Parallelization of direct simulation Monte Carlo method combined with monotonic Lagrangian grid

Abstract

The monotonic Lagrangian grid (MLG) and the direct simulation Monte Carlo (DSMC) methodology were combined on the Thinking Machines CM-5 to create a fast DSMC-MLG code with automatic grid adaptation based on local number densities. The MLG is a data structure in which particles that are close in physical space are also close in computer memory. Using the MLG data structure, physical space is divided into a number of templates (cells), each containing the same number of particles. An MLG-regularization method, stochastic grid restructuring, is implemented to minimize the occurrence of highly skewed cells. Parallelization of the DSMC-MLG is achieved by two different mapping techniques. First, simulated particles are mapped onto the parallel processors for the particle-oriented processes, such as convection, boundary interactions, and MLG sorting. Second, particle templates are mapped onto the processors for computing the macroscopic quantities (i.e., pressure, velocity, density, and temperature) and statistical sampling. In both levels of mapping, the code logic focuses on the structured and fast communications on the CM-5 architecture. The computing time required by the parallel DSMC-MLG code was significantly decreased compared with other parallel efforts and its parallel efficiency on 512 processors achieved approximately 80% for simulation involving one-half million particles.