A cell-centered finite volume method for arbitrary grid type

A linear reconstruction method (LRM), based on the least squares law, has been developed for cell-centered finite volume procedure in arbitrary grid type. The resolution and algorithm are independent of grid topology and quality. It does not suffer from a catastrophic loss of accuracy on a poor grid at the smooth region of solution. The shock can be captured in the absence of limiter. These advantages make it be easy in the application to the grid adaptation and multi-grid computations. In the transonic flow calculation, different grid topologies are included. Numerical results demonstrat the capabilities of new procedure for calculation of discontinuousness with different grid topologies. The data obtained are in good agreement with the experiments. The shock wave was obtained sharply, and non-physical vibration was avoided. Ringleb's flow is used to assess the accuracy in the low quality grids. Compared with the former reconstruction methods, the linear reconstruction method (LRM) is verified that the error norm is lower and the grid convergence is better. This character is further validated by calculation of viscous flow around tri-element airfoil. Relatively, the linear reconstruction method (LRM) obtained better data near the suction peaks.