Publication:
Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

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Authors
Yelash, L.
Müller, A.
Lukáčová­­ - Medviďovďá, M.
Giraldo, F.X.
Wirth, V.
Subjects
dry atmospheric convection
steady states
systems of hyperbolic balance laws
Euler equations
large time step
semi-implicit approximation
evolution Galerkin schemes
Advisors
Date of Issue
2014-03-25
Date
Publisher
AMS
Language
Abstract
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.
Type
Article
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
German Research Foundation DFG
Center of Computational Sciences in Mainz
National Science Foundation
ONR
Funder
LU 1470/2-2 (DFG)
LU 1470/2-3 (DFG)
SPP 1276 (DFG)
grant 1216700 (NSF)
grant PE-0602435N (ONR)
Format
43 p.
Citation
Yelash, L. Müller, A. Lukáĉová­­-Medviďovďá, M. Giraldo, F.X., Wirth, V., "Adaptive discontinuous evolution Galerkin method for dry atmospheric flow", Journal of Computational Physics, Volume 268, (1 July 2014), Pages 106-133.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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