A high order least square-based finite difference-finite volume method with lattice Boltzmann flux solver for simulation of incompressible flows on unstructured grids

Abstract

This paper presents a high order least square-based finite difference-finite volume (LSFD-FV) method together with lattice Boltzmann flux solver for accurate simulation of incompressible flows on unstructured grids. Within each control cell, a high order polynomial, which is based on Taylor series expansion, is applied to approximate the solution function. The derivatives in the Taylor series expansion are approximated by the functional values at the centers of neighboring cells using the mesh-free least square-based finite difference (LSFD) method developed by Ding et al. (2004) [36]. In the high order finite volume method, the recently developed lattice Boltzmann flux solver (LBFS) is applied to evaluate the inviscid and viscous fluxes physically and simultaneously at the cell interface by local reconstruction of lattice Boltzmann solution. Compared with traditional k-exact high-order finite volume method, the present method is more accurate and efficient. Various benchmark examples are tested to validate the high-order accuracy, high computational efficiency and flexibility of the proposed method on unstructured grids.