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.

在本文中，提出了冲击管中非定常冲击波/边界层相互作用的晶格玻尔兹曼模拟。这类问题包含具有冲击波和边界层的超音速粘性流的典型特征，很少在格子Boltzmann社区中得到很好的验证。这导致格子玻尔兹曼方法在具有边界层的超音速流中的应用很少。使用常规可压缩晶格玻尔兹曼方法模拟冲击波/边界层相互作用时，暴露出一些与数值耗散和稳定性有关的问题。研究了这种流动的格子玻尔兹曼的实现。作为格子Boltzmann方法的一个新问题，需要仔细解决三个主要问题，即格子Boltzmann模型，求解方案，和边界处理。对于第一个问题，由于我们先前已经证明了其在超音速粘性流中的可行性，因此采用了双分布函数可压缩晶格Boltzmann模型，在该模型中研究了晶格速度以确保仿真的稳定性。对于求解方案，测试了各种空间离散化方法以增强数值性能。同时，研究了重影层的边界处理。改进的格子Boltzmann实现的模拟结果与以前文献中报道的Navier-Stokes方程和气体动力学方案的结果非常吻合。这项工作探讨了非稳态冲击波/边界层相互作用的格子Boltzmann方法的数值实现，