Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations

TL;DR

This paper introduces a two-scale numerical method for the weakly compressible 1D isentropic Euler equations, leveraging two-scale convergence theory and finite volume schemes, with numerical results showing increased accuracy at lower Mach numbers.

Contribution

The paper develops a novel two-scale numerical approach for weakly compressible Euler equations, integrating two-scale convergence theory with finite volume methods.

Findings

The two-scale method improves accuracy as Mach number decreases.

Numerical simulations confirm the effectiveness of the approach.

The method offers a new way to handle weakly compressible flows numerically.

Abstract

Motivated by the difficulty to solve numerically the weakly compressible 1D isentropic Euler equations with classical methods, we develop in this paper a two scale numerical method on this model. This method is based on two scale convergence theory developped by N'Guetseng and Allaire, and finite volume scheme. Furthermore, we do some numerical simulations in order to verify that the two-scale numerical method is more and more accurate when the Mach number diminishes.