Lattice Boltzmann simulation for unsteady shock wave/boundary layer interaction in a shock tube

Abstract

In this paper, lattice Boltzmann simulation for unsteady shock wave/boundary layer interaction in a shock tube is presented. This kind of problem, which contains the typical characteristics of supersonic viscous flows with shock wave and boundary layer, has rarely been well validated in the lattice Boltzmann community. This leads to few application of lattice Boltzmann method in supersonic flows with boundary layer. Some problems related to numerical dissipation and stability are exposed when simulating shock wave/boundary layer interaction using the conventional compressible lattice Boltzmann approach. The implementations of lattice Boltzmann for this kind of flow are investigated. As a novel problem for the lattice Boltzmann method, three main issues need to be addressed carefully, i.e., lattice Boltzmann model, solving scheme, and boundary treatment. For the first issue, a double-distribution-function compressible lattice Boltzmann model, in which the lattice velocity is studied for the stability in the simulation, is employed since we have demonstrated its feasibility in supersonic viscous flow previously. For the solving scheme, various space discretization methods are tested to enhance numerical performance. Meanwhile, the boundary treatment for the ghost layer is studied. The simulation result by the improved lattice Boltzmann implementation agrees well with the results through Navier–Stokes equations and gas-kinetic scheme reported in previous literatures. This work probes the numerical implementations of lattice Boltzmann method for unsteady shock wave/boundary layer interaction, providing important theoretical support for lattice Boltzmann application in supersonic viscous flows with shock wave and boundary layer.