Attempts to simulate compressible flows with moderate Mach number to relatively high ones using Lattice Boltzmann Method (LBM) have been made by numerous researchers in the recent decade. The stability of the LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. The present study proposes an approach for simulation of inviscid flows by a compressible LB model in order to enhance the robustness using a combination of Essentially NonOscillatory (ENO) scheme and Shock-Detecting Sensor (SDS) procedure. A sensor is introduced with adjustable parameters which is active near the discontinuities and affects less on smooth regions. The validity of the improved model to capture shocks and to resolve contact discontinuity and rarefaction waves in the well-known benchmarks such as, Riemann problem, and shock reflection is investigated. In addition, the problem of supersonic flow in a channel with ramp is simulated using a skewed rectangular grid generated by an algebraic grid generation method. The numerical results are compared with analytical ones and those obtained by solving the original model. The numerical results show that the presented scheme is capable of generating more robust solutions in the simulation of compressible flows and is almost free of oscillations for high Mach numbers. Good agreements are obtained for all problems.
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.
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