Parallel multigrid finite volume computation of three-dimensional thermal convection

A parallel implementation of the finite volume method for three-dimensional, time-dependent, thermal convective flows is presented. The algebraic equations resulting from the finite volume discretization, including a pressure equation which consumes most of the computation time, are solved by a parallel multigrid method. A flexible parallel code has been implemented on the Intel Paragon, the Cray T3D, and the IBM SP2 by using domain decomposition techniques and the MPI communication software. The code can use 1D, 2D, or 3D partitions as required by different geometries, and is easily ported to other parallel systems. Numerical solutions for air (Prandtl number Pr = 0.733) with various Rayleigh numbers up to 107 are discussed.