A quantitative comparison of high-order asymptotic-preserving and asymptotically-accurate IMEX methods for the Euler equations with non-ideal gases
arXiv:2501.12733 · doi:10.1016/j.cma.2025.118037
Abstract
We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK approach involves an implicit coupling between the momentum and energy balance so as to avoid the acoustic CFL restriction, while the density can be treated in a fully explicit fashion. This approach leads to a mildly nonlinear equation for the pressure, which can be solved according to a fixed point procedure. An alternative strategy consists of employing a semi-implicit temporal integrator based on IMEX-RK methods (SI-IMEX-RK). The stiff dependence is carefully analyzed, so as to avoid the solution of a nonlinear equation for the pressure also for equations of state (EOS) of non-ideal gases. The spatial discretization is based on a Discontinuous Galerkin (DG) method, which naturally allows high-order accuracy. The asymptotic-preserving (AP) and the asymptotically-accurate (AA) properties of the two approaches are assessed on a number of classical benchmarks for ideal gases and on their extension to non-ideal gases.
References in corpus (14)
- An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations
- A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers
- Fast matrix-free evaluation of discontinuous Galerkin finite element operators
- lifex: a flexible, high performance library for the numerical solution of complex finite element problems
- High order pressure-based semi-implicit IMEX schemes for the 3D Navier-Stokes equations at all Mach numbers
- A structure-preserving staggered semi-implicit finite volume scheme for continuum mechanics
- High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
- An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases
- Truly multi-dimensional all-speed schemes for the Euler equations on Cartesian grids
- An all speed second order IMEX relaxation scheme for the Euler equations
- An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement
- An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation
- A filtering monotonization approach for DG discretizations of hyperbolic problems
- Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme