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1998•Europhysics Letters (EPL)Open access

Complete Galilean-invariant lattice BGK models for the Navier-Stokes equation

Yifang Qian, Ye Zhou

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Abstract

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (θ = 3) and two dimensions (θ = 1) for the Navier-Stokes equation have been obtained.

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Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (θ = 3) and two dimensions (θ = 1) for the Navier-Stokes equation have been obtained.

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Available abstract

Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (θ = 3) and two dimensions (θ = 1) for the Navier-Stokes equation have been obtained.

Key concepts: Galilean, Galilean invariance, Nonlinear system, Lattice (music), Invariant (physics), Advection, Galilean transformation, Mathematics

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