Shear stress in lattice Boltzmann simulations

Details Shear stress in lattice Boltzmann simulations Shear stress in lattice Boltzmann simulations

2008-12-17

arxiv.org/abs/0812.3242v2

Phys. Rev. E 79 (2009) 046704

Physics

Condensed Matter

Other Condensed Matter

15 pages, 4 figures, 2 tables

Scientific paper

10.1103/PhysRevE.79.046704

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time-dependence of the fluid density in terms of the Reynolds number, Mach number and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.

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