TY - JOUR
T1 - IMEX Large Time Step Finite Volume Methods for Low Froude Number Shallow Water Flows
AU - Georgij Bispen, K. R. Arun, Mária Lukáčová-Medvid'ová & Sebastian Noelle
JO - Communications in Computational Physics
VL - 2
SP - 307
EP - 347
PY - 2014
DA - 2014/08
SN - 16
DO - http://doi.org/10.4208/cicp.040413.160114a
UR - https://global-sci.org/intro/article_detail/cicp/7044.html
KW - Low Froude number flows
KW - asymptotic preserving schemes
KW - shallow water equations
KW - large time step
KW - semi-implicit approximation
KW - evolution Galerkin schemes.
AB - <p style="text-align: justify;">We present new large time step methods for the shallow water flows in the
low Froude number limit. In order to take into account multiscale 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 by means of a genuinely multidimensional
evolution operator. On the other hand, we approximate nonlinear advection part explicitly
in time and in space by means of the method 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.</p>