An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases

TL;DR

This paper introduces an efficient IMEX-DG solver tailored for simulating non-ideal gases in compressible Navier-Stokes equations, combining adaptive spatial discretization and advanced time-stepping to handle low Mach regimes with high accuracy.

Contribution

The paper presents a novel IMEX-DG solver with adaptive mesh refinement for non-ideal gases, achieving efficient, accurate simulations across a range of Mach numbers.

Findings

Effective simulation of low Mach number flows with reduced computational cost

Full second-order accuracy maintained across Mach regimes

Successful application to classical and real gas benchmarks

Abstract

We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equation describing non-ideal gases with general equations of state. The method, which is based on an $h-$adaptive Discontinuos Galerkin spatial discretization and on an Additive Runge Kutta IMEX method for time discretization, is tailored for low Mach number applications and allows to simulate low Mach regimes at a significantly reduced computational cost, while maintaining full second order accuracy also for higher Mach number regimes. The method has been implemented in the framework of the $deal.II$ numerical library, whose adaptive mesh refinement capabilities are employed to enhance efficiency. Refinement indicators appropriate for real gas phenomena have been introduced. A number of numerical experiments on classical benchmarks for compressible flows and their extension to real gases demonstrate the properties of the proposed method.