  This paper presents novel and efficient strategies to spatially adapt the
amount of computational effort applied based on the local dynamics of a free
surface flow, for both classic weakly compressible SPH (WCSPH) and
predictive-corrective incompressible SPH (PCISPH). Using a convenient and
readily parallelizable block-based approach, different regions of the fluid are
assigned differing time steps and solved at different rates to minimize
computational cost. Our approach for WCSPH scheme extends an asynchronous SPH
technique from compressible flow of astrophysical phenomena to the
incompressible free surface setting, and further accelerates it by entirely
decoupling the time steps of widely spaced particles. Similarly, our approach
to PCISPH adjusts the the number of iterations of density correction applied to
different regions, and asynchronously updates the neighborhood regions used to
perform these corrections; this sharply reduces the computational cost of
slowly deforming regions while preserving the standard density invariant. We
demonstrate our approaches on a number of highly dynamic scenarios,
demonstrating that they can typically double the speed of a simulation compared
to standard methods while achieving visually consistent results.
