An Investigation of Different Splitting Techniques for the Isentropic Euler Equations

Zeifang, Jonas; Kaiser, Klaus; Schütz, Jochen; Massa, Francesco Carlo; Beck, Andrea

doi:10.1007/978-3-030-33338-6_4

Cited by 1 publication

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“…Since IMEX flux splitting schemes have been found to be well suited for low Mach number computations within a discontinuous Galerkin framework [72,73], the idea in this work is to combine an IMEX flux splitting scheme with the sharp interface level set ghost fluid method (LSGFM). Although the fully implicit time discretization has been used within the LSGFM [31,37,47], IMEX flux splitting schemes have not been investigated in this context.…”

Section: Introductionmentioning

confidence: 99%

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Zeifang

Beck

2021

Commun. Appl. Math. Comput.

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Considering droplet phenomena at low Mach numbers, large differences in the magnitude of the occurring characteristic waves are presented. As acoustic phenomena often play a minor role in such applications, classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction. In this work, a novel scheme based on a specific level set ghost fluid method and an implicit-explicit (IMEX) flux splitting is proposed to overcome this timestep restriction. A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface. In this part of the domain, the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases. It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method. Applications to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

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