A graph-partitioned sharp-interface immersed boundary solver for efficient solution of internal flows

Highlights: • A graph-based parallel framework is developed for immersed boundary methods. • It enables efficient solution of internal flows in the cardiovascular system. • Benchmark tests show significant performance improvement. -- Abstract: In this Short Note, a graph-partitioning framework for a sharp-interface immersed boundary method is proposed so as to increase its computational efficiency for simulating internal flows on large-scale parallel computers. Immersed boundary methods are generally inefficient for internal flows with complex geometries due to the larger proportion of grid points that fall outside the fluid domain for such configurations. The graph-partitioning framework proposed here enables the solver to effectively ignore these points and focus the computation on the active points inside the fluid domain. A novel coarsening-partitioning process is proposed to ensure that sufficient overlapping layers are available at the sub-domain interfaces to accommodate computational stencils associated with the discretization as well as the sharp-interface boundary conditions. The benchmark test shows that the adoption of the graph topology reduces the computational cost (wall-time and memory cost) substantially. Moreover, the computational cost is shown to only scale with the number of computationally active grid points. The capability of the graph-partitioned solver is further demonstrated by simulating the flow inside an arterial network, a configuration which would otherwise be out of reach for most immersed boundary methods.