Load balancing and performance issues for the data parallel simulation of stiff chemical nonequilibrium flows

A data parallel program is presented that solves the reactive Euler equations for stiff chemical nonequilibrium flows on Connection Machines CM-2/200 and CM-5/5E. The program is written in CM Fortran and uses direction and time-step splitting to couple representations of the chemical and fluid dynamic processes on a structured Cartesian grid. An explicit high-order monotone algorithm with nonlinear damping is used to integrate the convection terms, and a hybrid asymptotic/modified-Euler approach is used to solve the system of ordinary differential equations from the chemical source terms. Integration of the fluid dynamics was conservatively determined to be 9.4 and 12.0 Gflops on a 512-node CM-5 and CM-5E, respectively. The fluid dynamics solver scaled well for large problems. Therefore, a new load-balancing algorithm was developed that reduces the chemistry integration time by a factor of six for the test problem, a detonation propagating in a hydrogen-oxygen-argon mixture. Moreover, the chemistry integration time, with the load balancing, is slightly less than the time required to integrate the fluid dynamics.

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