Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1997 · 805 citations · 0 references
EngineeringComputational EngineeringPhysicsComputational Fluid DynamicsComputational PhysicsFluid DynamicsBoltzmann Transport EquationHeat Transfer ModelingLattice Boltzmann MethodsThermal SimulationBoltzmann EquationsDiscrete ModelsDiscrete Velocity ModelsGridsLattice Boltzmann EquationNumerical SimulationNumerical Stability AnalysisNumerical Thermal Models
The lattice Boltzmann equation (LBE) is directly derived from the Boltzmann equation by discretization in both time and phase space. The authors present a systematic procedure to derive discrete velocity models and propose an LBE algorithm with arbitrary mesh grids, demonstrated on a backward‑facing step simulation. The method involves discretizing the Boltzmann equation in time and phase space to construct discrete velocity models and implementing the resulting LBE on arbitrary mesh grids for simulation. The simulation of the backward‑facing step shows good agreement with experimental and prior numerical data, and the study discusses improvements to LBE models and explains instability in existing thermal models.
The lattice Boltzmann equation (LBE) is directly derived from the Boltzmann equation by discretization in both time and phase space. A procedure to systematically derive discrete velocity models is presented. A LBE algorithm with arbitrary mesh grids is proposed and a numerical simulation of the backward-facing step is conducted. The numerical result agrees well with experimental and previous numerical results. Various improvements on the LBE models are discussed, and an explanation of the instability of the existing LBE thermal models is also provided.