Novel LBM scheme for Euler equations

Abstract

Lattice Boltzmann Method (LBM) as a relatively new numerical method has recently achieved considerable success in simulating compressible fluid flows. A hybrid method, which is a combination of the usual Finite Volume Method (FVM) and the LBM, is proposed here to solve the Euler Equations. The inter-cell parameters are obtained by solving the local Riemann problem for each inter-cell using LBM. LBM is a non-iterative process and is thus numerically inexpensive as compared to the Godunov scheme. The proposed scheme is benchmarked for several 1-D problems such as the shock tube problem, the Roe test and the Riemann problem. The results obtained using this hybrid method are compared with those obtained using the Godunov scheme.