A High-accuracy Compact Scheme And Its Applications In The Numerical Simulation Of Flow And Sediment Transportation

Convection diffusion equation is a kind of equations which can be used to describe many physical phenomena,such as river pollution,air pollution,pollutant concentration,fluid flow and heat transfer.There are a lot of methods solving these equations,such as finite element method,finite difference method,finite volume method,etc.Which finite difference method is the most common used numerical ways of solving ones.Because of its advantages of using less grid points to construct highaccuracy schemes easily.In this paper,based on this,the corresponding difference scheme is constructed on uniform grid and non-uniform grid.And the applicability and accuracy of present scheme is demonstrated,especially,there are certain advantages can be showed for the problem with great gradients and boundary layers.The problems of convection diffusion equation,in this paper,first of all,can be analyzed,based on the simple introduction of the constructed high accuracy compact difference scheme,after introducing the grid subdivision function,the corresponding difference scheme is constructed on uniform grid and non-uniform grid.And the applicability and accuracy of present scheme is demonstrated.Secondly,the high accuracy compact method is reconstructed based on the Pade' approximation and Richardson extrapolation method,therefore,not only will get high accuracy and handle the boundary conditions easily,stability and precision of the calculation results are guaranteed,but also save computation.Finally,will the constructed high accuracy compact difference scheme applied to the numerical simulation of flow and sediment transport.In order to make numerical simulation easily,in this paper,only choose descending section of Ningxia Daliushu reachs in the Yellow River in recent years,analyzed and compared with the measured values,and measured the practicability and accuracy of the validation method.