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

Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.375-384, September 2000

MESHING
RESEARCH
CORNER

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 cone constraint which dictates that the mesh faces cannot be steeper in the time direction than a specified angle function α(). This paper discusses algorithms that generate space-time meshes satisfying a non-uniform cone constraint (NUCC), i.e. α() varies through out the domain. We consider the extension of existing uniform cone constraint (UCC) meshing algorithms and present a new 1DxTIME meshing algorithm for handling NUCC.