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

TL;DR

This paper introduces a parallel finite-difference solver for incompressible flows that uses FFT-based transforms to accelerate pressure calculations, significantly reducing computational costs in large-scale simulations.

Contribution

It combines multi-block finite-difference methods with FFT-based eigenfunction expansions and multigrid solvers to enhance parallel performance and efficiency.

Findings

Achieves 2- to 8-fold reduction in computational cost

Validates the solver's accuracy and performance in parallel environments

Provides an open-source solver for the community

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. 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.