An IMEX-DG solver for atmospheric dynamics simulations with adaptive mesh refinement

Abstract

We present an accurate and efficient solver for atmospheric dynamics simulations that allows for non-conforming mesh refinement. The model equations are the conservative Euler equations for compressible flows. The numerical method is based on an $h-$adaptive Discontinuous Galerkin spatial discretization and on a second order Additive Runge Kutta IMEX method for time discretization, especially designed for low Mach regimes. The solver is implemented in the framework of the $deal.II$ library, whose mesh refinement capabilities are employed to enhance efficiency. A number of numerical experiments based on classical benchmarks for atmosphere dynamics demonstrate the properties and advantages of the proposed method.

References in corpus (2)

• An efficient IMEX-DG solver for the compressible Navier-Stokes equations for non-ideal gases
• An efficient and accurate implicit DG solver for the incompressible Navier-Stokes equations

Cited by in corpus (7)

• An implicit DG solver for incompressible two-phase flows with an artificial compressibility formulation
• 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