Graduate Seminar "Aktuelle Themen der Numerik"

Wednesday, Jun 26, 2013 12:00 am


AIMEX large time step finite volume methods for low Froude number shallow water flows

Dr. K. R. Arun (School of Mathematics, Indian Institute of Science Education and Research Trivandrum)
Joint work with:
Georgij Bispen
Maria Lukacova
Sebastian Noelle

We present new large time step finite volume methods for 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 the 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 realised 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 the stability, accuracy and robustness of these new large time step chemes with respect to small Froude number.

Time: 12:00 am

Location: Room 224.3, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen