A Parametric Kinetic Solver for Simulating Boundary-Dominated Turbulent Flow Phenomena

Abstract

Boundary layer flow plays a very important role in shaping the entire flow feature near and behind obstacles inside fluids. Thus, boundary treatment methods are crucial for a physically consistent fluid simulation, especially when turbulence occurs at a high Reynolds number, in which accurately handling thin boundary layer becomes quite challenging. Traditional Navier-Stokes solvers usually construct multi-resolution body-fitted meshes to achieve high accuracy, often together with near-wall and sub-grid turbulence modeling. However, this could be time-consuming and computationally intensive even with GPU accelerations. An alternative and much faster approach is to switch to a kinetic solver, such as the lattice Boltzmann model, but boundary treatment has to be done in a cut-cell manner, sacrificing accuracy unless grid resolution is much increased. In this paper, we focus on simulating the boundary-dominated turbulent flow phenomena with an efficient kinetic solver. In order to significantly improve the cut-cell-based boundary treatment for higher accuracy without excessively increasing the simulation resolution, we propose a novel parametric boundary treatment model, including a semi-Lagrangian scheme at the wall for non-equilibrium distribution functions, together with a purely link-based near-wall analytical mesoscopic model by analogy with the macroscopic wall modeling approach, which is yet simple to compute. Such a new method is further extended to handle moving boundaries, showing increased accuracy. Comprehensive analyses are conducted, with a variety of simulation results that are both qualitatively and quantitatively validated with experiments and real life scenarios, and compared to existing methods, to indicate superiority of our method. We highlight that our method not only provides a more accurate way for boundary treatment, but also a valuable tool to control boundary layer behaviors. This has not been achieved and demonstrated before in computer graphics, which we believe will be very useful in practical engineering.