Numerical solution of Navier–Stokes–Korteweg systems by Local Discontinuous Galerkin methods in multiple space dimensions

Dennis Diehl, Jenny Kremser, Dietmar Kröner and Christian Rohde

Applied Mathematics and Computation, 2016, vol. 272, issue P2, 309-335

Abstract: Compressible liquid–vapor flow with phase transitions can be described by systems of Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear higher-grade terms which take the form of either differential or nonlocal integral operators. A numerical approximation method on the basis of the Local Discontinuous Galerkin method in multiple space dimensions is suggested for isothermal flows. It relies on a specific discretization of a non-conservative formulation. To enhance the performance of the overall scheme two techniques are used: (i) local spatial adaptivity based on gradient indicators for the density and (ii) parallelism based on domain decomposition.

Keywords: Compressible multiphase flow; Liquid–vapor phase transition; Navier–Stokes–Korteweg; Discontinuous Galerkin methods; Adaptive mesh refinement (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:272:y:2016:i:p2:p:309-335

DOI: 10.1016/j.amc.2015.09.080

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