Multiresolution relaxation times lattice Boltzmann schemes with projection

TL;DR

This paper introduces an extension to multiresolution relaxation times lattice Boltzmann schemes by adding a projection step, which improves stability and reduces viscosity in fluid flow simulations.

Contribution

The paper develops a new extended lattice Boltzmann scheme with a projection step, demonstrating its theoretical validity and improved stability through numerical tests.

Findings

Projection step does not alter second-order asymptotic PDEs.

Enhanced stability and reduced bulk viscosity in simulations.

Successful application to various 2D fluid flow cases.

Abstract

We propose to extend the multiresolution relaxation times lattice Boltzmann schemes with an additional projection step. For the explicit example of the D2Q9 scheme, we define this extended method. We prove that in general the projection step does not change the asymptotic partial differential equations at second order. We present four numerical test cases. One concerns linear stability with a Fourier analysis with a single-vertex scheme. Three bidimensional fluid flows with a coarse mesh have been tested: the Minion and Brown sheared flow, the Ghia, Ghia and Shin lid-driven cavity and an unsteady acoustic wave. Our results indicate that the bulk viscosity can be dramatically reduced with a better stability than the initial scheme.