Efficient high-order radial basis-function-based differential quadrature-finite volume method for incompressible flows on unstructured grids.

Abstract

This paper presents an efficient high-order radial basis-function-based differential quadrature-finite volume method for incompressible flows on unstructured grids. In this method, a high-order polynomial based on the Taylor series expansion is applied within each control cell to approximate the solution. The derivatives in the Taylor series expansion are approximated by the mesh-free radial basis-function-based differential quadrature method. The recently proposed lattice Boltzmann flux solver is applied to simultaneously evaluate the inviscid and viscous fluxes at the cell interface by the local solution of the lattice Boltzmann equation. In the present high-order method, a premultiplied coefficient matrix appears in the time-dependent term, reflecting the implicit nature. The implicit time-marching techniques, i.e., the lower-upper symmetric Gauss-Seidel and the explicit first stage, singly diagonally implicit Runge-Kutta schemes, are incorporated to efficiently solve the resultant ordinary differential equations. Several numerical examples are tested to validate the accuracy, efficiency, and robustness of the present method on unstructured grids. Compared with the k-exact method, the present method enjoys higher accuracy and better computational efficiency.