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

Irina Ginzburg, Frederik Verhaeghe & Dominique d'Humières

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

Published online: 2008-03

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  • Abstract

For simple hydrodynamic solutions, where the pressure and 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 adapt them for corners, to examine the uniqueness of the obtained steady solutions 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.

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@Article{CiCP-3-519, author = {}, title = {Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {3}, pages = {519--581}, abstract = {

For simple hydrodynamic solutions, where the pressure and 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 adapt them for corners, to examine the uniqueness of the obtained steady solutions 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7865.html} }
TY - JOUR T1 - Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme JO - Communications in Computational Physics VL - 3 SP - 519 EP - 581 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7865.html KW - AB -

For simple hydrodynamic solutions, where the pressure and 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 adapt them for corners, to examine the uniqueness of the obtained steady solutions 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.

Irina Ginzburg, Frederik Verhaeghe & Dominique d'Humières. (2020). Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme. Communications in Computational Physics. 3 (3). 519-581. doi:
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