Supersonic shear and wall-bounded flows with body-fitted meshes using the semi-Lagrangian lattice Boltzmann method: Boundary schemes and applications

Lattice Boltzmann method (LBM) simulations of incompressible flows are nowadays common and well established. However, compressible supersonic flows with strong variable density and intrinsic compressibility effects pose particular challenges and are subject to ongoing research. The recently developed semi-Lagrangian lattice Boltzmann method (SLLBM) is capable of simulating two- and three-dimensional viscous compressible supersonic flows. This paper presents bounce-back, thermal, inlet, and outlet boundary conditions new to the method and their application to problems including heated or cooled walls, often required for supersonic flow cases. Using these boundary conditions, the SLLBM’s capabilities are demonstrated in various test cases, including a supersonic 2D NACA-0012 airfoil, flow around a 3D sphere, and, to the best of our knowledge, for the first time, the 3D simulation of a supersonic turbulent channel flow at a bulk Mach number of Ma = 1.5 and a 3D temporal supersonic compressible mixing layer at convective Mach numbers ranging from Ma = 0.3 to Ma = 1.2 . The results show that the compressible SLLBM is able to adequately capture intrinsic and variable density compressibility effects.