Lattice Boltzmann model in general curvilinear coordinates applied to exactly solvable 2D flow problems

Abstract

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Numerical simulation results of basic exactly solvable fluid flows using the previously proposed by H. Chen Lattice Boltzmann Method (LBM) formulated on a general curvilinear coordinate system are presented. As was noted in the theoretical work of H. Chen, such curvilinear Lattice Boltzmann Method preserves a fundamental one-to-one exact advection feature in producing minimal numerical diffusion, as the Cartesian lattice Boltzmann model. As we numerically show, the new model converges to exact solutions of basic fluid flows with the increase of grid resolution in the presence of both natural curvilinear geometry and/or grid non-uniform contraction, both for near equilibrium and non-equilibrium LBM parameter choices.

Keywords

• Lattice Boltzmann Method
• generalized coordinates
• Chapman–Enskog theory
• Boltzmann equation
• numerical methods
• fluid mechanics