An efficient semi-implicit solver for direct numerical simulation of compressible flows at all speeds

TL;DR

This paper introduces a semi-implicit solver for compressible Navier-Stokes equations that enhances computational efficiency and reduces resource consumption across various flow regimes by mitigating acoustic time step limitations.

Contribution

The paper presents a novel semi-implicit algorithm that simplifies matrix inversion and extends to multi-dimensional viscous flows, improving efficiency over existing methods.

Findings

Achieves up to 85% resource savings in low-subsonic flows.

Maintains accuracy in simulating turbulence and duct flows.

Demonstrates higher efficiency compared to classical methods.

Abstract

We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated with acoustic waves, in such a way to suppress, or at least mitigate the acoustic time step limitation. Together with replacement of the total energy equation with the entropy transport equation, this approach avoids the inversion of block-banded matrices involved in classical methods, which is replaced by less demanding inversion of standard banded matrices. The method is extended to deal with implicit integration of viscous terms and to multiple space dimensions through approximate factorization, and used as a building block of third-order Runge-Kutta time stepping scheme. Numerical experiments are carried out for isotropic turbulence, plane channel flow, and flow in a square duct. All available data support higher computational efficiency than existing methods, and saving of resources ranging from $85\%$ under low-subsonic flow conditions, to about $50\%$ in supersonic flow.