Supersonic Shear and Wall-Bounded Flows With Body-Fitted Meshes Using the Semi-Lagrangian Lattice Boltzmann Method: Boundary Schemes and Applications

TL;DR

This paper advances the semi-Lagrangian lattice Boltzmann method by developing new boundary schemes and demonstrating its application to complex supersonic flows, including turbulent channels and mixing layers, capturing key compressibility effects.

Contribution

It introduces novel boundary conditions for the semi-Lagrangian LBM and applies them to simulate complex 3D supersonic flows, a first in the field.

Findings

Successfully simulated 2D and 3D supersonic flows with the method.

Demonstrated capability to model variable density and compressibility effects.

First 3D simulation of a supersonic turbulent channel flow at Ma=1.5.

Abstract

Lattice Boltzmann method (LBM) simulations of incompressible flows are nowadays common and well-established. However, for compressible turbulent flows with strong variable density and intrinsic compressibility effects, results are relatively scarce. Only recently, progress was made regarding compressible LBM, usually applied to simple one and two-dimensional test cases due to the increased computational expense. The recently developed semi-Lagrangian lattice Boltzmann method (SLLBM) is capable of simulating two- and three-dimensional viscous compressible 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.