Message Passing Interface Parallelization for Two-Way Coupled Euler-Lagrange Simulation of Microbubble Enhanced HIFU

Microbubble enhanced high intensity focused ultrasound (HIFU) is of great interest to tissue ablation for tumor treatment such as in liver and brain cancers. To accurately characterize the acoustic and thermal fields during this process, a coupled Euler-Lagrange model is used. The ultrasound field is modeled using compressible Navier-Stokes equations on an Eulerian grid, while the microbubbles are tracked in a Lagrangian fashion. The coupling is realized through the void fraction computed from the instantaneous bubble volumes. To speed up the computations, an message passing interface parallelization scheme based on domain decomposition is herein proposed. During each time-step, message passing interface processors, each handling one subdomain, are first used to execute the fluid computation, and then the bubble computations. This is followed by the coupling procedure. The coupling is challenging as the effect of the bubbles through the void fraction at an Eulerian point near a subdomain border will require information from bubbles located in different subdomains, and vice versa. This is addressed by a special utilization of ghost cells surrounding each fluid subdomain, which allows bubbles to spread their void fraction effects across subdomain edges without the need of exchanging directly bubble information between subdomains and significantly increasing overhead. After a careful verification of gas effects conservation, this parallelization scheme is validated and illustrated on a typical microbubble enhanced HIFU problem, followed by parallelization scaling tests and efficiency analysis.