laboratoire de physique statistique
 
 
laboratoire de physique statistique

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COMMUNICATIONS IN COMPUTATIONAL PHYSICS 


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2008
1
Two-relaxation-time Lattice Boltzmann scheme: About parametrization, velocity, pressure and mixed boundary conditions - Ginzburg, Irina and Verhaeghe, Frederik and d'Humieres, Dominique
COMMUNICATIONS IN COMPUTATIONAL PHYSICS 3427-478 (2008)

Abstract : We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamic equations with variable source terms based on equivalent equilibrium functions. A special parametrization of the free relaxation parameter is derived. It controls, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopic steady solution and governs the spatial discretization of transient flows. In this framework, the multi-reflection approach [16,18] is generalized and extended for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary conditions. We propose second and third-order accurate boundary schemes and adapt them for corners. The boundary schemes are analyzed for exactness of the parametrization, uniqueness of their steady solutions, support of staggered invariants and for the effective accuracy in case of time dependent boundary conditions and transient flow. When the boundary scheme obeys the parametrization properly, the derived permeability values become independent of the selected viscosity for any porous structure and can be computed efficiently. The linear interpolations [5,46] are improved with respect to this property.
2
Study of simple hydrodynamic solutions with the two-relaxation-times lattice Boltzmann scheme - Ginzburg, Irina and Verhaeghe, Frederik and d'Humieres, Dominique
COMMUNICATIONS IN COMPUTATIONAL PHYSICS 3519-581 (2008)

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.