Relaxation Runge--Kutta methods: Fully discrete explicit entropy-stable schemes for the compressible Euler and Navier--Stokes equations
The framework of inner product norm preserving relaxation Runge--Kutta methods [DI
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …
Ketcheson, SIAM J. Numer. Anal., 57 (2019), pp. 2850--2870] is extended to general convex …
Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
The algebraic flux correction (AFC) schemes presented in this work constrain a standard
continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant …
continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant …
General relaxation methods for initial-value problems with application to multistep schemes
Recently, an approach known as relaxation has been developed for preserving the correct
evolution of a functional in the numerical solution of initial-value problems, using Runge …
evolution of a functional in the numerical solution of initial-value problems, using Runge …
[HTML][HTML] Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier–Stokes equations
Recently, relaxation methods have been developed to guarantee the preservation of a
single global functional of the solution of an ordinary differential equation. Here, we …
single global functional of the solution of an ordinary differential equation. Here, we …
Low dissipative entropy stable schemes using third order WENO and TVD reconstructions
A low dissipative framework is given to construct high order entropy stable flux by addition of
suitable numerical diffusion operator into entropy conservative flux. The framework is robust …
suitable numerical diffusion operator into entropy conservative flux. The framework is robust …
On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators
H Ranocha - IMA Journal of Numerical Analysis, 2021 - academic.oup.com
Abstract Explicit Runge–Kutta methods are classical and widespread techniques in the
numerical solution of ordinary differential equations (ODEs). Considering partial differential …
numerical solution of ordinary differential equations (ODEs). Considering partial differential …
[图书][B] Property-preserving numerical schemes for conservation laws
D Kuzmin, H Hajduk - 2024 - World Scientific
Many mathematical models of continuum mechanics are derived from integral conservation
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …
laws. Examples of such models include the Euler and Navier–Stokes equations of fluid …
Formulation of entropy-stable schemes for the multicomponent compressible Euler equations
A Gouasmi, K Duraisamy, SM Murman - Computer Methods in Applied …, 2020 - Elsevier
Abstract In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent
compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived …
compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived …
Sign stable arbitrary high order reconstructions for constructing non-oscillatory entropy stable schemes
High order sign stable reconstructions are much sought after to develop high order non-
oscillatory entropy stable schemes. This work presents a very simple but generic approach …
oscillatory entropy stable schemes. This work presents a very simple but generic approach …
Entropy production by explicit Runge–Kutta schemes
C Lozano - Journal of Scientific Computing, 2018 - Springer
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