A FFT-based finite-difference solver for massively-parallel direct numerical simulations of turbulent flows

TL;DR

This paper introduces a highly efficient FFT-based finite-difference solver for large-scale parallel simulations of turbulent flows, enabling faster computations with excellent scalability on supercomputers.

Contribution

The authors develop a general framework for FFT-based pressure solvers with various boundary conditions, implemented in a massively-parallel, open-source solver called CaNS.

Findings

Achieved excellent strong scaling up to 10,000 cores.

Validated solver accuracy against canonical flows.

Demonstrated capability to simulate flows with 10^9 spatial degrees of freedom.

Abstract

We present an efficient solver for massively-parallel direct numerical simulations of incompressible turbulent flows. The method uses a second-order, finite-volume pressure-correction scheme, where the pressure Poisson equation is solved with the method of eigenfunction expansions. This approach allows for very efficient FFT-based solvers in problems with different combinations of homogeneous pressure boundary conditions. Our algorithm explores all combinations of pressure boundary conditions valid for such a solver, in a single, general framework. The method is implemented in a 2D pencil-like domain decomposition, which enables efficient massively-parallel simulations. The implementation was validated against different canonical flows, and its computational performance was examined. Excellent strong scaling performance up to $10^4$ cores is demonstrated for a domain with $10^9$ spatial degrees of freedom, corresponding to a very small wall-clock time/time step. The resulting tool, CaNS, has been made freely available and open-source.