientific software packages for the purposes of automating difficult or menial tasks pertaining to computational biophysics. These software packages involve the analysis of molecular dynamics simulations, Brownian dynamics simulations, electrostatics, pocket volume measurement, solvent fragment mapping, binding site characterization, milestoning theory, and allosteric network communications. In addition to allowing my research group and me to approach biomedical challenges that would otherwise be intractable, I hope and intend that these tools will be useful to the computational and theoretical biophysics research community.</p>
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Gaines, Jessica Gabrielle. "Topics in the numerical simulation of pathwise solutions to stochastic differential equations." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/13867.

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This work contains several developments in the area of numerical solution of pathwise solutions to stochastic differential equations (SDE's). In the first chapter we define and motivate pathwise solutions and give a brief survey of numerical methods for approximating them. The main key to enlarging the scope of numerical methods for SDE's is a good representation of Brownian paths. A binary tree structure is an essential tool in Chapter Two, which presents a general method for solution of SDE's using variable time steps. In the case of a general SDE, improvement of the order of convergence compared with standard methods, demands generation of the Lévy area integrals. Chapter Three presents a method of random generation of the Lévy area for a Brownian path in <I>IR</I><SUP>2</SUP>. The method is based on Marsaglia's rectangle-wedge-tail method for fast generation of normally distributed deviates. Since the solution of an SDE generally depends on an infinite sequence of iterated integrals of the driving noise, it makes sense to examine these integrals and the algebraic relations between them. In Chapter Four, it is shown how known facts about shuffle algebras can be used to get a better understanding of stochastic iterated integrals of Ito and Stratonovich type and obtain practical algebraic bases for these two sets. We use the algebra to calculate moments of stochastic integrals, needed when calculating moments of error during numerical solutions of SDE's. The work on the generation of area integrals, described in Chapter Three, gives rise to general questions about the generation of random deviates, some of which are addressed in the last two chapters. In Chapter Five, we present a polynomial-time algorithm for finding the partition, into rectangles or triangles, of certain types of region in <I>IR</I><SUP>2</SUP>, that has the lowest entropy.
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Bhalala, Ashesh 1964. "Numerical solution algorithms in the DLANET program." Thesis, The University of Arizona, 1989. http://hdl.handle.net/10150/276957.

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Several methods to solve a system of linear equations with real and complex coefficients exist. The most popular methods are Gauss-Jordan, L-U Decomposition, Gauss-Seidel, and Matrix Reduction. These methods are utilized to optimize run-time of the DLANET circuit analysis program. As concluded by this study, the Matrix Reduction method which is presently utilized in the DLANET program, results in run-times which are faster than the other solution methods studied in this paper for lower order systems. Similarly, the L-U Decomposition and Gauss-Jordan methods result in faster run-times than the other techniques for higher order systems. Finally, the Gauss-Seidel Iterative method, when incorporated into the DLANET program, has proven to be much slower than the other solution methods considered in this paper.
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Etekpo, Kossi. "Numerical solution for subsurface reservoir simulation." Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/25007.

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Transport problems in porous media constitute an important field of scientific research in modern world, due to their broad applications in area such as petroleum engineering, water resources, pollutants transport and green- house gases sequestration to just mention few. The mathematical models that describe such problems have been developed and form one of the main classes of partial differential equations (PDEs) that scientists encounter in the real-world modeling. Nevertheless, in most of the cases, the exact solutions in the classical sense of those models are not available. The study of numerical approximation of PDEs is therefore an active research area and there is an extensive literature on numerical methods for PDEs. In this work, we review some numerical techniques, more precisely we present finite volume method with two-point flux approximation and mixed finite volume method for spatial discretization of elliptic and parabolic PDEs modeling transport flow in porous media. We then present some standard explicit and implicit methods, Rosenbrock schemes and exponential time stepping schemes for temporal discretization. We finally run some numerical simulations of advection-diffusion-reaction problems in a heterogeneous and an anisotropic porous media.
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Pinilla, Camilo Ernesto. "Numerical simulation of shear instability in shallow shear flows." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115697.

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The instabilities of shallow shear flows are analyzed to study exchanges processes across shear flows in inland and coastal waters, coastal and ocean currents, and winds across the thermal-and-moisture fronts. These shear flows observed in nature are driven by gravity and governed by the shallow water equations (SWE). A highly accurate, and robust, computational scheme has been developed to solve these SWE. Time integration of the SWE was carried out using the fourth-order Runge-Kutta scheme. A third-order upwind bias finite difference approximation known as QUICK (Quadratic Upstream Interpolation of Convective Kinematics) was employed for the spatial discretization. The numerical oscillations were controlled using flux limiters for Total Variation Diminishing (TVD). Direct numerical simulations (DNS) were conducted for the base flow with the TANH velocity profile, and the base flow in the form of a jet with the SECH velocity profile. The depth across the base flows was selected for the' balance of the driving forces. In the rotating flow simulation, the Coriolis force in the lateral direction was perfectly in balance with the pressure gradient across the shear flow during the simulation. The development of instabilities in the shear flows was considered for a range of convective Froude number, friction number, and Rossby number. The DNS of the SWE has produced linear results that are consistent with classical stability analyses based on the normal mode approach, and new results that had not been determined by the classical method. The formation of eddies, and the generation of shocklets subsequent to the linear instabilities were computed as part of the DNS. Without modelling the small scales, the simulation was able to produce the correct turbulent spreading rate in agreement with the experimental observations. The simulations have identified radiation damping, in addition to friction damping, as a primary factor of influence on the instability of the shear flows admissible to waves. A convective Froude number correlated the energy lost due to radiation damping. The friction number determined the energy lost due to friction. A significant fraction of available energy produced by the shear flow is lost due the radiation of waves at high convective Froude number. This radiation of gravity waves in shallow gravity-stratified shear flow, and its dependence on the convective Froude number, is shown to be analogous to the Mach-number effect in compressible flow. Furthermore, and most significantly, is the discovery from the simulation the crucial role of the radiation damping in the development of shear flows in the rotating earth. Rings and eddies were produced by the rotating-flow simulations in a range of Rossby numbers, as they were observed in the Gulf Stream of the Atlantic, Jet Stream in the atmosphere, and various fronts across currents in coastal waters.
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Tan, Don Bing Dong. "Is the precision of computed solutions more closely related with componentwise condition number than normwise condition number?" HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/153.

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We have a conjecture that “the precision of computed solutions for systems of linear equations is more closely related with componentwise condition number c(A) than normwise condition number κ(A). We conducted simulation experiments to verify this conjecture. A statistical tool, Hotelling-Williams T-Test is employed to check if difference between correlations is significant. Simulation results suggest that our conjecture is true for most of the well-known methods and matrix sizes. Keywords: condition numbers, simulation, correlation coefficients, Hotelling-Williams T-Test
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Figueroa, Leonardo E. "Deterministic simulation of multi-beaded models of dilute polymer solutions." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:4c3414ba-415a-4109-8e98-6c4fa24f9cdc.

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We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173--187, 1996). We extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le~Bris, Leli\`evre and Maday to the technically more complicated situation of the elliptic Fokker--Planck equation, where the role of the Laplace operator is played out by a high-dimensional Ornstein--Uhlenbeck operator with unbounded drift, of the kind that appears in Fokker--Planck equations that arise in bead-spring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a high-dimensional Cartesian product configuration space $\mathsf{D} = D_1 \times \dotsm \times D_N$ contained in $\mathbb{R}^{N d}$, where each set $D_i$, $i=1, \dotsc, N$, is a bounded open ball in $\mathbb{R}^d$, $d = 2, 3$. We exploit detailed information on the spectral properties and elliptic regularity of the Ornstein--Uhlenbeck operator to give conditions on the true solution of the Fokker--Planck equation which guarantee certain rates of convergence of the greedy algorithms. We extend the analysis to discretized versions of the greedy algorithms.
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Petrova, Nadezda. "Turbulence-chemistry interaction models for numerical simulation of aeronautical propulsion systems." Palaiseau, Ecole polytechnique, 2015. https://tel.archives-ouvertes.fr/tel-01138235/document.

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La modélisation de l'interaction turbulence-chimie est un point clé dans la simulation numérique des écoulements réactifs turbulents. Cette thèse est consacrée à l'adaptation et l'intégration de différents modèles de combustion turbulente dans le code d'écoulements diphasiques réactifs pour l'énergétique (CEDRE) de l'ONERA. La première partie de la thèse est dédiée à l'étude des équations quasi-linéaires hyperboliques stochastiques aux dérivées partielles (SPDEs) qui sont statistiquement équivalentes à une équation de transport pour la fonction de densité de probabilité (PDF) jointe vitesse-scalaires. Il est démontré que pour préserver l'équivalence entre les SPDEs et l'équation de transport pour la PDF jointe vitesse-scalaires, les solutions multivaluées des SPDEs doivent être prises en compte. Une nouvelle méthode stochastique pour résoudre les SPDEs, récemment proposée par O. Soulard [EmakoLetizia2014], est étudiée et validée sur des cas-tests unidimensionnels. Il est montré que cette méthode permet de trouver les solutions multivaluées des SPDEs au sens statistique. La résolution numérique des SPDEs étant particulièrement coûteuse, une seconde voie a été explorée au cours de cette thèse. Il s'agit, dans la deuxième partie de ce mémoire, de la mise en oeuvre du modèle "flammelettes tabulées pour la chimie" (FTC) et du modèle "réacteur partiellement mélangé étendu" (EPaSR). Avec le code CEDRE, l'approche FTC est mise à jour en supposant une distribution de type beta-PDF. L'adaptation LES/EPaSR [SabelnikovFureby2013] pour le RANS et son intégration dans CEDRE ont été réalisées. Les modèles EPaSR et "FTC avec beta-PDF présumée" ont été validés par rapport aux données expérimentales [MagreMoreau1988] sur une configuration de flamme stabilisée par une marche descendante. Il est montré que le calcul RANS/EPaSR donne un meilleur accord avec l'expérience que les autres approches évaluées<br>Modeling the turbulence-chemistry interaction is a key point in the numerical simulation of the combustion in the air- breathing engines. The present work is devoted to adaptation and integration of several different turbulent combustion models into the ONERA industrial code CFD package for diphasic reactive ows (CEDRE). The first part of the thesis is focused on the quasi-linear hyperbolic stochastic partial differential equations (SPDEs) which are statistically equivalent to a transport equation for the joint velocity-scalars probability density function (PDF). It is shown that in order to preserve the equivalence between the SPDEs and the transport equation for the joint velocity-scalars PDF, multivalued solutions of the SPDEs should be taken into account. A new stochastic method to solve the SPDEs, recently proposed by O. Soulard [Emako-Letizia2014], is considered and validated on one-dimensional test-cases. It is shown that this method is able to recover the multivalued solutions of the SPDEs in the statistical sense. The numerical solution of the SPDEs is time consuming, therefore the second part of the thesis is concerned with a flamelet tabulated chemistry (FTC) and an extended partially stirred reactor (EPaSR) models. In the framework of CEDRE CFD software the FTC approach is updated, presuming that the distribution is given by a beta-PDF. The adaptation of the LES/EPaSR model [SabelnikovFureby2013] to the RANS and its integration into CEDRE are done. The EPaSR and the FTC with the presumed beta-PDF are validated against experimental data [MagreMoreau1988] on a configuration of a backward-facing step combustor. It is shown that the RANS/EPaSR calculation yields the best agreement with the experiment compared to other considered approaches
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Hu, Guanghui. "Numerical simulations of the steady Euler equations on unstructured grids." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1106.

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Coussement, Axel. "Direct numerical simulation and reduced chemical schemes for combustion of perfect and real gases." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209765.

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La première partie de cette thèse traite du développement du code de simulation numérique directe YWC, principalement du développement des conditions aux limites. En effet, une forte contribution scientifique a été apportée aux conditions aux limites appelées "Three dimensional Navier-Stokes characteristic boundary condtions" (3D-NSCBC). Premièrement, la formulation de ces conditions aux arêtes et coins a été complétée, ensuite une extension de la formulation a été proposée pour supprimer les déformations observées en sortie dans le cas d'écoulements non-perpendiculaires à la frontière. <p>De plus, ces conditions ont été étendues au cas des gaz réels et une nouvelle définition du facteur de relaxation pour la pression a été proposée. Ce nouveau facteur de relaxation permet de supprimer les déformations observées en sortie pour des écoulements transcritiques. <p>Les résultats obtenus avec le code YWC ont ensuite été utilisés dans la seconde partie de la thèse pour développer une nouvelle méthode de tabulation basée sur l'analyse en composantes principales. Par rapport aux méthodes existante telles que FPI ou SLFM, la technique proposée, permet une identification automatique des variables à transporter et n'est, de plus, pas lié à un régime de combustion spécifique. Cette technique a permis d'effectuer des calculs d'interaction flamme-vortex en ne transportant que 5 espèces à la place des 9 requises pour le calcul en chimie détaillée complète, sans pour autant perdre en précision. <p>Finalement, dans le but de réduire encore le nombre d'espèces transportées, les techniques T-BAKED et HT-BAKED PCA ont été introduites. En utilisant une pondération des points sous-représentés, ces deux techniques permettent d'augmenter la précision de l'analyse par composantes principales dans le cadre des phénomènes de combustion.<p><br>Doctorat en Sciences de l'ingénieur<br>info:eu-repo/semantics/nonPublished
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Books on the topic "Numerical simulation of solutions"

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GAMM Workshop on the Numerical Simulation of Compressible Euler Flows (1986 INRIA). Numerical simulation of compressible Euler flows: A GAMM Workshop. Friedr. Vieweg & Sohn, 1989.

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Odile, Bristeau Marie, and GAMM Workshop on Numerical Simulation of Compressible Navier-Stokes Flows (1985 : Nice, France), eds. Numerical simulation of compressible Navier-Stokes flows: A GAMM workshop. F. Vieweg, 1987.

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Fitzgibbon, W. E. Applied and numerical partial differential equations: Scientific computing in simulation, optimization and control in a multidisciplinary context. Springer, 2010.

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Hulsen, Martinus Antonius. Analysis and numerical simulation of the flow of viscoelastic fluids. Delft University Press, 1988.

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M, Hafez M., and Kwak Dochan, eds. Numerical simulations of incompressible flows. World Scientific, 2003.

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Larson, Magnus. NMLONG: Numerical model for simulating longshore current. US Army Corps of Engineers, Engineer Research and Development Center, Coastal and Hydraulics Laboratory, 2002.

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1960-, Johnston Peter, ed. Computational inverse problems in electrocardiography. WIT, 2001.

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Jin-Chern, Chiou, Downer Janice Diane, and United States. National Aeronautics and Space Administration., eds. Staggered solution procedures for multibody dynamics simulation. Center for Space Structures and Controls, College of Engineering, University of Colorado, 1990.

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C, Chiou J., Downer J. D, and United States. National Aeronautics and Space Administration., eds. Staggered solution procedures for multibody dynamics simulation. Center for Space Structures and Controls, College of Engineering, University of Colorado, 1990.

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Center, Ames Research, ed. Navier-Stokes simulations of unsteady transonic flow phenomena. National Aeronautics and Space Administration, Ames Research Center, 1992.

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Book chapters on the topic "Numerical simulation of solutions"

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Deister, F., D. Rocher, E. H. Hirschel, and F. Monnoyer. "Self-Organizing Hybrid Cartesian Grid Generation and Solutions for Arbitrary Geometries." In Numerical Flow Simulation II. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44567-8_2.

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Deister, F., D. Rocher, E. H. Hirschel, and F. Monnoyer. "Adaptively Refined Cartesian Grid Generation and Euler Flow Solutions for Arbitrary Geometries." In Numerical Flow Simulation I. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-540-44437-4_2.

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Kircher, Roland, and Wolfgang Bergner. "Numerical Solution." In Three-Dimensional Simulation of Semiconductor Devices. Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7731-2_4.

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Wu, Lizhou, and Jianting Zhou. "Numerical Solutions to Infiltration Equation." In Rainfall Infiltration in Unsaturated Soil Slope Failure. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-9737-2_3.

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AbstractUnsaturated infiltration issues occur in many fields, such as rainfall-induced soil slope failures (Wu et al. in Hydro-mechanical analysis of rainfall-induced landslides. Springer, 2020a; Wu et al. in Appl Math Model 80:408–425, 2020b; Jiang et al. in Eng Comput 38:1–14, 2022), solute migration simulation (Cross et al. in Adv Water Resour 136, 2020), and coal seam water injection and coalbed methane extraction (Liu et al. 2018; Wang et al. in J Comput Appl Math 367, 2020).
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Platen, Eckhard, and Nicola Bruti-Liberati. "Exact Simulation of Solutions of SDEs." In Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13694-8_2.

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Piechna, Adam, and Marcin Pieniak. "Numerical simulation of the effect of supplying arteries occlusion on cerebral blood flow." In Advanced Mechatronics Solutions. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23923-1_27.

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Hock, Kiel, François Méot, and Vasiliy Morozov. "Spin Dynamics Tutorial: Numerical Simulations." In Polarized Beam Dynamics and Instrumentation in Particle Accelerators. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-16715-7_14.

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AbstractNumerical simulations are inescapable steps in spin dynamics studies and in the design of polarized beam accelerators and optical components. An integral part of the Summer 2021 USPAS Spin Class teachings, under the form of a 2-week miniworkshop, this chapter is also an initiation to the field, “hands on”: in a first Section, numerical simulation exercises are proposed which cover many of the theoretical aspects of hadron and electron spin dynamics addressed during the lectures, including resonant depolarization; preservation methods such as harmonic orbit correction, tune jump, the use of an ac dipole, or snakes; the effect of synchrotron radiation; spin diffusion and its suppression; spin matching. A second Section is dedicated to detailed solutions of these simulation exercises and includes tight comparisons of numerical outcomes and theoretical expectations from the lectures.
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Hackbusch, Wolfgang, Sabine Gutsch, Jean-François Maitre, and François Musy. "The appropriate numbering for the multigrid solution of convection dominated problems." In Numerical Flow Simulation I. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-540-44437-4_4.

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Tetzlaff, Daniel M., and John W. Harbaugh. "Numerical Solutions of the Flow Equations." In Simulating Clastic Sedimentation. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4757-0692-5_3.

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Adhikari, Nirajan, and D. Stephen Nichols. "Incompressible Solutions About High-Lift Wing Configurations." In Numerical Simulation of the Aerodynamics of High-Lift Configurations. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-62136-4_3.

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Conference papers on the topic "Numerical simulation of solutions"

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Watson, M. K., and J. Postlethwaite. "Numerical Simulation of Crevice Corrosion." In CORROSION 1990. NACE International, 1990. https://doi.org/10.5006/c1990-90156.

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Abstract The process of crevice corrosion consists of anodic metal dissolution from the alloy to the crevice solution, cathodic reduction of oxygen on the bold surface of the metal outside the crevice, metal ion hydrolysis reactions, and mass transfer between the crevice solution and the bulk solution. The mass transfer process mechanisms are ionic migration and diffusion. An improved mathematical model has been developed for the numerical simulation of the incubation period of crevice corrosion. The model utilizes a new equation for the transport processes, which includes both ionic migration and diffusion. An explicit finite-difference technique is applied to a uni-dimensional crevice along the crevice depth, with appropriate boundary conditions at both the crevice tip and bulk solution. Use of the surface profile of the crevice in the modelling of the ionic migration and diffusion processes leads to a much more accurate simulation of the crevice corrosion process. Narrow crevices within the overall crevice can achieve active corrosion, while the rest of the crevice remains completely passive, whether these narrow crevices are found at the tip, middle or mouth of the crevice. Therefore, active corrosion can occur for any crevice having a crevice depth that is greater than the depth required for deoxygenation, depending on the crevice gap profile.
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Evitts, R. W., M. K. Watson, and J. Postlethwaite. "Numerical Simulation of Crevice Corrosion of Titanium: Effect of the Bold Surface." In CORROSION 1996. NACE International, 1996. https://doi.org/10.5006/c1996-96121.

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Abstract A rigorous crevice corrosion model has been developed that accounts for the bold metal surfaces exterior to the crevice. The model predicts the time change in concentration of all specified chemical species in the crevice and bulk solution, and has the ability to predict active corrosion. It is applied to the crevice corrosion of a small titanium crevice in both oxygenated and anaerobic sodium chloride solutions. The numerical predictions confirm that oxygen is the driving force for crevice corrosion. During the simulations where oxygen is initially present in both the crevice and bulk solution an acidic chloride solution is developed; this is the precursor required for crevice corrosion. The anaerobic case displays no tendency to form such a solution. It is also confirmed that those areas in the crevice that are deoxygenated become anodic and the bold metal surface becomes cathodic. As expected, active corrosion is not attained as the simulations are based on electrochemical and chemical parameters at 25°C.
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Liu, Ko-Fei, and Ming-Chun Huang. "Numerical Simulation of Debris Flows." In ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/omae2009-79197.

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A numerical program developed for field application is presented in this paper. We use the generalized Julien and Lan (1991) rheological model to simulate debris flows. Due to the derivative discontinuous nature of the constitutive law, flow is separated into plug region and bottom region (with stress greater than yield stress). The program solves the plug flow layer solution first and then corrects the solution with the bottom layer approximation. Numerical scheme with upwind method and central difference in space and Adam-Bashforth 3rd order scheme in time is used for both layers. The scheme is tested against analytical solutions and laboratory experiments with very good results. Application to a field case with more complicated geometry, also achieves good agreement with error less than 5% compared with field measurements. Final example demonstrates how this numerical program is used in a preliminary design.
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Crowhurst, P., and Zhenquan Li. "Numerical Solutions of One-Dimensional Shallow Water Equations." In 2013 UKSim 15th International Conference on Computer Modelling and Simulation (UKSim 2013). IEEE, 2013. http://dx.doi.org/10.1109/uksim.2013.63.

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Bastakoti, Durga, Hongna Zhang, Wei-Hua Cai, and Feng-Chen Li. "NUMERICAL SIMULATION OF PULSATING HEAT PIPE WITH SURFACTANT SOLUTIONS." In International Heat Transfer Conference 16. Begellhouse, 2018. http://dx.doi.org/10.1615/ihtc16.ctm.022279.

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Dubief, Yves, Christopher M. White, Vincent E. Terrapon, Eric S. G. Shaqfeh, Sanjiva K. Lele, and Parviz Moin. "Numerical Simulation of High Drag Reduction Regime in Polymer Solutions (Keynote)." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45652.

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The simulation of drag reduced channel flows has to rely on consitituve models such as FENE-P. Their implementation is not straightforward to achieve convergence and stability of the solution. This paper discusses the problem of advection embedded in the FENE-P equation and the issue of the domain size. Finally we present results of simulations for High Drag Reduction regime, and show the subsequent modification of the vortical structures.
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Wang, Dong, Taro Arikawa, Shaowu Li, and Hayao Gen. "Numerical Simulation on Scour behind Seawalls Due to Tsunami Overflow." In Coastal Structures and Solutions to Coastal Disasters Joint Conference 2015. American Society of Civil Engineers, 2017. http://dx.doi.org/10.1061/9780784480311.014.

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Valencia, Hans F., and Hameed Metghalchi. "Numerical Simulation of a Closed Solar Regenerator." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0997.

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Abstract Many attempts have been made to use solar energy in absorption refrigeration systems. In all these systems an important component is the regenerator, in which the weak solution is reconcentrated. Among the regenerators found in the literature, open regenerators have received much attention because of their simplicity. However, problems with solution contamination, and low performance under humid climates have pointed towards alternative regenerators. It has been shown that covering the regenerator with glass solves these problems permanently. Still, an analysis of the energy and mass transfer processes occurring inside the regenerator has not been fully presented. In this paper, a one-dimensional theoretical simulation of a closed solar regenerator is developed. The theoretical model is constructed by combining three energy balances and three mass balances on infinitesimally thin slices of the solar regenerator, the solution, and the solution-vapor interface. These balances yield three independent ordinary differential equations in the three dependent variables: solution temperature, glass (condensed water) temperature and solution mass flow rate. Solutions to the differential equations have been obtained numerically and the performance of a typical aqueous solution is presented.
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Veprek, Ratko G., Sebastian Steiger, and Bernd Witzigmann. "Ellipticity and spurious solutions in k⋅p calculations of III-nitride nanostructures." In 2008 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD). IEEE, 2008. http://dx.doi.org/10.1109/nusod.2008.4668265.

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Gartner, K. "Existence of bounded discrete steady state solutions of the van Roosbroeck system on boundary conforming Delaunay grids." In 2007 International Conference on Numerical Simulation of Optoelectronic Devices. IEEE, 2007. http://dx.doi.org/10.1109/nusod.2007.4349035.

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Reports on the topic "Numerical simulation of solutions"

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Aursjø, Olav, Aksel Hiorth, Alexey Khrulenko, and Oddbjørn Mathias Nødland. Polymer flooding: Simulation Upscaling Workflow. University of Stavanger, 2021. http://dx.doi.org/10.31265/usps.203.

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There are many issues to consider when implementing polymer flooding offshore. On the practical side one must handle large volumes of polymer in a cost-efficient manner, and it is crucial that the injected polymer solutions maintain their desired rheological properties during transit from surface facilities and into the reservoir. On the other hand, to predict polymer flow in the reservoir, one must conduct simulations to find out which of the mechanisms observed at the pore and core scales are important for field behavior. This report focuses on theoretical aspects relevant for upscaling of polymer flooding. To this end, several numerical tools have been developed. In principle, the range of length scales covered by these tools is extremely wide: from the nm (10-9 m) to the mm (10-3 m) range, all the way up to the m and km range. However, practical limitations require the use of other tools as well, as described in the following paragraphs. The simulator BADChIMP is a pore-scale computational fluid dynamics (CFD) solver based on the Lattice Boltzmann method. At the pore scale, fluid flow is described by classical laws of nature. To a large extent, pore scale simulations can therefore be viewed as numerical experiments, and they have great potential to foster understanding of the detailed physics of polymer flooding. While valid across length scales, pore scale models require a high numerical resolution, and, subsequently, large computational resources. To model laboratory experiments, the NIORC has, through project 1.1.1 DOUCS, developed IORCoreSim. This simulator includes a comprehensive model for polymer rheological behavior (Lohne A. , Stavland, Åsen, Aursjø, &amp; Hiorth, 2021). The model is valid at all continuum scales; however, the simulator implementation is not able to handle very large field cases, only smaller sector scale systems. To capture polymer behavior at the full field scale, simulators designed for that specific purpose must be used. One practical problem is therefore: How can we utilize the state-of-the-art polymer model, only found in IORCoreSim, as a tool to decrease the uncertainty in full field forecasts? To address this question, we suggest several strategies for how to combine different numerical tools. In the Methodological Approach section, we briefly discuss the more general issue of linking different scales and simulators. In the Validation section, we present two case studies demonstrating the proposed strategies and workflows.
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Wang, Yi-Zun J., Ramagopal Ananth, and Patricia A. Tatem. Numerical Simulation of Solid Combustion with a Robust Conjugate-Gradient Solution for Pressure. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada405183.

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Watson, Mark, Martyn Wilmott, and Brian Erno. GRI-96-0452_2 Stress Corrosion Cracking Under Field Simulated Conditions II. Pipeline Research Council International, Inc. (PRCI), 1997. http://dx.doi.org/10.55274/r0011974.

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The pH of solutions found under disbonded polyethylene tape coatings in the field is generally in the range of 6.5 to 7.5. Electrochemically determining corrosion rates for pipeline steels exposed to neutral pH solutions in this pH range indicate that corrosion rates are too low to account for the observed crack growth rates from field excavation programs. This suggests that for the SCC process to be based on a simple dissolution mechanism then the pH at the crack tip would have to be lower than the bulk solution pH. A computer model was developed to determine solution chemistry changes within an SCC crack under anaerobic conditions as a function of time The numerical simulation model showed that the pH at a crack tip is lower by at least one pH unit than the trapped electrolyte outside the crack. A second thermodynamic model was used to show that under appropriate conditions dilute groundwater can be converted to a concentrated carl ornately bicarbonate solution. High temperatures were not required to concentrate on this solution. The concentration of this electrolyte under coal tar or asphalt coatings can occur by a cyclical process in which groundwater levels fluctuate and in tum influence the ability of cathodic protection to reach the steel surface. The high pH is generated by effective cathodic protection and the carbonate concentration is developed by absorption of CO2 from soil gases.
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Oliynyk, Kateryna, and Matteo Ciantia. Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil. University of Dundee, 2021. http://dx.doi.org/10.20933/100001230.

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In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.
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Hart, Carl, and Gregory Lyons. A tutorial on the rapid distortion theory model for unidirectional, plane shearing of homogeneous turbulence. Engineer Research and Development Center (U.S.), 2022. http://dx.doi.org/10.21079/11681/44766.

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The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is assumed that the time-varying velocity spectral tensor can be made stationary by substituting an eddy-lifetime parameter in place of time. General and particular RDT evolution equations for stochastic increments are derived in detail. Analytical solutions for the RDT evolution equation, with and without an effective eddy viscosity, are given. An alternative expression for the eddy-lifetime parameter is shown. The turbulence kinetic energy budget is examined for RDT. Predictions by RDT are shown for velocity (co)variances, one-dimensional streamwise spectra, length scales, and the second invariant of the anisotropy tensor of the moments of velocity. The RDT prediction of the second invariant for the velocity anisotropy tensor is shown to agree better with direct numerical simulations than previously reported.
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Malej, Matt, and Fengyan Shi. Suppressing the pressure-source instability in modeling deep-draft vessels with low under-keel clearance in FUNWAVE-TVD. Engineer Research and Development Center (U.S.), 2021. http://dx.doi.org/10.21079/11681/40639.

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This Coastal and Hydraulics Engineering Technical Note (CHETN) documents the development through verification and validation of three instability-suppressing mechanisms in FUNWAVE-TVD, a Boussinesq-type numerical wave model, when modeling deep-draft vessels with a low under-keel clearance (UKC). Many large commercial ports and channels (e.g., Houston Ship Channel, Galveston, US Army Corps of Engineers [USACE]) are traveled and affected by tens of thousands of commercial vessel passages per year. In a series of recent projects undertaken for the Galveston District (USACE), it was discovered that when deep-draft vessels are modeled using pressure-source mechanisms, they can suffer from model instabilities when low UKC is employed (e.g., vessel draft of 12 m¹ in a channel of 15 m or less of depth), rendering a simulation unstable and obsolete. As an increasingly large number of deep-draft vessels are put into service, this problem is becoming more severe. This presents an operational challenge when modeling large container-type vessels in busy shipping channels, as these often will come as close as 1 m to the bottom of the channel, or even touch the bottom. This behavior would subsequently exhibit a numerical discontinuity in a given model and could severely limit the sample size of modeled vessels. This CHETN outlines a robust approach to suppressing such instability without compromising the integrity of the far-field vessel wave/wake solution. The three methods developed in this study aim to suppress high-frequency spikes generated nearfield of a vessel. They are a shock-capturing method, a friction method, and a viscosity method, respectively. The tests show that the combined shock-capturing and friction method is the most effective method to suppress the local high-frequency noises, while not affecting the far-field solution. A strong test, in which the target draft is larger than the channel depth, shows that there are no high-frequency noises generated in the case of ship squat as long as the shock-capturing method is used.
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Wu, Yanlin, and R. B. White. Numerical simulation of Bootstrap Current. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10160602.

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Wu, Yanlin, and R. B. White. Numerical simulation of Bootstrap Current. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/6484029.

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Ramos, Nuno M. M., Joana Maia, Rita Carvalho Veloso, Andrea Resende Souza, Catarina Dias, and João Ventura. Envelope systems with high solar reflectance by the inclusion of nanoparticles – an overview of the EnReflect Project. Department of the Built Environment, 2023. http://dx.doi.org/10.54337/aau541621982.

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High reflectance materials constitute an attractive idea to reduce cooling loads, which is crucial for attaining the Nearly Zero Energy Buildings goal, also presenting the benefit of broadening the range of colours applicable in building facades. The EnReflect project intended to re-design envelope systems by increasing their solar reflectance through nanotechnology. The main idea was to produce novel nanomaterial-based coatings with high near-infrared (NIR) reflectance by tuning their optical properties and testing their compatibility with typical insulation technologies such as ETICS. As such, this project focused on the synthesis of nanoparticles with improved NIR reflectance, the evaluation of the hygrothermal-mechanical behaviour of thermal insulation systems with the application of the improved coating solutions, the characterization of the more relevant material properties and the durability assessment. One of the main achievements was the development of a facile synthesis of a nanocomposite with improved performance in the NIR region that allowed the reflectance improvement of a dark-finishing coating. Also, the incorporation of such nanoparticles had a positive effect on keeping their optical properties after accelerated ageing cycles. The development of numerical simulations allowed the estimation of the maximum surface temperature in Mediterranean climates under different optical parameters. The study of the hygrothermal behaviour of thermal enhanced façades led to the development of a new durability assessment methodology which contributed to closing a standardization gap.
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Zeda, Jason D. Numerical Simulation of Evaporating Capillary Jets. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada367314.

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