Repository: Freie Universität Berlin, Math Department

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

Yelash, L. and Müller, A. and Lukacova-Medvidova, M. and Giraldo, F.X. and Wirth, V. (2014) Adaptive discontinuous evolution Galerkin method for dry atmospheric flow. Journal of Computational Physics, 268C . 106 -133. ISSN 0021-9991

Full text not available from this repository.

Official URL:


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.

Item Type:Article
Uncontrolled Keywords:Dry atmospheric convection; Steady states; Systems of hyperbolic balance laws; Euler equations; Large time step; Semi-implicit approximation; Evolution Galerkin schemes
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1409
Deposited By: Ulrike Eickers
Deposited On:09 Apr 2014 14:18
Last Modified:09 Apr 2014 14:18

Repository Staff Only: item control page