New Approaches for Particle Tracing on Sparse Grids

Flow visualization tools based on particle methods continue to be an important utility of ow simulation. Additionally, sparse grids are of increasing interest in numerical simulations. In 13] we presented the advantages of particle tracing on uniform sparse grids. Here we present and compare two diierent approaches to accelerate particle tracing on sparse grids. Furthermore, a new approach is presented in order to perform particle tracing on curvilinear sparse grids. The method for curvilinear sparse grids consists of a modiied Stencil Walk algorithm and especially adapted routines to compute, store, and handle the required Jacobians. The accelerating approaches are on the on hand an adaptive method, where an error criterion is used to skip basis functions with minor contribution coeecients, and on the other hand the so-called combination technique, which uses a speciic selection of small full grids to emulate sparse grids.