SC²S Colloquium - August 26, 2014

Date:	August 26, 2014
Room:	02.07.023
Time:	3 pm, s.t.

Philipp Samfaß: Towards a Non-Hydrostatic Shallow Water extension for the Finite Volume Solver SWE: Implementation and case study

The simulation program SWE (http://www5.in.tum.de/wiki/index.php/SWE), which is developed at TUM and subsequently referred to as SWE solver, uses a finite volume approach to solve the two-dimensional shallow water equations (SWE), e.g. in order to simulate wave propagation in tsunami scenarios. In our current shallow water model, wave propagation occurs due to pressure gradients. It is assumed in the SWE that only hydrostatic pressure (i.e. pressure being a result of the weight of the water column) is given and vertical velocity components can be neglected. These assumptions apply to waves fulfilling the shallow water characteristic h/λ << 1, where λ denotes the characteristic wavelength. As the water depth is usually about 4000m and the wavelength about 100km for tsunamis, the latter can reasonably be simulated using the SWE. However, when approaching the coast, the ratio h/λ changes and vertical velocity components, non-hydrostatic pressure and dispersive effects indeed have a non-negligible impact on run-up. Therefore, in order to be able to also capture these effects, the existing model shall be modified. For this purpose, the governing non-hydrostatic equations in conservation law form are derived in this talk and the approach using the so-called pressure projection method to modify the existing model is explained afterwards.