Parallel Direct Method of DNS for Two-Dimensional Turbulent Rayleigh-Bénard Convection

A highly efficient parallelization scheme of direct numerical simulation (DNS) for two-dimensional Rayleigh-Bénard convection is presented. By introducing the parallel diagonal dominant (PDD) algorithm to solve the pressure Poisson equation and adjusting the domain decomposition accordingly, all-to-all communication as the usual obstacle to parallel computing can be eliminated. Excellent strong scaling and weak scaling for the parallel efficiency are achieved. Numerical results show that very complex structures in flow exist at very high Ra numbers. The required high resolution both in space and in time can be obtained by the present method at low parallel overhead.