A High-order Compact Difference Method On Non-uniform Grids And Its Applications In The Numerical Simulation Of Flow And Sediment Transportation

In this study, a high-order compact finite difference method on non-uniform grid is developed and applied for numerically simulation of flow and sediment transport in some parts of the Yellow River.Finite difference method is the most common and most widely used numerical way of discreting and solving fluid dynamical equation. Because of its advantages of using less grid points to construct high accuracy schemes, high-order compact finite difference method has been welcomed by scholars increasingly. Most of high-accuracy compact finite difference schemes for convection-diffusion equations are now proposed on uniform grid,the results will be greatly affected for the problem with great gradients and boundary layers.Therefore, a new high-order compact finite difference scheme on non-uniform grid by the existing method is proposed and is applied to simulate the flow and sediment transport of Shapotou and Daliushu Reaches in the Yellow River. This paper mainly includes the following contents:The first part, a high-order compact difference scheme based on non-uniform grid is constructed for one dimensional unsteady convection-diffusion equation. In the scheme,Taylor's formula is used to discretize the space region and a three point formula is used to discretize the time length. The accuracy and reliability of present scheme is demonstrated by numerical examples.The second part, based on the high-accuracy compact finite difference scheme for one dimensional convection-diffusion equation, a new high-order compact finite difference scheme on non-uniform grid is deduced for two dimensional unsteady convection-diffusion equation. The accuracy and reliability of the scheme is demonstrated by numerical examples.The third part, Numerical simulations are conducted for the flow and sediment transport in Shapotou and Daliushu Reaches in the Yellow River by the new high-accuracy compact finite difference method, and comparison between the numerical results and measured data indicates the validity of the method.