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Abstract: |
Shallow water equations (SWEs) with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. Since the SWEs admit non-trivial steady-state solutions, extra care need to be paid to approximate the source term numerically. Another important difficulty arising in the simulations is the appearance of dry areas. In this presentation, we will talk about recently developed high-order discontinuous Galerkin (DG) finite element methods, which can capture the general moving steady state well, and at the same time are positivity preserving without loss of mass conservation. Some numerical tests are performed to verify the positivity, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions. |
