#5515. A FFT-accelerated multi-block finite-difference solver for massively parallel simulations of incompressible flows

August 2026publication date
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Journal’s subject area:
Computer Networks and Communications;
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Abstract:
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.
Keywords:
Computational fluid dynamics; Direct numerical simulation; Fast Poisson solver; High-performance computing; Multi-block solver

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