A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

Abstract

In the present work, the spectral difference lattice Boltzmann method (SDLBM) is implemented on unstructured meshes for the solution methodology to be capable of accurately simulating the compressible flows over complex geometries. Both the inviscid and viscous compressible flows are computed by applying the unstructured SDLBM. The compressible form of the discrete Boltzmann–BGK equation with the Watari model is considered and the solution of the resulting system of equations is obtained by applying the spectral difference method on arbitrary quadrilateral meshes. The accuracy and robustness of the unstructured SDLBM for simulating the compressible flows are demonstrated by simulating four problems that are steady inviscid supersonic flow past a bump, steady inviscid subsonic flow over the two-element NACA 4412-4415 airfoil with and without the ground effect, steady viscous transonic flow around the NACA 0012 airfoil and unsteady viscous subsonic flow past two side-by-side cylinders. The results obtained by applying the unstructured SDLBM are in good agreement with those of the available high-order accurate Euler/Navier-Stokes solvers and also the experimental data. The present study introduces the unstructured SDLBM as an appropriate inviscid and viscous compressible LBM flow solver for accurately simulating fluid flows over practical problems.