Immersed boundary-lattice Boltzmann method based on quadtree grids

An immersed boundary-lattice Boltzmann method based on non-uniform quadtree grids is proposed in present paper. In order to retain continuous physical quantity, equal interval interpolation in temporal and spatial space is used on the different grid interface. Because quadtree grids have identical spatial size in the same grid level and identical temporal size in the neighbor temporal level, equal interval interpolation retains second-order accuracy in temporal and spatial space, has simple computational process, need less resource, and achieves utilization of arbitrary boundary refined grids in the lattice Boltzmann method. To take advantage of the merit of the Cartesian grid, the velocity correction method is adopted in immersed boundary, which ensures the non-slip boundary compared to the direct forcing method or the momentum exchange method in the conventional immersed boundary-lattice Boltzmann method. At the same time, the large-eddy simulation model is applied to immersed boundary-lattice Boltzmann method. In this paper, the proposed model combines with quardtree grids data structure, boundary treatment with large eddy simulation to simulate the flows with high Reynolds number around the obstacle. To validate these models, the incompressible flows around a circular cylinder with Re=200, 1000, 3900 are simulated, and the simulation results agree well with those of other methods.