Summary: SPACE-TIME DISCONTINUOUS GALERKIN METHOD FOR ROTATING SHALLOW WATER FLOWS
V. R. Ambati,, O. Bokhove
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands.
In the present work, we analyze the rotating shallow
water equations including bottom topography using a
space-time discontinuous Galerkin finite element method.
The method results in non-linear equations per element,
which are solved locally by establishing the element com-
munication with a numerical HLLC flux. To deal with
spurious oscillations around discontinuities, we employ
a stabilization operator only around discontinuities us-
ing Krivodonova's discontinuity detector. The numerical
scheme is verified and validated by comparing numeri-
cal and exact solutions, and analyzing bore-vortex inter-
actions. We conclude that the method is second order ac-
curate in both space and time for linear polynomials, and
correctly captures bore-vortex interactions.