A mesh‐free radial basis function–based semi‐Lagrangian lattice Boltzmann method for incompressible flows. (23rd June 2019) - Lin, Xingjian; Wu, Jie; Zhang, Tongwei
Summary: In this paper, a local radial basis function–based semi‐Lagrangian lattice Boltzmann method (RBF‐SL‐LBM) is proposed. This is a mesh‐free method that can be used for the simulation of incompressible flows. In this method, the collision step is performed locally, which is the same as in the standard LBM. In the meanwhile, the steaming step is solved in a semi‐Lagrangian framework. The distribution functions at the departure points, which may be not the grid points in general, are computed by the local radial basis function interpolation. Several numerical tests are conducted to validate the present method, including the lid‐driven cavity flow, the steady and unsteady flow past a circular cylinder, and the flow past an NACA0012 airfoil. The present results are in good agreement with those published in the previous literature, which demonstrates the capability of RBF‐SL‐LBM for the simulation of incompressible flows. Abstract : A variant of the lattice Boltzmann method is proposed in this paper. In this method, the collision step is performed locally, and the steaming step is solved in a semi‐Lagrangian framework. The distribution functions at the departure points are computed by the local RBF interpolation. This method is a mesh‐free method, and its capability for the simulation of incompressible flows has been validated by several numerical tests.