Modeling inertial flows with meshless Lattice Boltzmann Method

Abstract: One of the limitations of the Lattice Boltzmann Method in simulating inertial flows is the coupling of the discretization of space to the velocity discretization. It requires an increase of the size of computational lattices in order to increase the Reynolds number at a fixed velocity and viscosity. In this work, we adopt the recently proposed meshless formulation of Lattice Boltzmann Method to the problem of inertial flows. In contrast to the standard algorithm, it allows to decouple space and velocity discretizations. Thus, one can change the conversion factors from lattice to physical units for length, velocity, and body force by scaling the streaming distance. In turn, one increases the Reynolds number without increasing the size of the discretization. We measure the accuracy and efficiency of this approach in the K\'{a}rm\'{a}n vortex street behind a circular obstacle and the flow through a porous sample in Darcy and inertial regime. Additionally, we apply the meshless streaming step to the recently proposed fixed relaxation time $\tau=1$ LBM to extend its applicability to model inertial flows.