On the investigation of shock wave/boundary layer interaction with a high-order scheme based on lattice Boltzmann flux solver

Shock wave/boundary layer interaction (SWBLI) continues to pose a significant challenge in the field of aerospace engineering. This paper aims to address this issue by proposing a novel approach for predicting aerodynamic coefficients and heat transfer in viscous supersonic and hypersonic flows using a high-order flux reconstruction technique. Currently, finite volume methods are extensively employed for the computation of skin aerodynamic coefficients and heat transfer. Nevertheless, these numerical methods exhibit considerable susceptibility to a range of factors, including the inviscid flux function and the computational mesh. The application of high-order flux reconstruction techniques offers promising potential in alleviating these challenges. In contrast to other high-order methods, the flux reconstruction is combined with the lattice Boltzmann flux solver in this study. The current method evaluates the common inviscid flux at the cell interface by locally reconstructing the lattice Boltzmann equation solution from macroscopic flow variables at solution points. Consequently, this framework performs a positivity-preserving, entropy-based adaptive filtering method for shock capturing. The present approach is validated by simulating the double Mach reflection, and then simulating some typical viscous problems. The results demonstrate that the current method accurately predicts aerodynamic coefficients and heat transfer, providing valuable insights into the application of high-order methods for shock wave/boundary layer interaction.