Applications using DUNE - FEM

Local Discontinuous Galerkin method for shallow 3D free surface flows

Short Description

The Local Discontinuous Galerkin (LDG) method is a higher order discretization method for advection-diffusion equations. A recently finished diploma thesis deals with a conservative LDG method for the simulation of incompressible hydrostatic free surface flows using σ-transformed coordinates. The time-dependent computational domain representing the fluid region is transformed onto a domain that is fixed in time. The advantage of solving the resulting transformed system of partial differential equations is that unlike in moving mesh strategies there is no need to smooth the discrete surface elevation for grid adaptation.

Numerical results

Evolution in time of horizontal (x-)velocity in a quasi-dam-break test case; piecewise lineaer base polynomials, computed on 20 cpu.

Evolution in time of horizontal (y-)velocity in the same test case, seen from above.

The numerical solution is computed using a special grid implementation of a semi-structured prism-grid.

References

• Christoph Gersbacher, "Local Discontinuous Galerkin Verfahren zur Simulation flacher dreidimensionaler Strömungen mit freier Oberfläche", ("Simulation of Shallow Incompressible 3D Free Surface Flows using a Local Discontinuous Galerkin Method"), Diploma thesis, University of Freiburg, 2008.