Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method (Communications in Computational Physics, 2020)
Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions, which involve gradients evaluated at theboundaries, are implemented locally. A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galileaninvariance is also investigated. Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence. The lattice Boltzmannstress field is studied and shown to depart significantly from the Newtonian viscousstress when the ratio of Mach to Reynolds numbers is not negligibly small.