三维湍流Rayleigh-Bénard热对流的高效并行直接求解方法

高Ra数Rayleigh-Bénard热对流的湍流特性研究是当前国际上的一个热门研究课题, DNS模拟计算是研究该课题的重要手段之一. 当计算规模增大而网格数巨大时计算工作难以实现, 高Ra湍流热对流的数值模拟研究面临重大挑战. 本文创建了大规模高效并行计算的三维湍流热对流直接求解方法. 采用FFT变换解耦压力泊松方程, 将其变换成沿z方向上的块三对角方程组, 并利用块三对角方程的MPI与OpenMP联立的大规模高效并行近似解求解方案, 创建了可以高效并行计算的热对流直接求解方法. 通过对该方法并行效率的验证计算, 证明新的直接求解并行计算方法具有很好的并行效率和计算时效. 三维窄方腔热对流的计算结果表明, 本文方法计算的三维热对流特性是合理的. 本文创建的可大规模高效并行计算的三维湍流热对流直接求解方法, 也很可能是关于计算流体力学不可压NS方程大规模高效并行计算在特殊情况中计算技术上的一个突破.

Direct solution method of efficient large-scale parallel computation for 3D turbulent Rayleigh-Bénard convection

Research of turbulence Rayleigh-Bénard convection with high Ra number is a hot topic in physics research in the world. DNS simulation is one of the important means to study the subject. The computing work is hard to achieve when the calculation size is increased and the grid number is bigger. Numerical simulation for high Ra turbulent convection faces some major challenges. So the direct (non iterative) solution method of efficient large-scale parallel computation for the 3D turbulent convection is created in this paper. Main difficulties are the parallel computing technology for the pressure Poisson equation. The mass efficient parallel approximate solution with the block tridiagonal equations of OpenMP and MPI used simultaneously after decoupling pressure Poisson equation using FFT is presented. Through the validation of the efficiency of this method in parallel computing, the new method for direct solution of parallel computing have good parallel efficiency and computational time. Results of thermal convection in 3D narrow cavity show that the convection characteristics calculated by using the new method is reasonable. The direct solution method for efficient large-scale parallel computation of 3D turbulent convection created in this paper also is likely to be a breakthrough in computing technology about efficient large-scale parallel computing incompressible NS equations in some special cases.