Space-Time Meshes for Non-linear Hyperbolic Problems Satisfying a Non-uniform Cone Constraint

Alper Üngör, Alla Sheffer, Robert Haber

Abstract:

Space-time Discontinuous Galerkin (DG) methods provide a solution for a wide variety of numerical problems. For an element-by-element procedure to be used to solve a DG system, the space-time mesh has to satisfy a {\em cone constraint}, which dictates that the mesh faces cannot be steeper in the time direction than a specified angle function $\alpha()$. This paper discusses algorithms that generate space-time meshes satisfying a {\em non-uniform cone constraint} (NUCC), i.e. $\alpha()$ varies through out the domain. We consider the extension of existing {\em uniform cone constraint} (UCC) meshing algorithms and present a new 1D$\times$TIME meshing algorithm for handling NUCC.