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Добірка наукової літератури з теми "Dissipative Scheme"

Автор: Grafiati

Опубліковано: 30 листопада 2024

Оновлено: 5 липня 2025

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Статті в журналах з теми "Dissipative Scheme"

HANSEN, JAKOB, ALEXEI KHOKHLOV, and IGOR NOVIKOV. "PROPERTIES OF FOUR NUMERICAL SCHEMES APPLIED TO A NONLINEAR SCALAR WAVE EQUATION WITH A GR-TYPE NONLINEARITY." International Journal of Modern Physics D 13, no. 05 (2004): 961–82. http://dx.doi.org/10.1142/s021827180400502x.

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We study stability, dispersion and dissipation properties of four numerical schemes (Itera-tive Crank–Nicolson, 3rd and 4th order Runge–Kutta and Courant–Fredrichs–Levy Nonlinear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar nonlinear wave equation with a type of nonlinearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant–Fredrichs–Levy Nonlinear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4th order Runge–Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.

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Burkhardt, Ulrike, and Erich Becker. "A Consistent Diffusion–Dissipation Parameterization in the ECHAM Climate Model." Monthly Weather Review 134, no. 4 (2006): 1194–204. http://dx.doi.org/10.1175/mwr3112.1.

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Abstract The diffusion–dissipation parameterizations usually adopted in GCMs are not physically consistent. Horizontal momentum diffusion, applied in the form of a hyperdiffusion, does not conserve angular momentum and the associated dissipative heating is commonly ignored. Dissipative heating associated with vertical momentum diffusion is often included, but in a way that is inconsistent with the second law of thermodynamics. New, physically consistent, dissipative heating schemes due to horizontal diffusion (Becker) and vertical diffusion (Becker, and Boville and Bretherton) have been developed and tested. These schemes have now been implemented in 19- and 39-level versions of the ECHAM4 climate model. The new horizontal scheme requires the replacement of the hyperdiffusion with a ∇2 scheme. Dissipation due to horizontal momentum diffusion is found to have maximum values in the upper troposphere/lower stratosphere in midlatitudes and in the winter hemispheric sponge layer, resulting in a warming of the area around the tropopause and of the polar vortex in Northern Hemispheric winter. Dissipation associated with vertical momentum diffusion is largest in the boundary layer. The change in parameterization acts to strengthen the vertical diffusion and therefore the associated dissipative heating. Dissipation due to vertical momentum diffusion has an indirect effect on the upper-tropospheric/stratospheric temperature field in northern winter, which is to cool and strengthen the northern polar vortex. The warming in the area of the tropopause resulting from the change in both dissipation parameterizations is quite similar in both model versions, whereas the response in the temperature of the northern polar vortex depends on the model version.

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Chen, Xiaowei, Mingzhan Song, and Songhe Song. "A Fourth Order Energy Dissipative Scheme for a Traffic Flow Model." Mathematics 8, no. 8 (2020): 1238. http://dx.doi.org/10.3390/math8081238.

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We propose, analyze and numerically validate a new energy dissipative scheme for the Ginzburg–Landau equation by using the invariant energy quadratization approach. First, the Ginzburg–Landau equation is transformed into an equivalent formulation which possesses the quadratic energy dissipation law. After the space-discretization of the Fourier pseudo-spectral method, the semi-discrete system is proved to be energy dissipative. Using diagonally implicit Runge–Kutta scheme, the semi-discrete system is integrated in the time direction. Then the presented full-discrete scheme preserves the energy dissipation, which is beneficial to the numerical stability in long-time simulations. Several numerical experiments are provided to illustrate the effectiveness of the proposed scheme and verify the theoretical analysis.

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Najafiyazdi, Mostafa, Luc Mongeau, and Siva Nadarajah. "Low-dissipation low-dispersion explicit Taylor-Galerkin schemes from the Runge-Kutta kernels." International Journal of Aeroacoustics 17, no. 1-2 (2018): 88–113. http://dx.doi.org/10.1177/1475472x17743657.

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A multi-stage approach was adopted to investigate similarities and differences between the explicit Taylor-Galerkin and the explicit Runge-Kutta time integration schemes. It was found that the substitution of some, but not all, of second-order temporal derivatives in a Taylor-Galerkin scheme by additional stages makes it analogous to a Runge-Kutta scheme while preserving its original dissipative property for node-to-node oscillations. The substitution of all second-order temporal derivatives transforms Taylor-Galerkin schemes into Runge-Kutta schemes with zero attenuation at the grid cut-off. The application of this approach to an existing two-stage Taylor-Galerkin scheme yields a low-dissipation low-dispersion Taylor-Galerkin formulation. Two one-dimensional benchmarks were simulated to study the performance of this new scheme. The reverse process yields a general approach for transforming m-stage Runge-Kutta schemes into ( m−1)-stage Taylor-Galerkin schemes while preserving the same order of accuracy. The dissipation and dispersion properties for several new Taylor-Galerkin schemes were compared to those of their corresponding Runge-Kutta form.

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Zlotnik, Alexander, and Timofey Lomonosov. "VERIFICATION OF AN ENTROPY DISSIPATIVE QGD-SCHEME." Mathematical Modelling and Analysis 24, no. 2 (2019): 179–94. http://dx.doi.org/10.3846/mma.2019.013.

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An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh L1-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for L2-dissipativity of the Cauchy problem for a linearized QGD-scheme.

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Appadu, A. R. "Numerical Solution of the 1D Advection-Diffusion Equation Using Standard and Nonstandard Finite Difference Schemes." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/734374.

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Three numerical methods have been used to solve the one-dimensional advection-diffusion equation with constant coefficients. This partial differential equation is dissipative but not dispersive. We consider the Lax-Wendroff scheme which is explicit, the Crank-Nicolson scheme which is implicit, and a nonstandard finite difference scheme (Mickens 1991). We solve a 1D numerical experiment with specified initial and boundary conditions, for which the exact solution is known using all these three schemes using some different values for the space and time step sizes denoted byhandk, respectively, for which the Reynolds number is 2 or 4. Some errors are computed, namely, the error rate with respect to theL1norm, dispersion, and dissipation errors. We have both dissipative and dispersive errors, and this indicates that the methods generate artificial dispersion, though the partial differential considered is not dispersive. It is seen that the Lax-Wendroff and NSFD are quite good methods to approximate the 1D advection-diffusion equation at some values ofkandh. Two optimisation techniques are then implemented to find the optimal values ofkwhenh=0.02for the Lax-Wendroff and NSFD schemes, and this is validated by numerical experiments.

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Lin, F. B., and F. Sotiropoulos. "Assessment of Artificial Dissipation Models for Three-Dimensional Incompressible Flow Solutions." Journal of Fluids Engineering 119, no. 2 (1997): 331–40. http://dx.doi.org/10.1115/1.2819138.

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Various approaches for constructing artificial dissipation terms for three-dimensional artificial compressibility algorithms are presented and evaluated. Two, second-order accurate, central-differencing schemes, with explicitly added scalar and matrix-valued fourth-difference artificial dissipation, respectively, and a third-order accurate flux-difference splitting upwind scheme are implemented in a multigrid time-stepping procedure and applied to calculate laminar flow through a strongly curved duct. Extensive grid-refinement studies are carried out to investigate the grid sensitivity of each discretization approach. The calculations indicate that even the finest mesh employed, consisting of over 700,000 grid nodes, is not sufficient to establish grid independent solutions. However, all three schemes appear to converge toward the same solution as the grid spacing approaches zero. The matrix-valued dissipation scheme introduces the least amount of artificial dissipation and should be expected to yield the most accurate solutions on a given mesh. The flux-difference splitting upwind scheme, on the other hand, is more dissipative and, thus, particularly sensitive to grid resolution, but exhibits the best overall convergence characteristics on grids with large aspect ratios.

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Zhang, Yang, Laiping Zhang, Xin He, and Xiaogang Deng. "An Improved Second-Order Finite-Volume Algorithm for Detached-Eddy Simulation Based on Hybrid Grids." Communications in Computational Physics 20, no. 2 (2016): 459–85. http://dx.doi.org/10.4208/cicp.190915.240216a.

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AbstractA hybrid grid based second-order finite volume algorithm has been developed for Detached-Eddy Simulation (DES) of turbulent flows. To alleviate the effect caused by the numerical dissipation of the commonly used second order upwind schemes in implementing DES with unstructured computational fluid dynamics (CFD) algorithms, an improved second-order hybrid scheme is established through modifying the dissipation term of the standard Roe's flux-difference splitting scheme and the numerical dissipation of the scheme can be self-adapted according to the DES flow field information. By Fourier analysis, the dissipative and dispersive features of the new scheme are discussed. To validate the numerical method, DES formulations based on the two most popular background turbulence models, namely, the one equation Spalart-Allmaras (SA) turbulence model and the two equationk–ωShear Stress Transport model (SST), have been calibrated and tested with three typical numerical examples (decay of isotropic turbulence, NACA0021 airfoil at 60° incidence and 65° swept delta wing). Computational results indicate that the issue of numerical dissipation in implementing DES can be alleviated with the hybrid scheme, the resolution for turbulence structures is significantly improved and the corresponding solutions match the experimental data better. The results demonstrate the potentiality of the present DES solver for complex geometries.

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Lu, Changna, Qianqian Gao, Chen Fu, and Hongwei Yang. "Finite Element Method of BBM-Burgers Equation with Dissipative Term Based on Adaptive Moving Mesh." Discrete Dynamics in Nature and Society 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/3427376.

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A finite element model is proposed for the Benjamin-Bona-Mahony-Burgers (BBM-Burgers) equation with a high-order dissipative term; the scheme is based on adaptive moving meshes. The model can be applied to the equations with spatial-time mixed derivatives and high-order derivative terms. In this scheme, new variables are needed to make the equation become a coupled system, and then the linear finite element method is used to discretize the spatial derivative and the fifth-order Radau IIA method is used to discretize the time derivative. The simulations of 1D and 2D BBM-Burgers equations with high-order dissipative terms are presented in numerical examples. The numerical results show that the method keeps a second-order convergence in space and provides a smaller error than that based on the fixed mesh, which demonstrates the effectiveness and feasibility of the finite element method based on the moving mesh. We also study the effect of the dissipative terms with different coefficients in the equation; by numerical simulations, we find that the dissipative termuxxplays a more important role thanuxxxxin dissipation.

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Mai-Duy, N., N. Phan-Thien, and T. Tran-Cong. "An improved dissipative particle dynamics scheme." Applied Mathematical Modelling 46 (June 2017): 602–17. http://dx.doi.org/10.1016/j.apm.2017.01.086.

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Дисертації з теми "Dissipative Scheme"

Fiebach, André [Verfasser]. "A dissipative finite volume scheme for reaction-diffusion systems in heterogeneous materials / André Fiebach." Berlin : Freie Universität Berlin, 2014. http://d-nb.info/1057869732/34.

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Avila, Jorge Andrés Julca. "Solução numérica em jatos de líquidos metaestáveis com evaporação rápida." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/3/3150/tde-13082008-010924/.

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Este trabalho estuda o fenômeno de evaporação rápida em jatos de líquidos superaquecidos ou metaestáveis numa região 2D. O fenômeno se inicia, neste caso, quando um jato na fase líquida a alta temperatura e pressão, emerge de um diminuto bocal projetando-se numa câmara de baixa pressão, inferior à pressão de saturação. Durante a evolução do processo, ao cruzar-se a curva de saturação, se observa que o fluido ainda permanece no estado de líquido superaquecido. Então, subitamente o líquido superaquecido muda de fase por meio de uma onda de evaporação oblíqua. Esta mudança de fase transforma o líquido superaquecido numa mistura bifásica com alta velocidade distribuída em várias direções e que se expande com velocidades supersônicas cada vez maiores, até atingir a pressão a jusante, e atravessando antes uma onda de choque. As equações que governam o fenômeno são as equações de conservação da massa, conservação da quantidade de movimento, e conservação da energia, incluindo uma equação de estado precisa. Devido ao fenômeno em estudo estar em regime permanente, um método de diferenças finitas com modelo estacionário e esquema de MacCormack é aplicado. Tendo em vista que este modelo não captura a onda de choque diretamente, um segundo modelo de falso transiente com o esquema de \"shock-capturing\": \"Dispersion-Controlled Dissipative\" (DCD) é desenvolvido e aplicado até atingir o regime permanente. Resultados numéricos com o código ShoWPhasT-2D v2 e testes experimentais foram comparados e os resultados numéricos com código DCD-2D v1 foram analisados. This study analyses the rapid evaporation of superheated or metastable liquid jets in a two-dimensional region. The phenomenon is triggered, in this case, when a jet in its liquid phase at high temperature and pressure, emerges from a small aperture nozzle and expands into a low pressure chamber, below saturation pressure. During the evolution of the process, after crossing the saturation curve, one observes that the fluid remains in a superheated liquid state. Then, suddenly the superheated liquid changes phase by means of an oblique evaporation wave. This phase change transforms the liquid into a biphasic mixture at high velocity pointing toward different directions, with increasing supersonic velocity as an expansion process takes place to the chamber back pressure, after going through a compression shock wave. The equations which govern this phenomenon are: the equations of conservation of mass, momentum and energy and an equation of state. Due to its steady state process, the numerical simulation is by means of a finite difference method using the McCormack method of Discretization. As this method does not capture shock waves, a second finite difference method is used to reach this task, the method uses the transient equations version of the conservation laws, applying the Dispersion-Controlled Dissipative (DCD) scheme. Numerical results using the code ShoWPhasT-2D v2 and experimental data have been compared, and the numerical results from the DCD-2D v1 have been analysed.

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Bensaid, Bilel. "Analyse et développement de nouveaux optimiseurs en Machine Learning." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0218.

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Ces dernières années, l’intelligence artificielle (IA) est confrontée à deux défis majeurs (parmi d’autres), à savoir l’explicabilité et la frugalité, dans un contexte d’intégration de l’IA dans des systèmes critiques ou embarqués et de raréfaction des ressources. Le défi est d’autant plus conséquent que les modèles proposés apparaissent commes des boîtes noires étant donné le nombre faramineux d’hyperparamètres à régler (véritable savoir-faire) pour les faire fonctionner. Parmi ces paramètres, l’optimiseur ainsi que les réglages qui lui sont associés ont un rôle critique dans la bonne mise en oeuvre de ces outils [196]. Dans cette thèse, nous nous focalisons sur l’analyse des algorithmes d’apprentissage/optimiseurs dans le contexte des réseaux de neurones, en identifiant des propriétés mathématiques faisant écho aux deux défis évoqués et nécessaires à la robustesse du processus d’apprentissage. Dans un premier temps, nous identifions des comportements indésirables lors du processus d’apprentissage qui vont à l’encontre d’une IA explicable et frugale. Ces comportements sont alors expliqués au travers de deux outils: la stabilité de Lyapunov et les intégrateurs géométriques. Empiriquement, la stabilisation du processus d’apprentissage améliore les performances, autorisant la construction de modèles plus économes. Théoriquement, le point de vue développé permet d’établir des garanties de convergence pour les optimiseurs classiquement utilisés dans l’entraînement des réseaux. La même démarche est suivie concernant l’optimisation mini-batch où les comportements indésirables sont légions: la notion de splitting équilibré est alors centrale afin d’expliquer et d’améliorer les performances. Cette étude ouvre la voie au développement de nouveaux optimiseurs adaptatifs, issus de la relation profonde entre optimisation robuste et schémas numériques préservant les invariants des systèmes dynamiques Over the last few years, developping an explainable and frugal artificial intelligence (AI) became a fundamental challenge, especially when AI is used in safety-critical systems and demands ever more energy. This issue is even more serious regarding the huge number of hyperparameters to tune to make the models work. Among these parameters, the optimizer as well as its associated tunings appear as the most important leverages to improve these models [196]. This thesis focuses on the analysis of learning process/optimizer for neural networks, by identifying mathematical properties closely related to these two challenges. First, undesirable behaviors preventing the design of explainable and frugal networks are identified. Then, these behaviors are explained using two tools: Lyapunov stability and geometrical integrators. Through numerical experiments, the learning process stabilization improves the overall performances and allows the design of shallow networks. Theoretically, the suggested point of view enables to derive convergence guarantees for classical Deep Learning optimizers. The same approach is valuable for mini-batch optimization where unwelcome phenomenons proliferate: the concept of balanced splitting scheme becomes essential to enhance the learning process understanding and improve its robustness. This study paves the way to the design of new adaptive optimizers, by exploiting the deep relation between robust optimization and invariant preserving scheme for dynamical systems

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Petropoulos, Ilias. "Study of high-order vorticity confinement schemes." Thesis, Paris, ENSAM, 2018. http://www.theses.fr/2018ENAM0001/document.

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Les tourbillons sont des structures importantes pour une large gamme d'écoulements de fluides, notamment les sillages, l'interaction fluide-structure, les décollements de couche limite et la turbulence. Cependant, les méthodes numériques classiques n'arrivent généralement pas à donner une représentation précise des tourbillons. Ceci est principalement lié à la dissipation numérique des schémas qui, si elle n'est pas spécifiquement calibrée pour le calcul des écoulements tourbillonnaires, conduit à une diffusion artificielle très rapide des tourbillons dans les calculs. Parmi d'autres approches, la méthode "Vorticity Confinement" (VC) de J. Steinhoff permet de compenser la dissipation des schémas au sein des tourbillons en introduisant une anti-dissipation non-linéaire, mais elle n’est précise qu’au premier ordre. D’autre part, des progrès significatifs ont récemment été accomplis dans le développement de méthodes numériques d’ordre élevé. Celles-ci permettent de réduire ce problème de dissipation excessive, mais la diffusion des tourbillons reste importante pour de nombreuses applications. La présente étude vise à développer des extensions d’ordre élevé de la méthode VC pour réduire cette dissipation excessive des tourbillons, tout en préservant la précision d'ordre élevé des schémas. Tout d'abord, les schémas de confinement sont analysés dans le cas de l'équation de transport linéaire, à partir de discrétisations couplées et découplées en espace et en temps. Une analyse spectrale de ces schémas est effectuée analytiquement et numériquement en raison de leur caractère non linéaire. Elle montre des propriétés dispersives et dissipatives améliorées par rapport aux schémas linéaires de base à tous les ordres de précision. Dans un second temps, des schémas VC précis au troisième et cinquième ordre sont développés pour les équations de Navier-Stokes compressibles. Les termes correctifs restent conservatifs, invariants par rotation et indépendants du schéma de base, comme la formulation originale VC2. Les tests numériques valident l'ordre de précision et la capacité des extensions VC d’ordre élevé à réduire la dissipation dans les tourbillons. Enfin, les schémas avec VC sont appliqués au calcul des écoulements turbulents, dans une approche de simulation de grandes échelles implicite (ILES). Les schémas numériques avec VC présentent une résolvabilité améliorée par rapport à leur version linéaire de base, et montrent leur capacité à décrire de façon cohérente ces écoulements tourbillonnaires complexes Vortices are flow structures of primary interest in a wide range of fluid dynamics applications including wakes, fluid-structure interaction, flow separation and turbulence. Albeit their importance, standard Computational Fluid Dynamics (CFD) methods very often fail to provide an accurate representation of vortices. This is primarily related to the schemes’ numerical dissipation which, if inadequately tuned for the calculation of vortical flows, results in the artificial spreading and diffusion of vortices in numerical simulations. Among other approaches, the Vorticity Confinement (VC) method of J. Steinhoff allows balancing the baseline dissipation within vortices by introducing non-linear anti-dissipation in the discretization of the flow equations, but remains at most first-order accurate. At the same time, remarkable progress has recently been made on the development of high-order numerical methods. These allow reducing the problem of excess dissipation, but the diffusion of vortices remains important for many applications. The present study aims at developing high-order extensions of the VC method to reduce the excess dissipation of vortices, while preserving the accuracy of high-order methods. First, the schemes are analyzed in the case of the linear transport equation, based on time-space coupled and uncoupled formulations. A spectral analysis of nonlinear schemes with VC is performed analytically and numerically, due to their nonlinear character. These schemes exhibit improved dispersive and dissipative properties compared to their linear counterparts at all orders of accuracy. In a second step, third- and fifth-order accurate VC schemes are developed for the compressible Navier-Stokes equations. These remain conservative, rotationally invariant and independent of the baseline scheme, as the original VC2 formulation. Numerical tests validate the increased order of accuracy and the capability of high-order VC extensions to balance dissipation within vortices. Finally, schemes with VC are applied to the calculation of turbulent flows, in an implicit Large Eddy Simulation (ILES) approach. In these applications, numerical schemes with VC exhibit improved resolvability compared to their baseline linear version, while they are capable of producing consistent results even in complex vortical flows

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Wajid, Hafiz Abdul. "Dispersive and dissipative properties of high order schemes for computational wave propagation." Thesis, University of Strathclyde, 2009. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=11530.

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Lee, Dongwook. "An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics a staggered dissipation-control differencing algorithm /." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3842.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2006. Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Nazari, Farshid. "Strongly Stable and Accurate Numerical Integration Schemes for Nonlinear Systems in Atmospheric Models." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32128.

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Nonlinearity accompanied with stiffness in atmospheric boundary layer physical parameterizations is a well-known concern in numerical weather prediction (NWP) models. Nonlinear diffusion equations, furthermore, are a class of equations which are extensively applicable in different fields of science and engineering. Numerical stability and accuracy is a common concern in this class of equation. In the present research, a comprehensive effort has been made toward the temporal integration of such equations. The main goal is to find highly stable and accurate numerical methods which can be used specifically in atmospheric boundary layer simulations in weather and climate prediction models, and extensively in other models where nonlinear differential equations play an important role, such as magnetohydrodynamics and Navier-Stokes equations. A modified extended backward differentiation formula (ME BDF) scheme is adapted and proposed at the first stage of this research. Various aspects of this scheme, including stability properties, linear stability analysis, and numerical experiments, are studied with regard to applications for the time integration of commonly used nonlinear damping and diffusive systems in atmospheric boundary layer models. A new temporal filter which leads to significant improvement of numerical results is proposed. Nonlinear damping and diffusion in the turbulent mixing of the atmospheric boundary layer is dealt with in the next stage by using optimally stable singly-diagonally-implicit Runge-Kutta (SDIRK) methods, which have been proved to be effective and computationally efficient for the challenges mentioned in the literature. Numerical analyses are performed, and two schemes are modified to enhance their numerical features and stability. Three-stage third-order diagonally-implicit Runge-Kutta (DIRK) scheme is introduced by optimizing the error and linear stability analysis for the aforementioned nonlinear diffusive system. The new scheme is stable for a wide range of time steps and is able to resolve different diffusive systems with diagnostic turbulence closures, or prognostic ones with a diagnostic length scale, with enhanced accuracy and stability compared to current schemes. The procedure implemented in this study is quite general and can be used in other diffusive systems as well. As an extension of this study, high-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes are analyzed and introduced, based on the optimization of amplification and phase errors for wave propagation, and various optimized schemes can be obtained. The new scheme shows no dissipation. It is illustrated mathematically and numerically that the new scheme preserves fourth-order accuracy. The numerical applications contain the wave equation with and without a stiff nonlinear source term. This shows that different optimized schemes can be investigated for the solution of systems where physical terms with different behaviours exist.

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Azim, Riasat. "Low-Storage Hybrid MacCormack-type Schemes with High Order Temporal Accuracy for Computational Aeroacoustics." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1515720270119389.

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Huart, Robin. "Simulation numérique d'écoulements magnétohydrodynamiques par des schémas distribuant le résidu." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14480/document.

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Au cours de ce travail, nous nous sommes attaché à la résolution numérique des équations de la Magnétohydrodynamique (MHD) auxquelles s'ajoute une loi hyperbolique de transport des erreurs de divergence.La première étape consista à symétriser le nouveau système de la MHD idéale afin d'en étudier le système propre, ce qui fut l'occasion de rappeler le rôle de l'entropie au niveau de ce calcul comme à celui de l'inégalité de Clausius-Duhem. La suite de cette thèse eut pour objectif la résolution de ces équations idéales à l'aide de schémas distribuant le résidu (notés RD). Les quatre principaux schémas connus furent testés, et nous avons montré entre autres que le schéma N, qui a fait ses preuves sur les équations d'Euler en mécanique des fluides, n'était pas adapté aux équations de la MHD. Les stratégies classiques de limitation et de stabilisation purent être revisitées à ce moment. Les équations étant instationnaires, il fallut intégrer une discrétisation en temps et une distribution spatiale des termes d'évolution (et d'éventuelles sources). Nous avons d'emblée opté pour une approche implicite permettant d'être performant sur les simulations longues des expériences de tokamaks, et de traiter la correction de la divergence d'une manière originale et efficace. Les problèmes de convergence de la méthode de Newton-Raphson n'ayant pas été pleinement résolus, nous nous sommes tournés vers une alternative explicite de type Runge-Kutta. Enfin, nous avons réétabli les principes de la montée en ordre (en théorie, jusqu'à des ordres arbitraires, en prenant en compte le phénomène de Gibbs) à l'aide de tout type d'élément fini (bien construit) 2D ou 3D, sans avoir pu valider tous ces aspects. Nous avons également pris en compte les équations complètes de la MHD réelle classique (i.e. sans effet Hall) à l'aide d'un couplage RD/Galerkin During this thesis, we worked on the numerical resolution of the Magnetohydrodynamic (MHD) equations, to which we added a hyperbolic transport equation for the divergence errors of the magnetic field.The first step consisted in symmetrizing the new ideal MHD system in order to study its eigensystem, which was the opportunity to remind the role of the entropy in this calculation as well as in the Clausius-Duhem inequality. Next, we aimed at solving these ideal equations by the mean of Residual Distribution (RD) schemes.The four main schemes were tested, and we showed among other things that the N scheme (although it has been proven very efficient with Euler equations in Fluid Mechanics) could not give satisfying results with the MHD equations. Classical strategies for the limitation and the stabilization were revisited then. Moreover,since we dealt with unsteady equations, we had to formulate atime discretization and a spatial distribution of the unsteady terms (as well as possible sources). We first choosed an implicit approach allowing us to be powerful on the long simulations needed for tokamak experiments, and to treat the divergence cleaning part in an original and efficient way. The convergence problems of our Newton-Raphson algorithm having not been fully resolved, we turned to an explicit alternative (Runge-Kutta type).Finally, we discussed about the principles of higher order schemes (theoretically, up to arbitrary orders, taking into account the Gibbs phenomenon) thanks to any type of 2D or 3D finite element (properly defined), without having been able to to validate all these aspects. We also implemented the dissipative part of the full MHD equations (in the classical sense, i.e. omitting the Hall effect) by the use of a RD/Galerkin coupling

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Langenberg, Marcel Simon Verfasser], Marcus [Akademischer Betreuer] Müller, Marcus [Gutachter] Müller, et al. "Energy dissipation and transport in polymeric switchable nanostructures via a new energy-conserving Monte-Carlo scheme / Marcel Simon Langenberg ; Gutachter: Marcus Müller, Reiner Kree, Cynthia Volkert, Krüger, Annette Zippelius, Stefan Klumpp ; Betreuer: Marcus Müller." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2018. http://d-nb.info/1156460581/34.

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Книги з теми "Dissipative Scheme"

Yeffet, Amir. A non-dissipative staggered fourth-order accurate explicit finite difference scheme for the time-domain Maxwell's equations. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Roe, P. L. Linear bicharacteristic schemes without dissipation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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Institute for Computer Applications in Science and Engineering., ed. Linear bicharacteristic schemes without dissipation. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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R, Radespiel, Turkel E, and Institute for Computer Applications in Science and Engineering., eds. Comparison of several dissipation algorithms for central difference schemes. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Swanson, R. Charles. On central-difference and upwind schemes. National Aeronautics and Space Administration, Langley Research Center, Institute for Computer Applications in Science and Engineering, 1990.

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Wen, Chih-Yung, Yazhong Jiang, and Lisong Shi. "Non-dissipative Core Scheme of CESE Method." In Engineering Applications of Computational Methods. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0876-9_2.

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AbstractThis chapter is devoted to demonstrating the basic ideas in the CESE method. These ideas include the adoption of a space–time integral form of governing equations as the starting point of scheme construction, as well as the introduction of conservation element (CE) and solution element (SE) in the discretization of space–time domain. Then, the non-dissipative core scheme of the CESE method will be presented in detail.

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Poluru, Venkata Reddy. "A Low Dissipative Scheme for Hyperbolic Conservation Laws." In Lecture Notes in Mechanical Engineering. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9956-9_57.

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Wen, Chih-Yung, Yazhong Jiang, and Lisong Shi. "CESE Schemes with Numerical Dissipation." In Engineering Applications of Computational Methods. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0876-9_3.

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AbstractAs depicted in Chap. 2, the interface between the two sub-CEs (CD in Fig. 2.7), belongs to the SE of (j, n). The flux FC needs to be calculated through the Taylor expansion at point (j, n) toward the inverse time direction. As a result, the a scheme is reversible. This violates the second law of thermodynamics. Thus, the non-dissipative core suffers from the unphysical oscillations for practical applications.

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Aristova, Elena N. "Hermitian Grid-Characteristic Scheme for Linear Transport Equation and Its Dissipative-Dispersion Properties." In Smart Modelling for Engineering Systems. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4619-2_5.

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Fu, Lei, Chenliang Gu, and Jiachang Shi. "Dissipative Control for Singular T-S Fuzzy Systems Under Dynamic Event-Triggered Scheme." In Proceedings of International Conference on Image, Vision and Intelligent Systems 2023 (ICIVIS 2023). Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-0855-0_68.

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Wen, Chih-Yung, Yazhong Jiang, and Lisong Shi. "Multi-dimensional CESE Schemes." In Engineering Applications of Computational Methods. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0876-9_4.

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Yang, Yan. "Hybrid Scheme for Compressible MHD Turbulence." In Energy Transfer and Dissipation in Plasma Turbulence. Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-8149-2_3.

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Yee, H. C., and B. Sjögreen. "Designing Adaptive Low Dissipative High Order Schemes." In Computational Fluid Dynamics 2002. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-59334-5_15.

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Sonar, Thomas. "Entropy Dissipation in Finite Difference Schemes." In Nonlinear Hyperbolic Problems: Theoretical, Applied, and Computational Aspects. Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-87871-7_66.

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Wu, Xinyuan, and Bin Wang. "Linearly-Fitted Conservative (Dissipative) Schemes for Nonlinear Wave Equations." In Geometric Integrators for Differential Equations with Highly Oscillatory Solutions. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0147-7_8.

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Тези доповідей конференцій з теми "Dissipative Scheme"

Hou, Daizheng, Yanfei Zhang, and Yafu Zhou. "A Novel Heat Dissipation Optimization Design Scheme of Printed Circuit Board." In 2024 3rd International Conference on Energy, Power and Electrical Technology (ICEPET). IEEE, 2024. http://dx.doi.org/10.1109/icepet61938.2024.10627435.

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Henke, Jan-Wilke, Yujia Yang, F. Jasmin Kappert, et al. "Probing the Formation of Nonlinear Optical States with Free Electrons." In CLEO: Fundamental Science. Optica Publishing Group, 2024. http://dx.doi.org/10.1364/cleo_fs.2024.fw3p.3.

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Combining nonlinear integrated photonics with electron microscopy, we probe the formation of optical dissipative structures in Si3N4 microresonators with free electrons and find unique spectral fingerprints in the electron spectrum that enable new electron beam modulation schemes.

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Pinho, Pedro V., André G. Primo, Natália C. Carvalho, et al. "Quadrature-Resolved Dissipative Optomechanical Measurement." In CLEO: Fundamental Science. Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cleo_fs.2023.fth1b.2.

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Primo, André G., Pedro V. Pinho, Natália C. Carvalho, et al. "Homodyne Detection of Dissipative Optomechanical Interactions." In Latin America Optics and Photonics Conference. Optica Publishing Group, 2022. http://dx.doi.org/10.1364/laop.2022.m4d.6.

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We present and validate a novel route to directly probe the dissipative optomechanical coupling in a balanced homodyne detection scheme. The ratio between dissipative and dispersive coupling is determined as G κ e / G ω ≈ − 0.007 ± 0.001 .

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Kim, Dehee, and Jang Hyuk Kwon. "A Low Dissipative and Dispersive Scheme with a High Order WENO Dissipation for Unsteady Flow Analyses." In 34th AIAA Fluid Dynamics Conference and Exhibit. American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-2705.

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Matsuo, T., E. Torii, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Dissipative Linearly-Implicit Scheme for the Ginzburg-Landau Equation." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241623.

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Poe, Nicole M. W., and D. Keith Walters. "A Low-Dissipation Optimization-Based Gradient Reconstruction (OGRE) Scheme for Finite Volume Simulations." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-01013.

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Finite volume methods employing second-order gradient reconstruction schemes are often utilized to computationally solve the governing equations of transport. These reconstruction schemes, while not as dissipative as first-order schemes, frequently produce either dispersive or oscillatory solutions, especially in regions of discontinuities, and/or unsatisfactory levels of dissipation in smooth regions of the variable field. A novel gradient reconstruction scheme is presented in this work which shows significant improvement over traditional second-order schemes. This Optimization-based Gradient REconstruction (OGRE) scheme works to minimize an objective function based on the mismatch between local reconstructions at midpoints between cell stencil neighbors, i.e. the degree to which the projected values of a dependent variable and its gradients in a given cell differ from each of these values in neighbor cells. An adjustable weighting parameter is included in the definition of the objective function that allows the scheme to be tuned towards greater accuracy or greater stability. This scheme is implemented using the User Defined Function capability available in the commercially available CFD solver, Ansys FLUENT. Various test cases are presented that demonstrate the ability of the new method to calculate superior predictions of both a scalar transported variable and its gradients. These cases include calculation of a discontinuous variable field, several sinusoidal variable fields and a non-uniform velocity field. Results for each case are determined on both structured and unstructured meshes, and the scheme is compared with existing standard first- and second-order upwind discretization methods.

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Tian, Cheng, Song Fu, and Siya Jiang. "Numerical Dissipation Effects on Detached Eddy Simulation of Turbomachinery Flows." In GPPS Xi'an21. GPPS, 2022. http://dx.doi.org/10.33737/gpps21-tc-74.

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Detached eddy simulation (DES) is a high-resolution method for predicting complex unsteady flows in turbomachinery. Recent researches have shown that in DES the numerical dissipation from the spatial discretization scheme should be limited to a reasonable extent. Through the test-case of decaying isotropic turbulence, the impact of the Roe scheme is assessed with three reconstruction approaches: the 3rd-order MUSCL, the 5th-order WENO, and the 4th-order minimized dispersion and controllable dissipation (MDCD) scheme. From the results, however, even with the least dissipative 4th-order MDCD scheme, the Roe scheme possesses high numerical damping for the small-scale turbulent structures. To further decrease the dissipation, the Roe scheme is modified via an adaptive factor. This adaptive scheme has small dissipation in the LES region to capture multiscale turbulent structures and returns to the original Roe scheme near shock waves to suppress numerical oscillations. The scheme with adaptive dissipation is also used to calculate flows in a centrifugal compressor. The resolution of small vortex structures, such as the tip leakage vortices and the wake vortices, is well improved.

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Bahrainian, Seyed Saied. "Effect of Dissipative Terms on the Quality of Two and Three-Dimensional Euler Flow Solutions." In ASME 2008 Fluids Engineering Division Summer Meeting collocated with the Heat Transfer, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/fedsm2008-55221.

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The Euler equations are a set of non-dissipative hyperbolic conservation laws that can become unstable near regions of severe pressure variation. To prevent oscillations near shockwaves, these equations require artificial dissipation terms to be added to the discretized equations. A combination of first-order and third-order dissipative terms control the stability of the flow solutions. The assigned magnitude of these dissipative terms can have a direct effect on the quality of the flow solution. To examine these effects, subsonic and transonic solutions of the Euler equations for a flow passed a circular cylinder has been investigated. Triangular and tetrahedral unstructured grids were employed to discretize the computational domain. Unsteady Euler equations are then marched through time to reach a steady solution using a modified Runge-Kutta scheme. Optimal values of the dissipative terms were investigated for several flow conditions. For example, at a free stream Mach number of 0.45 strong shock waves were captured on the cylinder by using values of 0.25 and 0.0039 for the first-order and third-order dissipative terms. In addition to the shock capturing effect, it has been shown that smooth pressure coefficients can be obtained with the proper values for the dissipative terms.

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Ma, Yian, Qijun Tan, Ruoshi Yuan, Bo Yuan, and Ping Ao. "Decomposition scheme in continuous dissipative chaotic systems and role of strange attractors." In 2013 International Conference on Noise and Fluctuations (ICNF). IEEE, 2013. http://dx.doi.org/10.1109/icnf.2013.6578915.

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Cabot, B., D. Eliason, and L. Jameson. A Wavelet Based Dissipation Method for ALE Schemes. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/793693.

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ANALYSIS OF THE SEISMIC BEHAVIOR OF INNOVATIVE ALUMINIUM ALLOY ENERGY DISSIPATION BRACES. The Hong Kong Institute of Steel Construction, 2022. http://dx.doi.org/10.18057/icass2020.p.341.

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In this study the employment of aluminium alloy buckling-restrained braces (ALBRBs) as energy dissipation dampers is attempted for seismic performance upgrading of single layer dome and the effectiveness of ALBRBs to protect structures against strong earthquakes is numerically studied. With buckling restrained, ALBRB members can provide stable energy dissipation capacity and thus damage of the whole structure under major earthquakes can be mitigated. ALBRBs are then placed at certain locations on the example single layer dome to replace some normal members with two schemes, and the effect of the two installation schemes of ALBRBs for seismic upgrading is investigated by non-linear time-history analyses under various ground motions representing major earthquake events. Compared with the seismic behaviour of the original structure without ALBRBs, satisfactory seismic performance is seen in the upgraded models, which clarifies the effectiveness of the proposed upgrading method and it can serve as an efficient solution for earthquake-resistant new designs and retrofit of existing spatial structure.

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