Diffuse bounce back condition for lattice Boltzmann method

Abstract The lattice Boltzmann method has been widely used in curved and moving boundary fluid simulations. Both explicit and implicit treatments are studied to recover proper boundary conditions on Cartesian grids. These methods can describe curved boundaries more accurately and more smoothly than the staircase approximation. However, to improve the order of accuracy and to reduce the fluctuation of force, complicated modifications have been applied to the collision step of lattice Boltzmann equation. In this study, a new boundary scheme based on diffuse geometry is proposed for lattice Boltzmann method. The scheme is derived by directly incorporating the bounce back condition into the weak form of the streaming step of discretized Boltzmann equation. The new method does not change the collision operator. Therefore it can be easily combined with complex collision models. Although diffuse boundary is introduced, this scheme recovers exact bounce back condition at sharp boundary limit, regardless of the shapes and motions of the boundaries. Numerical tests show that the accuracy of this method is first order and depends on several lattice Boltzmann parameters and the boundary thickness. In moving boundary problems, the fluctuation of force can be largely reduced compared to popular sharp boundary conditions because it does not require extrapolation to fulfil the unknown information of the newly generated fluid nodes around the boundaries. In this paper the detailed derivation for the new scheme is explained and the benchmark problems are solved to test its accuracy and the effect of different parameters.