IMEX finite volume evolution Galerkin scheme for three-dimensional weakly compressible flows

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Georgij Bispen Mária Lukáčová-Medviďová Leonid Yelash

Abstract

In this paper we will derive an implicit-explicit (IMEX) finite volume evolution Galerkin scheme for three-dimensional Euler equations. We will in particular concentrate  a singular limit of weakly compressible flows when the Mach number is about ${\cal O}(10^{-2}) - {\cal O}(10^{-6}).$  In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravitational waves and a non-stiff nonlinear part that models nonlinear advection effects. We use stiffly accurate second order IMEX scheme for time discretization to approximate stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. Furthermore in order to take multdimensional effects of flow propagation into account we apply three-dimensional evolution Galerkin operator. 

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How to Cite
BISPEN, Georgij; LUKÁČOVÁ-MEDVIĎOVÁ, Mária; YELASH, Leonid. IMEX finite volume evolution Galerkin scheme for three-dimensional weakly compressible flows. Proceedings of the Conference Algoritmy, [S.l.], p. 62-73, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/395>. Date accessed: 22 sep. 2017.
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