Application of WENO-schemes for modelling shockwave processes

F. A. Belolutskiy, V. V. Shepelev, S. V. Fortova

ICAD RAS

Abstract: The present paper is concerned with the analysis of WENO-schemes for the solution of one-dimensional Euler equations with a Mie–Grüneisen type equation of state. The least dissipative and oscillatory modifications of WENO-schemes in characteristic variables with a monotonicity-preserving (MP) limiter are presented. A modified scheme, MP-WENO-SM, is developed, demonstrating the smallest amplitude of oscillations in the solution of the test problems with discontinuous initial data.

Keywords: WENO, computational fluid dynamics, equations of state, shock waves in metals.

Received: 27.06.2023
Revised: 21.09.2023
Accepted: 04.12.2023

DOI: 10.20948/mm-2024-02-02

 English version: Mathematical Models and Computer Simulations, 2024, 16:4, 536–547