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

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Georgij Bispen Mária Lukáčová-Medviďová Leonid Yelash


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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Bispen, G., Lukáčová-Medviďová, M., & Yelash, L. (2016). IMEX finite volume evolution Galerkin scheme for three-dimensional weakly compressible flows. Proceedings Of The Conference Algoritmy, , 62-73. Retrieved from


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