Multiple relaxation time lattice Boltzmann schemes for advection-diffusion equations with application to radar image processing

Abstract

Motivated by marine radar image processing, we investigate the accuracy of multiple relaxation time lattice Boltzmann schemes designed to simulate two-dimensional convection-diffusion equations. The context of application requires to deal with non-constant advection velocity. Using Taylor expansions, instead of the widely used Chapman-Enskog expansions, we show how to control the accuracy of these schemes when deriving equivalent partial differential equations. On the one hand, a third order analysis is conducted on a scheme involving a constant advection velocity and no source term. First, this analysis derives the stability region through the von Neumann analysis. Second, a numerical convergence rate of three is obtained thanks to an appropriate choice of parameters. On the other hand, non-constant advection velocity together with non-zero source term, introduce additional terms at the second order. Regarding the targeted application, these extra terms are shown to be negligible and experiments on real data show that such multiple relaxation time lattice Boltzmann schemes are relevant for marine radar denoising and enhancement.