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