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Academic literature on the topic 'Euler Equation - Numerical Solution'

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Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Euler Equation - Numerical Solution"

1

Čiegis, Raimondas. "NUMERICAL SOLUTION OF HYPERBOLIC HEAT CONDUCTION EQUATION." Mathematical Modelling and Analysis 14, no. 1 (March 31, 2009): 11–24. http://dx.doi.org/10.3846/1392-6292.2009.14.11-24.

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Hyperbolic heat conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which automatically introduces sufficient amount of numerical viscosity. Results of numerical experiments are presented.

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Siddiqui, Maryam, Mhamed Eddahbi, and Omar Kebiri. "Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts." Mathematics 11, no. 17 (August 31, 2023): 3755. http://dx.doi.org/10.3390/math11173755.

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This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 12. Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example.

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Wang, Qi, Huabin Chen, and Chenggui Yuan. "A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations." Mathematics 10, no. 6 (March 9, 2022): 866. http://dx.doi.org/10.3390/math10060866.

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This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler–Maruyama numerical solution to this equation. In addition, the Borel–Cantelli lemma and the stochastic analysis theory are incorporated to discuss the almost sure exponential stability for this numerical solution of such equations.

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Wang, Jinhuan, Yicheng Pang, and Yu Zhang. "Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 3-4 (May 26, 2019): 461–73. http://dx.doi.org/10.1515/ijnsns-2018-0263.

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AbstractIn this paper, we consider limit behaviors of Riemann solutions to the isentropic Euler equations for a non-ideal gas (i.e. van der Waals gas) as the pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for van der Waals gas is solved. Then it is proved that, as the pressure vanishes, any Riemann solution containing two shock waves to the isentropic Euler equation for van der Waals gas converges to the delta shock solution to the transport equations and any Riemann solution containing two rarefaction waves tends to the vacuum state solution to the transport equations. Finally, some numerical simulations completely coinciding with the theoretical analysis are demonstrated.

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Blaszczyk, Tomasz, and Mariusz Ciesielski. "Numerical Solution of Euler-Lagrange Equation with Caputo Derivatives." Advances in Applied Mathematics and Mechanics 9, no. 1 (October 11, 2016): 173–85. http://dx.doi.org/10.4208/aamm.2015.m970.

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AbstractIn this paper the fractional Euler-Lagrange equation is considered. The fractional equation with the left and right Caputo derivatives of orderα∈ (0,1] is transformed into its corresponding integral form. Next, we present a numerical solution of the integral form of the considered equation. On the basis of numerical results, the convergence of the proposed method is determined. Examples of numerical solutions of this equation are shown in the final part of this paper.

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Shieh, C. F., and R. A. Delaney. "An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows." Journal of Turbomachinery 109, no. 3 (July 1, 1987): 346–53. http://dx.doi.org/10.1115/1.3262112.

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Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the three-dimensional time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud two-dimensional O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.

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7

Sarhan, Falah, and LIU JICHENG. "Euler-Maruyama approximation of backward doubly stochastic differential delay equations." International Journal of Applied Mathematical Research 5, no. 3 (July 25, 2016): 146. http://dx.doi.org/10.14419/ijamr.v5i3.6358.

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In this paper, we attempt to introduce a new numerical approach to solve backward doubly stochastic differential delay equation ( shortly-BDSDDEs ). In the beginning, we present some assumptions to get the numerical scheme for BDSDDEs, from which we prove important theorem. We use the relationship between backward doubly stochastic differential delay equations and stochastic controls by interpreting BDSDDEs as some stochastic optimal control problems, to solve the approximated BDSDDEs and we prove that the numerical solutions of backward doubly stochastic differential delay equation converge to the true solution under the Lipschitz condition.

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CHINVIRIYASIT, W., and S. CHINVIRIYASIT. "NUMERICAL SOLUTION OF NONLINEAR EQUATION TO COMBINED DETERMINISTIC AND NARROW-BAND RANDOM EXCITATION." International Journal of Modern Physics B 22, no. 21 (August 20, 2008): 3655–75. http://dx.doi.org/10.1142/s0217979208048528.

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The Duffing oscillator to combined deterministic and narrow-band random excitation, which is a nonlinear equation, is studied and solved numerically using three numerical methods based on finite difference schemes. Method 1, the well-known Euler method, is an explicit method; Method 2 is an implicit first-order method which does not bring contrived chaos into the solution; and Method 3 is based on two first-order methods which is second-order method and is chaos-free. In a series of numerical experiments, it is seen that the proposed methods have superior stability properties to those of the well-known Euler and fourth-order Runge-Kutta methods to which they are compared. When extended to the numerical solution of Duffing oscillator to combined deterministic and narrow-band random excitation, the developed methods give the correct steady-state solutions compared with the literature.

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Zhang, X., X. X. Chen, and C. L. Morfey. "Acoustic Radiation from a Semi-Infinite Duct With a Subsonic Jet." International Journal of Aeroacoustics 4, no. 1-2 (January 2005): 169–84. http://dx.doi.org/10.1260/1475472053730075.

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The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using an optimised prefactored compact scheme for spatial discretisation. Far field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far field prediction is compared with analytic solutions with good agreement.

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Khaldi, Rabah, and Assia Guezane-Lakoud. "On generalized nonlinear Euler-Bernoulli Beam type equations." Acta Universitatis Sapientiae, Mathematica 10, no. 1 (August 1, 2018): 90–100. http://dx.doi.org/10.2478/ausm-2018-0008.

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Abstract This paper is devoted to the study of a nonlinear Euler-Bernoulli Beam type equation involving both left and right Caputo fractional derivatives. Differently from the approaches of the other papers where they established the existence of solution for the linear Euler-Bernoulli Beam type equation numerically, we use the lower and upper solutions method with some new results on the monotonicity of the right Caputo derivative. Furthermore, we give the explicit expression of the upper and lower solutions. A numerical example is given to illustrate the obtained results.

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Dissertations / Theses on the topic "Euler Equation - Numerical Solution"

1

Latypov, Azat. "Numerical solution of Euler equations on streamline-aligned meshes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0010/NQ52411.pdf.

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Sykes, L. A. "On the numerical solution of compressible flows containing shock discontinuities." Thesis, University of Hertfordshire, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234329.

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Ungun, Yigit. "Numerical Solution Of One Dimensional Detonation Tube With Reactive Euler Equations Using High Resolution Method." Master's thesis, METU, 2012. http://etd.lib.metu.edu.tr/upload/12614128/index.pdf.

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In this thesis, numerical simulation of one dimensional detonation tube problem is solved with finite rate chemistry. For the numerical simulation, Euler equations have been used. Since detonation tube phenomena occurs in high speed flows, viscosity eects and gravity forces are negligible. In this thesis, Godunov type methods have been studied and afterwards high resolution method is used for the numerical solution of the detonation tube problem. To solve the chemistry aspect of the problem ZND theory have been used. For the numerical solution, a FORTRAN code is written and the numerical solution of the problems compared with the exact ZND solutions.

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Onur, Omer. "Effect Of Jacobian Evaluation On Direct Solutions Of The Euler Equations." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/2/1098268/index.pdf.

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A direct method is developed for solving the 2-D planar/axisymmetric Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes, and the resulting nonlinear system of equations are solved using Newton&
#8217
s Method. Both analytical and numerical methods are used for Jacobian calculations. Numerical method has the advantage of keeping the Jacobian consistent with the numerical flux vector without extremely complex or impractical analytical differentiations. However, numerical method may have accuracy problem and may need longer execution time. In order to improve the accuracy of numerical method detailed error analyses were performed. It was demonstrated that the finite-difference perturbation magnitude and computer precision are the most important parameters that affect the accuracy of numerical Jacobians. A relation was developed for optimum perturbation magnitude that can minimize the error in numerical Jacobians. Results show that very accurate numerical Jacobians can be calculated with optimum perturbation magnitude. The effects of the accuracy of numerical Jacobians on the convergence of flow solver are also investigated. In order to reduce the execution time for numerical Jacobian evaluation, flux vectors with perturbed flow variables are calculated for only related cells. A sparse matrix solver based on LU factorization is used for the solution, and to improve the Jacobian matrix solution some strategies are considered. Effects of different flux splitting methods, higher-order discretizations and several parameters on the performance of the solver are analyzed.

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Morrelll, J. M. "A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations." Thesis, University of Reading, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.440088.

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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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SHELLEY, MICHAEL JOHN. "THE APPLICATION OF BOUNDARY INTEGRAL TECHNIQUES TO MULTIPLY CONNECTED DOMAINS (VORTEX METHODS, EULER EQUATIONS, FLUID MECHANICS)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188100.

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Very accurate methods, based on boundary integral techniques, are developed for the study of multiple, interacting fluid interfaces in an Eulerian fluid. These methods are applied to the evolution of a thin, periodic layer of constant vorticity embedded in irrotational fluid. Numerical regularity experiments are conducted and suggest that the interfaces of the layer develop a curvature singularity in infinite time. This is to be contrasted with the more singular vorticity distribution of a vortex sheet developing such a singularity in a finite time.

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Bright, Theresa Ann. "New solutions to the euler equations using lie group analysis and high order numerical techniques." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/29990.

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Williams, Rhys L. "Exact, asymptotic and numerical solutions to certain steady, axisymmetric, ideal fluid flow problems in IRÂ³." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299262.

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Paillere, Henri J. "Multidimensional upwind residual distribution schemes for the Euler and Navier-Stokes equations on unstructured grids." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212553.

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Une approche multidimensionelle pour la résolution numérique des équations d'Euler et de Navier-Stokes sur maillages non-structurés est proposée. Dans une première partie, un exposé complet des schémas de distribution, dits de "fluctuation-splitting" ,est décrit, comprenant une étude comparative des schémas décentrés, positifs et de 2ème ordre, pour résoudre l'équation de convection à coefficients constants, ainsi qu'une étude théorique et numérique de la précision des schémas sur maillages réguliers et distordus. L'extension à des lois de conservation non-linéaires est aussi abordée, et une attention particulière est portée au problème de la linéarisation conservative. Dans une deuxième partie, diverses discrétisations des termes visqueux pour l'équation de convection-diffusion sont développées, avec pour but de déterminer l'approche qui offre le meilleur compromis entre précision et coût. L'extension de la méthode aux systèmes des lois de conservation, et en particulier à celui des équations d'Euler de la dynamique des gaz, représente le noyau principal de la thèse, et est abordée dans la troisième partie. Contrairement aux schémas de distribution classiques, qui reposent sur une extension formelle du cas scalaire, l'approche développée ici repose sur une décomposition du résidu par élément en équations scalaires, modélisant le transport de variables caracteristiques. La difficulté vient du fait que les équations d'Euler instationnaires ne se diagonalisent pas, et admettent une infinité de solutions élémentaires (ondes simples) se propageant dans toutes les directions d'espace. En régime stationnaire, en revanche, les équations se diagonalisent complètement dans le cas des écoulements supersoniques, et partiellement dans le cas des écoulements subsoniques. Ainsi, les équations sous forme conservative peuvent être remplacées par un système équivalent comprenant deux équations totalement découplées, exprimant l'invariance de l'entropie et de l'enthalpie totale le long des lignes de courant, et deux autres équations, modélisant les effets purement acoustiques. En régime supersonique, celles-ci se découplent aussi, et expriment la convection le long des lignes de Mach d'invariants de Riemann généralisés. La discrétisation de ces équations par des schémas scalaires décentrés permet de simuler des écoulements continus et discontinus avec une grande précision et sans oscillations. Finalement, dans une dernière partie, l'extension aux équations de Navier-Stokes est abordée, et la discrétisation des termes visqueux par une approche éléments finis est proposée. Les résultats numériques confirment la précision et la robustesse de la méthode.

Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

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Books on the topic "Euler Equation - Numerical Solution"

1

Fuhrer, Claus. Formulation and numerical solution of the equations of constrained mechanical motion. Koln: DFLVR, 1989.

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2

Anderson, W. Kyle. Grid generation and flow solution method for Euler equations on unstructured grids. [Washington, DC]: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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3

K, Taylor Lafayette, and United States. National Aeronautics and Space Administration., eds. Numerical solution of the two-dimensional time-dependent incompressible Euler equations. Mississippi State, MS: Mississippi State University, Computational Fluid Dynamics Laboratory, NSF Engineering Research Center for Computational Field Simulation, 1994.

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K, Taylor Lafayette, and United States. National Aeronautics and Space Administration., eds. Numerical solution of the two-dimensional time-dependent incompressible Euler equations. Mississippi State, MS: Mississippi State University, Computational Fluid Dynamics Laboratory, NSF Engineering Research Center for Computational Field Simulation, 1994.

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5

Pelant, Jaroslav. Numerical solution of flow of ideal fluid through cascade in a plane. Praha, Czechoslovakia: Information Centre for Aeronautics, 1987.

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6

Shapiro, Richard A. Adaptive finite element solution algorithm for the Euler equations. Braunschweig: Vieweg, 1991.

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7

Wilkinson, Andrew R. Numerical solution of the Euler equations for transonic airfoil flows using unstructured grids. Ottawa: National Library of Canada = Bibliothèque nationale du Canada, 1992.

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8

Das, Arabindo. Numerical solution of flow fields around delta wings using Euler equation methods. Pt. II. Analysis of the results and comparison with experiments. Braunschweig: DFVLR, 1986.

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9

Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Felici, Helene M. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows. Cambridge, Mass: Gas Turbine Laboratory, Massachusetts Institute of Technology, 1992.

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Book chapters on the topic "Euler Equation - Numerical Solution"

1

Quartapelle, L. "Incompressible Euler equations." In Numerical Solution of the Incompressible Navier-Stokes Equations, 209–42. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8579-9_8.

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Kim, Kyu Hong, Chongam Kim, Oh-Hyun Rho, and Kyung-Tae Lee. "Uncertainty of Solution in Euler Equations and Numerical Instability." In Computational Fluid Dynamics 2002, 146–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-59334-5_19.

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Wesseling, Pieter. "Numerical solution of the Euler equations in general domains." In Principles of Computational Fluid Dynamics, 503–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05146-3_12.

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Drela, M., M. Giles, and W. T. Thompkins. "Newton Solution of Coupled Euler and Boundary-Layer Equations." In Numerical and Physical Aspects of Aerodynamic Flows III, 143–54. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-4926-9_8.

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Lynn, John F., Bram van Leer, and Dohyung Lee. "Multigrid solution of the euler equations with local preconditioning." In Fifteenth International Conference on Numerical Methods in Fluid Dynamics, 172–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0107097.

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Van den Abeele, Kris, Jan Ramboer, Ghader Ghorbaniasl, and Chris Lacor. "Numerical Solution of the Linearized Euler Equations Using Compact Schemes." In Computational Fluid Dynamics 2006, 837–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-92779-2_132.

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Oosterlee, C. W., H. Ritzdorf, A. Schüller, and B. Steckel. "Experiences with a parallel multiblock multigrid solution technique for the Euler equations." In Notes on Numerical Fluid Mechanics (NNFM), 192–203. Wiesbaden: Vieweg+Teubner Verlag, 1995. http://dx.doi.org/10.1007/978-3-663-14125-9_16.

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Koren, Barry, and Stefan Spekreijse. "Multigrid and Defect Correction for the Efficient Solution of the Steady Euler Equations." In Research in Numerical Fluid mechanics, 87–100. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-89729-9_7.

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Shapiro, Richard A. "Prediction of Dispersive Errors in Numerical Solution of the Euler Equations." In Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications, 552–61. Wiesbaden: Vieweg+Teubner Verlag, 1989. http://dx.doi.org/10.1007/978-3-322-87869-4_54.

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Bramkamp, F., and J. Ballmann. "Solution of the Euler Equations on Locally Adaptive B-Spline Grids." In New Results in Numerical and Experimental Fluid Mechanics III, 281–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45466-3_34.

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Conference papers on the topic "Euler Equation - Numerical Solution"

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David, R., and J. Holman. "NUMERICAL SOLUTION OF EULER EQUATIONS USING ROTATED-HYBRID RIEMANN SOLVER." In Topical Problems of Fluid Mechanics 2019. Institute of Thermomechanics, AS CR, v.v.i., 2019. http://dx.doi.org/10.14311/tpfm.2019.009.

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DADONE, A., and B. GROSSMAN. "Surface boundary conditions for the numerical solution of the Euler equations." In 11th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-3334.

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Wiemann, D., F. Lehr, and D. Mewes. "Numerical Calculation of the Flow Field in Bubble Columns Using a Simplified Form of the Population Balance Equation." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31124.

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The three dimensional velocity field is numerically calculated for bubble columns using an Euler-Euler approach with an additional transport equation for the interfacial area. The spacial bubble number density is obtained by solving the population balance equation numerically. In order to reduce the numerical effort or to avoid restrictive assumptions for bubble break-up and coalescene processes a partial solution of the population balance is derived. It is valid asymptotically as the bubble swarm moves away from the distributor. The approximate solution leads to a transport equation for the mean bubble volume, which is solved in dependence of the bubble break-up and coalescence processes. Both phenomena are considered. For the numerical calculations the interfacial area transport equation is coupled with the balance equations for mass and momentum transport. The calculations are performed for instationary, three-dimensional flows in cylindrical bubble columns with diameters up to 0.29 m and 4.425 m of height.

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4

Shieh, C. F., and R. A. Delaney. "An Accurate and Efficient Euler Solver for Three-Dimensional Turbomachinery Flows." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-200.

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Accurate and efficient Euler equation numerical solution techniques are presented for analysis of three-dimensional turbomachinery flows. These techniques include an efficient explicit hopscotch numerical scheme for solution of the 3-D time-dependent Euler equations and an O-type body-conforming grid system. The hopscotch scheme is applied to the conservative form of the Euler equations written in general curvilinear coordinates. The grid is constructed by stacking from hub to shroud 2-D O-type grids on equally spaced surfaces of revolution. Numerical solution results for two turbine cascades are presented and compared with experimental data to demonstrate the accuracy of the analysis method.

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5

MOITRA, A. "Numerical solution of the Euler equations for high-speed, blended wing-body configurations." In 23rd Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1985. http://dx.doi.org/10.2514/6.1985-123.

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Xu, Yufeng, and Om P. Agrawal. "Numerical Solutions of Generalized Oscillator Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12705.

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Harmonic oscillators play a fundamental role in many areas of science and engineering, such as classical mechanics, electronics, quantum physics, and others. As a result, harmonic oscillators have been studied extensively. Classical harmonic oscillators are defined using integer order derivatives. In recent years, fractional derivatives have been used to model the behaviors of damped systems more accurately. In this paper, we use three operators called K-, A- and B-operators to define the equation of motion of an oscillator. In contrast to fractional integral and derivative operators which use fractional power kernels or their variations in their definitions, the K-, A- and B-operators allow the kernel to be arbitrary. In the case when the kernel is a power kernel, these operators reduce to fractional integral and derivative operators. Thus, they are more general than the fractional integral and derivative operators. Because of the general nature of the K-, A- and B-operators, the harmonic oscillators are called the generalized harmonic oscillators. The equations of motion of a generalized harmonic oscillator are obtained using a generalized Euler-Lagrange equation presented recently. In general, the resulting equations cannot be solved in closed form. A numerical scheme is presented to solve these equations. To verify the effectiveness of the numerical scheme, a problem is considered for which a closed form solution could be found. Numerical solution for the problem is compared with the analytical solution. It is demonstrated that the numerical scheme is convergent, and the order of convergence is 2. For a special kernel, this scheme reduces to a scheme presented recently in the literature.

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Jasim, Abdulghafoor, and Ali Asmael. "Studying Some Stochastic Differential Equations with trigonometric terms with Application." In 3rd International Conference of Mathematics and its Applications. Salahaddin University-Erbil, 2020. http://dx.doi.org/10.31972/ticma22.13.

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In this paper we look at several (trigonometric) stochastic differential equations , we find the general form for such nonlinear stochastic differential equation by using the I'to formula. Then we find the exact solution for the different trigonometric stochastic differential equations by the use of stochastic integrals. Ilustrate the approach with various examples. (precise solution using the Ito integral formula) and approximate solution (numerical approximation (the Euler-Maruyama technique and the Milstein method) were compared to the exact solutions with the error of those approaches.

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He, L., and J. D. Denton. "Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 1 — Description of the Method." In ASME 1991 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/91-gt-125.

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An efficient coupled approach between inviscid Euler and integral boundary layer solutions has been developed for quasi 3-D unsteady flows induced by vibrating blades. For unsteady laminar and turbulent boundary layers, steady correlations are adopted in a quasi-steady way to close the integral boundary layer model. This quasi-steady adoption of the correlations is assessed by numerical test results using a direct solution of the unsteady momentum integral equation. To conduct the coupling between the inviscid and viscous solutions for strongly interactive flows, the unsteady Euler and integral boundary layer equations are simultaneously time-marched using a multi-step Runge-Kutta scheme, and the boundary layer displacement effect is accounted for by a first order transpiration model. This time-resolved coupling method converges at conditions with considerable boundary layer separation.

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E, Qin, Fengwei Li, and Guowei Yang. "Numerical solution of the Euler equations for the transonic flow about the complete aircraft." In 14th Applied Aerodynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-2406.

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YANG, J. "Numerical solution of the two-dimensional Euler equations by second-order upwind difference schemes." In 23rd Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1985. http://dx.doi.org/10.2514/6.1985-292.

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Reports on the topic "Euler Equation - Numerical Solution"

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Wang, C. Y., M. D. Carter, D. B. Batchelor, and E. F. Jaeger. Numerical solution of a tunneling equation. Office of Scientific and Technical Information (OSTI), April 1994. http://dx.doi.org/10.2172/10167991.

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2

Kellogg, R. B. Numerical Solution of Convection Diffusion Equation. Fort Belvoir, VA: Defense Technical Information Center, August 1991. http://dx.doi.org/10.21236/ada244563.

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Harvey, John V., JR Medina, and Richard L. Numerical Solution of the Extended Nonlinear Schrodinger Equation. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada463325.

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Chao, E. H., S. F. Paul, R. C. Davidson, and K. S. Fine. Direct numerical solution of Poisson`s equation in cylindrical (r, z) coordinates. Office of Scientific and Technical Information (OSTI), July 1997. http://dx.doi.org/10.2172/304205.

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Morgan, D. L. Jr. Numerical solution of the Schroedinger integral equation for dt. mu. Progress report. Office of Scientific and Technical Information (OSTI), August 1986. http://dx.doi.org/10.2172/5167930.

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Samn, Sherwood. Numerical Solution of a Singular Integral Equation Arising from a Sequential Probability Ratio Test. Fort Belvoir, VA: Defense Technical Information Center, March 1995. http://dx.doi.org/10.21236/ada293463.

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POWELL, JENNIFER L. Finite Element Numerical Solution of a Self-Adjoint Transport Equation for Coupled Electron-Photon Problems. Office of Scientific and Technical Information (OSTI), August 2000. http://dx.doi.org/10.2172/760742.

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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.), July 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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A numerical solution for the diffusion equation in hydrogeologic systems. US Geological Survey, 1989. http://dx.doi.org/10.3133/wri894027.

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HIGH PRECISION IDENTIFICATION METHOD OF MASS AND STIFFNESS MATRIX FOR SHEAR-TYPE FRAME TEST MODEL. The Hong Kong Institute of Steel Construction, June 2023. http://dx.doi.org/10.18057/ijasc.2023.19.2.6.

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In the direct method of identifying the physical parameters of the shear-type frame structures through the frequencies and modes from the experimental modal analysis (EMA), the accuracy of the lumped mass depends on the initial mass, while the identified mass matrix and stiffness matrix are prone to generate some matrix elements without any physical meaning. In this paper, based on the natural frequencies and modes obtained from the EMA, an iterative constrained optimization solution for correcting mass matrix and a least squares solution for the lateral stiffness are proposed. The method takes the total mass of the test model as the constraint condition and develops an iterative correction method for the lumped mass, which is independent of the initial lumped mass. When the measured modes are exact, the iterative solution converges to the exact solution. On this basis, the least squares calculation equation of the lateral stiffness is established according to the natural frequencies and modes. Taking the numerical model of a 3-story steel frame structure as an example, the influence of errors of measured modes on the identification accuracy is investigated. Then, a 2-story steel frame test model is used to identify the mass matrix and stiffness matrix under three different counterweights. Numerical and experimental results show that the proposed method has good accuracy and stability, and the identified mass matrix and stiffness matrix have clear physical significance.

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