A More Robust Compressible Lattice Boltzmann Model by using the Numerical Filters

The stability of the lattice Boltzmann model (LBM) is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. This study, proposes a complementary scheme for simulation of inviscid compressible flows by the lattice Boltzmann models using the numerical filters to improve the stability. The advantages and disadvantages of the implementation of numerical filters on the primitive and conservative variables, in addition to, mesoscopic and macroscopic variables are investigated. Moreover, a shock-detecting sensor, which activates a second-order linear filter near the discontinuities and a higher-order linear filter in smooth regions, is described and assessed. This study demonstrates that the proposed complementary scheme is practical. Also the accuracy and robustness of the utilized LB models are improved for inviscid compressible flows by implementation of the numerical filters on primitive variables. The validity of the procedure to capture shocks and to resolve contact discontinuity and rarefaction waves in well-known benchmarks is investigated and good agreements are obtained for all test cases.