用于不可压缩流大规模并行模拟的FFT加速多块有限差分求解器
A FFT-accelerated multi-block finite-difference solver for massively parallel simulations of incompressible flows
摘要：
本文提出了一种适用于不可压缩流动大规模并行直接数值模拟（DNS）的多块有限差分求解器。该算法结合了多块求解器的通用性和特征函数展开的方法，以加速压力泊松方程的求解。这是通过采用基于FFT的变换沿一个均匀的方向，有效地降低了问题的复杂性，在低成本。这些基于FFT的扩展是在一个框架中实现的，该框架统一了这种方法的边界条件的所有有效组合。随后，几何多重网格求解器被用来解决减少泊松方程在多块几何。这里特别注意，以保证多重网格求解器的并行性能时，解决减少线性系统方程。我们已经验证了整体数值算法，并评估其性能在大规模并行设置。结果表明，利用FFT加速泊松方程的解决方案时，可以很容易地实现2至8倍的计算成本降低。求解器SNaC已经在MIT许可证的条款下免费提供和开源。
英文摘要：
We present a multi-block finite-difference solver for massively parallel Direct Numerical Simulations (DNS) of incompressible flows. The algorithm combines the versatility of a multi-block solver with the method of eigenfunctions expansions, to speedup the solution of the pressure Poisson equation. This is achieved by employing FFT-based transforms along one homogeneous direction, which effectively reduce the problem complexity at a low cost. These FFT-based expansions are implemented in a framework that unifies all valid combinations of boundary conditions for this type of method. Subsequently, a geometric multigrid solver is employed to solve the reduced Poisson equation in a multi-block geometry. Particular care was taken here, to guarantee the parallel performance of the multigrid solver when solving the reduced linear systems equations. We have validated the overall numerical algorithm and assessed its performance in a massively parallel setting. The results show that 2- to 8-fold reductions in computational cost may be easily achieved when exploiting FFT acceleration for the solution of the Poisson equation. The solver, SNaC, has been made freely available and open-source under the terms of an MIT license.
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