A Parallel Local Remeshing Approach For Flow Computations With Moving Boundaries

Simulating flows around geometries that may change their shape and/or position with time has commonly occurred in many important areas in relation with fundamental studies and industry applications. Among numerous researches reported in abundant literatures, the dynamic unstructured grid approach is one of the main solutions for such simulations. It adopts a single consistent unstructured grid at every time step. To accommodate the geometry change between different time steps, the grid nodes can be moved while the node connectivity is kept primarily unchanged. However, this kind of grid deformation method could sometimes result in badly shaped or even inverted elements when large-scale movements are involved during simulations. In order to continue the solution process, the local remeshing algorithm is adopted to cut some holes in regions where the local element quality is deteriorated, and then generate new grids to fill these holes. After that, the solution on these new grids can be obtained by interpolating the results from the old grids and the process is continuously advanced in time on the new grids until convergence.A sequential local remeshing algorithm has become the major performance bottleneck when the simulations involving millions of elements and hundreds of computer cores are considered. Parallelization is a feasible way to overcome the performance bottleneck induced by a sequential local remeshing step. The existing parallel local remeshing approach requires combining a single hole initially spanning multiple processors into one processor so that the sequential results can be reproduced. Therefore, if the remeshed hole is too large, this approach may encounter performance bottlenecks in terms of both memory usage and computing time. By contrast, the new parallel remeshing approach proposed in this study can avoid this limit by decomposing the initially distributed holes into many sub-holes and distributing them evenly on the involved computer cores for loading balance. The domain decomposition approach employed in this study could ensure the generation of a well-shaped inter-hole boundary always. Therefore, the subsequent remeshing step can fix the inter-hole boundary without compromising the quality of elements around this boundary. In the meantime, because the remeshing procedure involves no communications, its parallel efficiency is very high.Besides, the point location algorithm is revisited. Given a new grid point, this algorithm finds an element in the old grid that contains this point, referring to as a base element hereafter. The efficiency of this algorithm is key to the efficiency of the solution reconstruction step since it need be repeated for each new grid point. The prevailing solution is based on spatial decomposition structures such as quadtrees or octrees. In this study, a different algorithm based on the walk-through technique is proposed. It does not depend on any spatial decomposition structure and is therefore more memory-saving. Meanwhile, this algorithm need averagely visit a very small number of elements to find the base element. Therefore, it is observed in our numerical experiments that its timing performance is better than its counterpart based on octrees.