Optimization of time-dependent particle tracing using tetrahedral decomposition

An efficient algorithm is presented for computing particle paths, streak lines and time lines in time-dependent flows with moving curvilinear grids. The integration, velocity interpolation, and step size control are all performed in physical space which avoids the need to transform the velocity field into computational space. This leads to higher accuracy because there are no Jacobian matrix approximations, and expensive matrix inversions are eliminated. Integration accuracy is maintained using an adaptive step size control scheme which is regulated by the path line curvature. The problem of point location and interpolation in physical space is simplified by decomposing hexahedral cells into tetrahedral cells. This enables the point location to be done analytically and substantially faster than with a Newton-Raphson iterative method. Results presented show this algorithm is up to six times faster than particle tracers which operate on hexahedral cells, and produces almost identical traces.