Parallel Computing Strategy for Multi-Size-Mesh, Multi-Time-Step DRP Scheme

The multi-size-mesh multi-time-step DRP scheme (Tam&Kurbatskii2003) is suited for numerical simulations of multiple-scales aeroacoustics problems. In regions where there are high flow gradients (jet or flow near walls), small grid sizes to resolve small scales are needed. In regions where sound dominates, larger grid sizes for long sound wave lengths may be used to save computation resources. Time steps are controlled by local grid sizes for numerical stability and accuracy. It is very inefficient to use a single time step for all the mesh points, as unnecessary computation has to be performed over mesh points with large mesh sizes. One unique feature of the DRP scheme is its multi-time step marching capability. The scheme synchronizes the size of the time step with the spatial mesh size. Half of the computations are done over regions with the highest resolution where time scale is the shortest.