Volume 3, Issue 3
Study of Simple Hydrodynamic Solutions with the Two-relaxation-times Lattice Boltzmann Scheme

Irina Ginzburg ,  Frederik Verhaeghe and Dominique d'Humières

Commun. Comput. Phys., 3 (2008), pp. 519-581.

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  • Abstract

For simple hydrodynamic solutions, where the pressureand the velocity are polynomial functions of the coordinates, exact microscopic solutions are constructed for the two-relaxation-time (TRT) Lattice Boltzmann model with variable forcing and supported by exact boundary schemes. We show how simple numerical and analytical solutions can be interrelated for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) multi-reflection (MR) type schemes. Special care is taken to adaptthemforcorners, toexaminetheuniqueness oftheobtainedsteadysolutions and staggered invariants, to validate their exact parametrization by the non-dimensional hydrodynamic and a “kinetic” (collision) number. We also present an inlet/outlet “constant mass flux” condition. We show, both analytically and numerically, that the kinetic boundary schemes may result in the appearance of Knudsen layers which are beyond the methodology of the Chapman-Enskog analysis. Time dependent Dirichlet boundary conditions are investigated for pulsatile flow driven by an oscillating pressure drop or forcing. Analytical approximations are constructed in order to extend the pulsatile solution for compressible regimes.

  • History

Published online: 2008-03

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