Spacetime discontinuous Galerkin discretization of rotating shallow water equations on moving grids
Ambati, V.R. and Bokhove, O. (2006) Spacetime discontinuous Galerkin discretization of rotating shallow water equations on moving grids. [Report]

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Abstract:  A spacetime discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the spacetime DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the finite element boundaries. When discontinuities are present, we locally apply dissipation around these discontinuities with the help of Krivodonova's discontinuity indicator such that spurious oscillations are suppressed. The nonlinear algebraic system resulting from the discretization is solved using a pseudotime integration with a secondorder fivestage RungeKutta method. A thorough verification of the spacetime DG finite element method is undertaken by comparing numerical and exact solutions. We also carry out a discrete Fourier analysis of the one dimensional linear rotating shallow water equations to show that the method is unconditionally stable with minimal dispersion and dissipation error. The numerical scheme is validated in a novel way by considering various simulations of borevortex interactions in combination with a qualitative analysis of PV generation by nonuniform bores. Finally, the spacetime DG method is particularly suited for problems where dynamic grid motion is required. To demonstrate this we simulate waves generated by a wave maker and verify these for low amplitude waves where linear theory is approximately valid. 
Item Type:  Report 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/66375 
Official URL:  http://www.math.utwente.nl/publications 
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