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

• Adding temperature and equilibrium boundary conditions to the semi-Lagrangian lattice Boltzmann method (SLLBM). • The increased efficiency by employing cubature rules to derive a reduced velocity space for the SLLBM is, for the first time, applied to 3D cooled flows and flows around objects. • Demonstrating the capabilities of the SLLBM for simulating the supersonic flow around a NACA-0012 airfoil in 2D and around a sphere in 3D. • For the first time, to the best of our knowledge, using the LBM to simulate the 3D supersonic flow in a turbulent channel and in a temporal compressible mixing layer. 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.