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

作　　者：Georgij Bispen K.R.Arun Mária Lukácová-Medvid’ová Sebastian Noelle 

机构地区：[1]Institute of Mathematics,University of Mainz,Germany [2]School of Mathematics,Indian Institute of Science Education and Research Thiruvananthapuram,India [3]IGPM,RWTH Aachen,Germany.

出　　处：《Communications in Computational Physics》2014年第7期307-347,共41页计算物理通讯（英文）

基　　金：supported by the German Science Foundation under the grants LU 1470/2-2 and No 361/3-2.The second author has been supported by the Alexander-von-Humboldt Foundation through a postdoctoral fellowship.M.L.and G.B.would like to thank Dr.Leonid Yelash(JGU Mainz)for fruitful discussions.

摘　　要：We present new large time step methods for the shallow water flows in the lowFroude number limit.In 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 advection.We propose to approximate fast linear waves implicitly in time and in space bymeans of a genuinely multidimensional evolution operator.On the other hand,we approximate nonlinear advection part explicitly in time and in space bymeans of themethod of characteristics or some standard numerical flux function.Time integration is realized by the implicit-explicit(IMEX)method.We 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 limit.Numerical 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 

分 类 号：O17[理学—数学]