Solving complex flows with BGK equation and the Discrete Velocity Method (DVM), may require a large number of velocity grid points and hence the resolution becomes very slow. However, locally, in each space cell, the distribution function is supported only on a sub-set of the velocity grid and is zero elsewhere. Thus, solving the equation for such velocities is useless. A local adaptive velocity grid approach is proposed and compared to a "global velocity grid" BGK solution. Simulations in 1D and 2D are presented for different Knudsen numbers showing the computational gain of the proposed approach.
A Local Velocity Grid Approach for BGK Equation