Implicit-Explicit Bicompact Schemes for Hyperbolic Systems of Conservation Laws

High-order bicompact schemes for hyperbolic systems of conservation laws are considered. We aim to significantly speed up these schemes. Implicit-explicit Runge–Kutta methods are proposed for time discretization, instead of the previously used diagonally implicit methods. The global Lax–Friedrichs–R...

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Veröffentlicht in:	Mathematical models and computer simulations 2023-02, Vol.15 (1), p.1-12
1. Verfasser:	Bragin, M. D.
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Sprache:	eng
Schlagworte:	Conservation laws Gas dynamics Hyperbolic systems Implicit methods Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Runge-Kutta method Simulation and Modeling
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creator	Bragin, M. D.
description	High-order bicompact schemes for hyperbolic systems of conservation laws are considered. We aim to significantly speed up these schemes. Implicit-explicit Runge–Kutta methods are proposed for time discretization, instead of the previously used diagonally implicit methods. The global Lax–Friedrichs–Rusanov flux splitting is a premise for the implicit-explicit approximation. It is shown that implicit-explicit bicompact schemes are stable for any ratio of steps in time and space. The accuracy of the new implicit-explicit schemes and the substantial speed-up achieved are demonstrated on multidimensional gas dynamics problems.
doi_str_mv	10.1134/S2070048223010064
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subjects	Conservation laws Gas dynamics Hyperbolic systems Implicit methods Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Runge-Kutta method Simulation and Modeling
title	Implicit-Explicit Bicompact Schemes for Hyperbolic Systems of Conservation Laws
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