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 ...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.展开更多
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.
文摘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.
