Improving the accuracy and reducing the computation time of the inviscid compressible flow solution using the Spectral Difference Lattice Boltzmann Method

In this research, the capabilities of the Spectral Difference Lattice Boltzmann Method for solution of two-dimensional inviscid compressible flows on structured grids have been enhanced. The published results of this method for solving compressible flow have so far been obtained using the model proposed by Watari. Here, by employing the model proposed by Qu and colleagues, the execution time of the numerical solution for inviscid compressible flow using the spectral difference lattice Boltzmann method has been significantly decreased. To assess the accuracy of the proposed method for solving compressible flows with and without discontinuities, this method has been applied to solve the stationary isentropic vortex problem and the shock–vortex interaction problem on the two-dimensional structured grids. The results obtained from solving these problems using the enhanced third-order spectral difference lattice Boltzmann method are presented and compared with the exact solutions and numerical results. In this research, it has been demonstrated that the enhanced third-order Spectral Difference Lattice Boltzmann Method (SDLBM) provides the following improvements: (1) the computational time for the numerical solution of inviscid compressible flows is reduced to approximately one-third of that required by the conventional SDLBM; (2) comparisons with the exact solution confirm that the accuracy of the results is improved over the conventional SDLBM; and (3) shock capturing is accomplished without employing any filters or limiters, which attests to the stability of the enhanced SDLBM