A finite difference lattice Boltzmann method (FDLBM) is employed to simulate the compressible inviscid/viscous flows. The robustness of the employed approach is tested for the shock tube or Riemann problem in some distinct cases including strong pressure shock, the stationary contact discontinuity and the weak acoustic wave. The Results are compared with the exact solutions, as well as other classical finite volume CFD techniques (Steger-Warming, Roe and AUSM flux). The validity of the employed LBM approach is studied. This research reveals some of the challenges involved in simulating the compressible flows using FDLBM.

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