The CABARET scheme for a relaxation approximation of scalar hyperbolic conservation laws

V. M. Goloviznin^ab, A. V. Serzhantov<sup>a

a</sup> Lomonosov Moscow State University Branch in the City of Sarov
^b Lomonosov Moscow State University

Abstract: When numerically solving quasilinear hyperbolic equations, so-called “acoustic points” can arise, i.e., when the slope coefficient of the characteristic changes sign in neighboring computational cells. This requires special consideration within the framework of the balance-characteristic approach. The problem can be circumvented by approximating the original equation with a system of two hyperbolic relaxation-type equations that exclude the formation of acoustic points (The Jin–Xin model).

Keywords: numerical algorithms, hyperbolic equations, CABARET scheme, The Jin-Xin model.

Received: 03.02.2025
Revised: 03.02.2025
Accepted: 17.03.2025

DOI: 10.20948/mm-2025-06-01