Dynamic Rupture Modelling on Unstructured Meshes Using a Discontinuous Galerkin Method

Abstract eng:
We will present recent developments concerning the extensions of the ADERDG method to solve three dimensional dynamic rupture problems on unstructured tetrahedral meshes. A remarkable feature of this method is the combination of the DG scheme and a time integration method using Arbitrarily high-order DERivatives (ADER) to provide high accuracy in space and time with the discretization on unstructured meshes. In the resulting discrete velocity-stress formulation of the elastic wave equations variables are naturally discontinuous at the interfaces between elements. The so-called Riemann problem can then be solved to obtain well-defined values of the variables at the discontinuity itself. This is in particular valid for the fault at which a given friction law has to be evaluated. Hence, the fault’s geometry is honored by the computational mesh. This way, complex fault planes can be modeled adequately with small elements while fast mesh coarsening is possible with increasing distance from the fault. A further advantage of the scheme is that it avoids spurious high-frequency contributions in the slip rate spectra and therefore does not require artificial Kelvin-Voigt damping or filtering of synthetic seismograms.

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