Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

JOURNAL OF COMPUTATIONAL PHYSICS

卷:268

Article

Yelash, L.¹  Mueller, A.²  Lukacova-Medvid'ova, M.¹  Giraldo, F. X.²  Wirth, V.³ 

[1] Johannes Gutenberg Univ Mainz, Inst Math, D-55099 Mainz, Germany

[2] Naval Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA

[3] Johannes Gutenberg Univ Mainz, Inst Atmospher Phys, D-55127 Mainz, Germany

关键词: Dry atmospheric convection;    Steady states;    Systems of hyperbolic balance laws;    Euler equations;    Large time step;    Semi-implicit approximation;    Evolution Galerkin schemes;   

DOI  :  10.1016/j.jcp.2014.02.034

来源: Elsevier

【 摘 要 】

We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows, nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realized by the IMEX type approximation using the semi-implicit second-order backward differentiation formula (BDF2). Moreover in order to approximate efficiently small scale phenomena, adaptive mesh refinement using the space filling curves via the AMATOS function library is employed. Four standard meteorological test cases are used to validate the new discontinuous evolution Galerkin method for dry atmospheric convection. Comparisons with the Rusanov flux, a standard one-dimensional approximate Riemann solver used for the flux integration, demonstrate better stability and accuracy, as well as the reliability of the new multidimensional DEG method. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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