Sharif Digital Repository

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... 

A new shock-detecting sensor for properly switching between a second-order and a higher-order filter is developed and assessed. The sensor is designed based on an order analysis. The nonlinear filter with the proposed sensor ensures damping of the high-frequency waves in smooth regions and at the same time removes the Gibbs oscillations around the discontinuities when using high-order compact finite difference schemes. In addition, a suitable scaling is proposed to have dissipation proportional to the shock strength and also to minimize the effects of the second-order filter on the very small scales. Several numerical experiments are carried out and the accuracy of the nonlinear filter with...