Graduate Seminar "Aktuelle Themen der Numerik"
Tuesday, Jul 15, 2014, 11:00 am
A stable and well balanced generalized Riemann problem method for the shallow water equations with bottom topography
Prof. Dr. Guoxian Chen (Wuhan University)
In this talk, we extend the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method is solved directly in Eulerian coordinates, and used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included into the numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid-point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method into data reconstruction step. The GRP solver is stabilized near equilibria by using the Rankine–Hugoniot condition to remove a singularity from the GRP solver.
Time: 11:00 am
Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen