Simulating anisotropic flows with isotropic lattice models via coordinate and velocity transformation

摘要

We propose a rectangular lattice Boltzmann model for anisotropic flows based on coordinate and velocity transformation. Unlike other existing rectangular models which tuned the lattice Boltzmann algorithm to fit the rectangular or cuboid lattice grids, here we apply the general lattice Boltzmann method to solve the transformed system over regular square lattice grids. The method is tested with simulations of representative anisotropic flows, including flows in narrow straight and wavy channels, the Taylor-Green vortex flow, and the flow through an elliptical particle array. These simulations show that in general our method produces satisfactory results; however, the aspect ratio a(y) is limited to relatively large values (>= 0.5). The effects of a(y) on simulation accuracy and stability have been carefully examined, and a possible remedy to improve these concerns has been proposed. The method and analysis could be useful for future development of more robust and practical anisotropic lattice Boltzmann models for realistic simulations.