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In this article, a coupled Two-relaxation-time Lattice Boltzmann-Volumepenalization (TRT-LBM-VP) method is presented to simulate flows past obstacles.Two relaxation times are used in the collision operator, of which one isrelated to the fluid viscosity and the other one is related to the numericalstability and accuracy. The volume penalization method is introduced into theTRT-LBM by an external forcing term. In the procedure of the TRT-LBM-VP, theprocesses of interpolating velocities on the boundaries points and distributingthe force density to the Eulerian points are unneeded. Performing theTRT-LBM-VP on a certain point, only the variables of this point are needed. Asa consequence, the TRT-LBM-VP can be conducted parallelly. From the comparisonbetween the result of the cylindrical Couette flow solved by the TRT-LBM-VP andthat solved by the Single-relaxation-time LBM-VP (SRT-LBM-VP), the accuracy ofthe TRT-LBM-VP is higher than that of the SRT-LBM-VP. Flows past a singlecircular cylinder, a pair of cylinders in tandem and side-by-side arrangements,two counter-rotating cylinders and a NACA-0012 airfoil are chosen as numericalexperiments to verify the present method further. Good agreements between thepresent results and those in the previous literatures are achieved.

A Coupled Two-relaxation-time Lattice Boltzmann-Volume Penalization method for Flows Past Obstacles