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

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.

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Cited by in corpus (7)

• An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement
• A new family of semi-implicit Finite Volume / Virtual Element methods for incompressible flows on unstructured meshes
• Robust and accurate simulations of flows over orography using non-conforming meshes
• Impact of curved elements for flows over orography with a Discontinuous Galerkin scheme
• A quantitative comparison of high-order asymptotic-preserving and asymptotically-accurate IMEX methods for the Euler equations with non-ideal gases
• Efficient and scalable atmospheric dynamics simulations using non-conforming meshes
• Improving the scalability of a high-order atmospheric dynamics solver based on the deal.II library