Pritpal Matharu: The incompressible Navier-Stokes limit from the lattice BGK Boltzmann equation

Abstract:

The lattice Boltzmann method, is a successful and promising numerical scheme for simulating fluid flows. In this talk, we present that a local weak solution to the \(d\)-dimensional incompressible Navier-Stokes equations (\(d \ge 2\)) can be constructed by taking the hydrodynamic limit of a velocity-discretized Boltzmann equation with a simplified BGK collision operator. In the case when the dimension is \(d = 2, 3\), we characterize the combinations of finitely many particle velocities and probabilities that lead to the incompressible Navier-Stokes equations in the hydrodynamic limit. Moreover, we highlight the utilization of numerical computations conducted in 2D to provide information about the rate with which this hydrodynamic limit is achieved when the Knudsen number tends to zero.