Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization, Velocity, Pressure and Mixed Boundary Conditions
Year: 2008
Communications in Computational Physics, Vol. 3 (2008), Iss. 2 : pp. 427–478
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-CiCP-7862
Communications in Computational Physics, Vol. 3 (2008), Iss. 2 : pp. 427–478
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 52