Differential Quadrature Method for Numerical Solution of the Mesoscopic Variables of LBM in Riemann Problem

Abstract

This study introduces an innovative approach to simulating inviscid flows using a compressible lattice Boltzmann (LB) model. The proposed method combines semi-discrete schemes to form a system of ordinary differential equations (ODEs) with the differential quadrature method (DQM) to enhance robustness. To validate the approach, a benchmark case is employed to solve the mesoscopic variables of the LB model in the context of the Riemann problem. The results demonstrate excellent agreement, showcasing the effectiveness of the method.