Particle tracing in curvilinear grids

Computational fluid dynamics simulations result in large multivariate data sets with information such as pressure, temperature and velocity available at grid points for a sequence of steps. Velocity data is typically visualized by displaying a particle animation or streamlines. We present an efficient method for calculating particle paths based on velocity data from curvilinear grids. In order to compute the path, a velocity must be determined at arbitrary points inside the grid. We use a tetrahedral decomposition of the curvilinear grid. Each voxel, formed by eight points, is divided into five tetrahedra. The point of intersection of a particle’s path and the boundary of a tetrahedron is calculated and look-up tables are used to determine which tetrahedron the particle enters next. The new velocity is computed by interpolating the velocity at the four tetrahedron grid points. Tracing through the tetrahedra eliminates the need for searching through the curvilinear grid and eliminates additional sampling error caused by imposing a regular grid. Using our method, the time to update the position of a particle for a single time step is essentially a constant (O(1)).