Implementations of multi-fluid hydrodynamic simulations on distributed memory computer with a fully parallelizable preconditioned Bi-CGSTAB method

摘要

This paper reports recent work in implementing a multi-phase fluid dynamic code on a super computer system with distributed memory architecture. In the numerical model, the dynamics of different fluids is formulated based on a unified framework for general continuum. The computational code was constructed so that it is easily implemented on a distributed memory machine. A projection procedure for solving the flows of various compressibilities results in a pressure Poisson equation which has large discontinuities and singularities in the coefficients and the right-hand side terms. A preconditioned Bi-CGSTAB method is used to solve the Poisson equation. A tridiagonal factorization preconditioner is adopted to utilize the large scale pipeline structure of the hardware. To get perfect parallelism, we made use of a Jacobi splitting to invert the tri-diagonal system in the partitioning direction. The resulting preconditioner is tested with a problem that has large jumps and singularities. A satisfying vector processor utilization and a parallel speed-up of the fluid code are achieved.