Mathematics > Numerical Analysis
[Submitted on 14 Nov 2024]
Title:Theory of the lattice Boltzmann method: discrete effects due to advection
View PDFAbstract:Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space derivatives. Several previous works have been devoted to analyzing the accuracy of these models with special emphasis on deviations from pure Newtonian viscous behaviour, related to higher order space derivatives of even order. The presentcontribution concentrates on possible inaccuracies of the advection behaviour linked to space derivatives of odd order. Detailed properties of advection-diffusion and athermal fluids are presented for two-dimensional situations allowing to propose situations that are accurate to third order in space derivatives. Simulations of the advection of a gaussian dot or vortex are presented. Similar results are discussed in appendices for three-dimensional advection-diffusion.
Submission history
From: Francois Dubois [view email] [via CCSD proxy][v1] Thu, 14 Nov 2024 09:44:23 UTC (887 KB)
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