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

Giuseppe Orlando, Tommaso Benacchio, Luca Bonaventura

2023Journal of Computational and Applied Mathematics16 citationsDOI Open Access PDF

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.

Topics & Concepts

DiscretizationSolverAdaptive mesh refinementDiscontinuous Galerkin methodMach numberMathematicsBackward Euler methodApplied mathematicsEuler equationsRunge–Kutta methodsComputational scienceCompressibilityNumerical analysisMathematical optimizationComputer scienceFinite element methodMathematical analysisMechanicsPhysicsThermodynamicsComputational Fluid Dynamics and AerodynamicsAdvanced Numerical Methods in Computational MathematicsMeteorological Phenomena and Simulations