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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.
Email: v.r.ambati@math.utwente.nl
Abstract
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.
Introduction
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