A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows (Advances in Applied Mathematics and Mechanics, 2021)
In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed forsimulation of viscous compressible flows. In the solver, the finite volume method isapplied to solve the Navier-Stokes equations. Different from conventional Navier-Stokessolvers, in this work, the inviscid flux across the cell interface is evaluated bylocal reconstruction of solution using one-dimensional lattice Boltzmann model, whilethe viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS [28–31], whichis used for simulation of inviscid flows. The first one is its ability to simulate viscousflows by including evaluation of viscous flux. The second one is its ability to effectivelycapture both strong shock waves and thin boundary layers through introduction of aswitch function for evaluation of inviscid flux, which takes a value close to zero inthe boundary layer and one around the strong shock wave. Numerical experimentsdemonstrate that the present solver can accurately and effectively simulate hypersonicviscous flows.