Load Balancing for Immersed Boundaries in Coupled Simulations

Abstract

The simulation of engineering problems usually involves different physics and scales that need to be addressed appropriately. A monolithic computation on the finest scale of such complex problems results in overly expensive computations, unfeasible to solve even on today’s supercomputing facilities. To facilitate accurate simulations of such problems we suggest a partitioned coupling approach. The strategy is, to decompose the simulation domain according to the physics into subdomains and solve each of them with the best suited numerical approximation. All subdomains are weakly connected to each other at the boundaries (coupling interface), while a coupling approach takes care of the communication and the data-exchange between them. With that we can not only address specific requirements of the physics individually but also reduce the computational cost when compared to the monolithic scenario, where the entire domain is treated with the same equations and numerical scheme. One drawback we face in coupled simulations is the implied load imbalance, which is due to the different treatment of each subdomain and the communication and interpolation between them. These additional loads do not affect the complete domain equally and a balancing strategy within the subdomains is required for efficient computation. To represent geometries in our setups, we employ a penalization method that fits well with high-order discretization schemes, but introduces volumes, where the solution is not of interest. By reducing the scheme order selectively in those regions that are not of interest, the impact of this strategy on the computational effort can be minimized but this introduces another factor of load imbalance. In this work we present observations on these load imbalances and how they can be balanced in the coupled setup, enabling the efficient computation of complex setups as found for example in direct aero-acoustic simulations.