An analysis of the performance enhancement with adaptive mesh refinement for spray problems. (July 2021) - Kuo, Chia-Wei; Trujillo, Mario F.
Highlights: AMR suffers degradation in performance in spray problems. Performance deterioration is due to growth in computational cell number and a decline in cell-based speedup. An analytical expression for cell-based speedup is derived in terms of the Frobenius number and other quantities. The theoretical development provide an explanation of the results from simulations. Abstract: Adaptive mesh refinement (AMR) provides an attractive means of significantly reducing computational costs while simultaneously maintaining a high degree of fidelity in regions of the domain requiring it. In the present work, an analysis of the performance of AMR supported by simulations is undertaken for liquid injection and spray formation problems. These problems are particularly challenging from a computational cost perspective since the associated interfacial area typically grows by orders of magnitude, leading to similar growth in the number of highly refined cells. While this increase in cell numbers directly contributes to a declining performance for AMR, a second less obvious factor is the decaying trend for the cell-based speedup, Θ . A theoretical analysis is presented, leading to a closed-form estimate for this cell-based speedup, namely Θ E = κ F, S M / κ F, A M R, where κ F is the Frobenius condition number, and SM corresponds to a static mesh case. It is shown that for spray formation problems, the typical growth in κ F, A M R is more pronounced than κ F, S M causing a decline in Θ and consequently diminishing the AMR performance. Additional contributing sources are also examined, which include the role of load balancing and the choice of linear solvers for the Poisson system.