This article is cited in 3 papers

Implicit-explicit bicompact schemes for hyperbolic systems of conservation laws

M. D. Bragin

Keldysh Institute of Applied Mathematics RAS

Abstract: High-order bicompact schemes for hyperbolic systems of conservation laws are considered. The goal is to achieve a significant speed-up for 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 high accuracy of the new implicit-explicit schemes and the substantial speed-up are demonstrated on multidimensional gas dynamics problems.

Keywords: compact schemes, bicompact schemes, implicit-explicit Runge-Kutta methods, high-order schemes, hyperbolic systems of equations.

Received: 14.03.2022
Revised: 14.03.2022
Accepted: 18.04.2022

DOI: 10.20948/mm-2022-06-01

 English version: Mathematical Models and Computer Simulations, 2023, 15:1, 1–12

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