Navier-Stokes solver using Green's functions II: spectral integration of channel flow and plane Couette flow

TL;DR

This paper presents a spectral integration method using Green's functions for channel and plane Couette flow, enabling efficient turbulence simulation with large grid points and leveraging LAPACK for solving linear systems.

Contribution

It introduces a new spectral integration approach with triangular matrices for the Kleiser-Schumann algorithm, improving turbulence simulation efficiency.

Findings

Simulated turbulence at Re=80,000 with 10^9 grid points.

Demonstrated the method's compatibility with LAPACK functions.

Assessed transient elimination time in initial turbulence simulations.

Abstract

The Kleiser-Schumann algorithm has been widely used for the direct numerical simulation of turbulence in rectangular geometries. At the heart of the algorithm is the solution of linear systems which are tridiagonal except for one row. This note shows how to solve the Kleiser-Schumann problem using perfectly triangular matrices. An advantage is the ability to use functions in the LAPACK library. The method is used to simulate turbulence in channel flow at $Re=80,000$ (and $Re_{\tau}=2400$) using $10^{9}$ grid points. An assessment of the length of time necessary to eliminate transient effects in the initial state is included.