Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions
By Irina Ginzburg, Frederik Verhaeghe, Dominique d'Humières. Communications in Computational Physics, 2008
391 citations recorded by the source corpus.
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. PACS: 47.10.ad, 47.56+r, 02.60-x
Subfields: Applied Mathematics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d423fd123368220f1fa5e8db0d7dfa1a3c71f63e
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In Applied Mathematics
In Statistical and Nonlinear Physics
Citations in the corpus
- Optimal Stability of Advection-Diffusion Lattice Boltzmann Models with Two Relaxation Times for Positive/Negative Equilibrium (2010, background): “The effect of Λ on the accuracy of boundary [4, 14, 23], interface [10] and overall truncation errors [8, 28] has already been reported.”
- Lattice Boltzmann methods for single-phase and solid-liquid phase-change heat transfer in porous media: A review (2018, methodology): “p efficient and accurate LB methods from different points of view. In the past two decades, several alternative LB methods, such as the entropic LB method [114,115], the two-relaxation-time LB method [116,117], and the cascaded (or central moment) LB method [112,118, 119, 120, 121, 122], have been p”