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Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds

Communications in Computational Physics 2011年第7期10卷 371-404页

作者： Andreas Bollermann sebastian noelle Maria Lukacova-Medvid’ova IGPM RWTH AachenTemplergraben 5552062 AachenGermany Institut fur Mathematik Universitat MainzStaudingerweg 955099 MainzGermany.

We present a new Finite Volume Evolution Galerkin(FVEG)scheme for the solution of the shallow water equations(SWE)with the bottom topography as a source *** new scheme will be based on the FVEG methods presented in(noelle and Kraft,***.,221(2007)),but adds the possibility to handle dry *** most important aspect is to preserve the positivity of the water *** present a general approach to ensure this for arbitrary finite volume *** main idea is to limit the outgoing fluxes of a cell whenever they would create negative water ***,this corresponds to the absence of fluxes in the presence of *** is then re-established by splitting gravitational and gravity driven parts of the ***,a new entropy fix is introduced that improves the reproduction of sonic rarefaction waves.

关键词： Well-balanced schemes dry boundaries shallow water equations evolution Galerkin schemes source terms

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A Novel Full-Euler Low Mach Number IMEX Splitting

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Communications in Computational Physics 2020年第1期27卷 292-320页

作者： Jonas Zeifang Jochen Schutz Klaus Kaiser Andrea Beck Maria Lukacova-Medvid’ova sebastian noelle IAG Universiẗat StuttgartPfaffenwaldring 21DE-70569 StuttgartGermany Faculty of Sciences Hasselt UniversityAgoralaan Gebouw DBE-3590 DiepenbeekBelgium IGPM RWTH Aachen UniversityTemplergraben 55DE-52062 AachenGermany Institut f̈ur Mathematik Johannes Gutenberg-Universiẗat MainzStaudingerweg 9DE-55128 MainzGermany

In this paper,we introduce an extension of a splitting method for singularly perturbed equations,the socalled RS-IMEX splitting[Kaiser et al.,Journal of Scientific Computing,70(3),1390–1407],to deal with the fully compressible Euler *** straightforward application of the splitting yields sub-equations that are,due to the occurrence of complex eigenvalues,not hyperbolic.A modification,slightly changing the convective flux,is introduced that overcomes this *** is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler equations;numerical results using finite volume and discontinuous Galerkin schemes show the potential of the discretization.

关键词： Euler equations low-Mach IMEX Runge-Kutta RS-IMEX

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IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows

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Communications in Computational Physics 2014年第7期16卷 307-347页

作者： Georgij Bispen K.R.Arun Mária Lukácová-Medvid’ová sebastian noelle Institute of Mathematics University of MainzGermany School of Mathematics Indian Institute of Science Education and Research ThiruvananthapuramIndia IGPM RWTH AachenGermany.

We present new large time step methods for the shallow water flows in the lowFroude number *** order to take into accountmultiscale phenomena that typically appear in geophysical flows nonlinear fluxes are split into a linear part governing the gravitational waves and the nonlinear *** propose to approximate fast linear waves implicitly in time and in space bymeans of a genuinely multidimensional evolution *** the other hand,we approximate nonlinear advection part explicitly in time and in space bymeans of themethod of characteristics or some standard numerical flux *** integration is realized by the implicit-explicit(IMEX)*** apply the IMEX Euler scheme,two step Runge Kutta Cranck Nicolson scheme,as well as the semi-implicit BDF scheme and prove their asymptotic preserving property in the low Froude number *** experiments demonstrate stability,accuracy and robustness of these new large time step finite volume schemes with respect to small Froude number.

关键词： LowFroude number flows asymptotic preserving schemes shallowwater equations large time step semi-implicit approximation evolution Galerkin schemes

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