Wall distance search algorithm using voxelized marching spheres

Minimum distance to a solid wall is a commonly used parameter in turbulence closure formulations associated with the Reynolds Averaged form of the Navier Stokes Equations (RANS). This paper presents a new approach to efficiently compute the minimum distance between a set of points and a surface. The method is based on sphere voxelization, and uses fast integer arithmetic algorithms from the field of computer graphics. Using a simple test case where the number of points (NpNp) and surface elements (NbNb) can be independently specified, the present method is empirically estimated to be O(Np0.8Nb0.5). An unstructured grid around an aircraft configuration (DLR-F6) is chosen as the test case for demonstration and validation. Multi-processor computations (up to 256 processors) are conducted to study efficiency and scalability. Encouraging results are obtained, with the sphere voxelization algorithm demonstrated to be more efficient than all of the alternate methods for computing minimum distances. However, a load imbalance does exist, which negatively impacts the scalability for large number of cores. A simple method for load re-balancing is formulated and tested, which results in significant improvements in both efficiency and scalability.