SPACE-TIME ADAPTIVITY WITH MULTIGRID REDUCTION IN TIME FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

A parallelized fully-adaptive space-time mesh refinement algorithm using multigrid reduction-in-time (MGRIT) is applied to the unsteady compressible Navier-Stokes equations to solve fluids problems. Previously, fully-adaptive space-time methods have primarily used sequential time marching to integrate the time domain. Despite parallelization in the spatial domain, wall clock times have remained high due to the computational cost per time-step and the large number of desired time-steps. Furthermore, architectural trends in high-performance computing have shifted from ever-increasing clock speeds to greater concurrency. This motivates a need to parallelize the time domain. The spatial parallelization consists of a partitioning of the domain into a nested hierarchy of Cartesian grids that is adaptively refined at regions and flow features of interest. The MGRIT algorithm is demonstrated using an explicit time integration scheme applied to Couette flow, where error is compared to the analytic solution and a convergence study is performed. The eventual goal, after further development and optimization, is to conduct a performance comparison against a sequential-in-time version of the algorithm.