Research On Plane Two Dimension Water & Sediment Mathematical Model Based On The Theory Of Minimum Rate Of Energy Dissipation

With the rapid development of the computer technology and the incessant consummation of the theory of sediment study, the water&sediment mathematical model is adopted more and more when it comes to the movement law of water&sediment and evolution process in the river. The research domain now has expanded from one-dimension research to two-dimension, even three-dimension research. The water&sediment mathematical model has become an important method when solving the diversified and practical engineering problems due to its characteristics of convenience, high effectiveness and low cost. In this paper, reviewed the research what predecessors have done and a plane two dimension water&sediment mathematical model based on the theory of minimum rate of energy dissipation for fluvial river has been established. The main contents in this paper are as follows :Aiming at the sinuous and irregular boundary in the natural river, the curvilinear grid plane in two dimension is generated adopted the technique of orthogonal body-fitted coordinate transform to adapt the regular calculating region to the irregular physical region.This grid can maintain uprightness near the boundaries, and can control spacing and maintain smoothness.The action of the water turbulence viscous item and sediment diffused item are taken into account to the governing equations in this model. This can simulate circumfluence which is caused by the irregular boundary in the natural river well. And the sedimentation rate of the nonuniform sediment and the sediment cayying capacity are also taken into account to advace the precision of the results. The uncoupling method is used to solve the water&sediment equations. The finite difference method for governing equations of flow in body-fited coordinates is ADI method and the finite difference method is used to disperse the sediment equations and the deformation of river bed equations, and the solution of matrix is evaluated with pursuit method.Then the calculation of the equations is complete.The theory of minimum rate of energy dissipation is introduced into this mathematical model in order to ascertain the movement law of the fluvial width.It overcome the disfigurment that many mathematical models only can calculate hydraulic factor under the fluvial width is invariable.The model is verified by the measured data of the QingTongxia reservoir of Yellow River. The results are satistying and also indicate the mathematical model and method' s reliability and adaptability.