Research And Application Of Water Environment Mathematical Model In Forward Modeling And Inversion Numerical Method

Water is the source of the life, water is indispensable in the social development and progress of mankind, it is also the most active factor and influence widely in ecological environment system. Water resource requirement is increasing constantly with the development of economy. The imbalance between supply and demand is conspicuous day by day. The phenomenon, such as water wastes, the shortage of water, source of water are exhausted, water pollution and so on are increasing quickly. It has already influenced human's life and social development. So, water environment protection which is researching by all the countries has already become one of the most important problem in the world.Water environmental mathematical model includes groundwater model, surface water model and non-point model. When the water environmental mathematical model was built, it should reflect the changing rule (including physics and chemistry) of pollutant in the medium environmental, and also should make a plan of preventing the pollution. So, setting up the water environment mathematical model is one of the science research contents in water environment.The inversion question is about to the forward question in environment model. The forward question is trying to solve questions and determining the quality feature of the process evolution when equation type was given, such as equation coefficient, primary function, initial condition and boundary condition. The same feature of forward question is solving "results" which is according to "reasons" and "conditions".The forward problem of differential equation is usually to seek a solution that meet known equation, initial condition and boundary condition (maybe not initial condition and not boundary condition in some problems). If in the forward problem of differential equation, a variable or some variable in original known quantity change into unknown quality, but original unknown quantity, now or known, or some information that is related to the quantity is known (the new known conditions call auxiliary condition) .At this time, the problem settles the unknown quantity, by means of known equation, boundary condition (maybe include initial condition and boundary condition) and auxiliary condition, that is called inversion problem. In theory, inversion problem's main difficulty lies in its high nonlinear and ill-posed quantity. The research aim of inversion problem is to find math method and implemental plan that can appropriately settle two problems. With modern science and technology rapid developments, today, the nonlinear science has already become front line's task of natural science and technology development .It researches nonlinear complex phenomenon in different domain and different system of the natural science, and reveals all kinds of nonlinear phenomenon's common quality. From 1960s, people began to research thoroughly nonlinear science's relevant task, so far has already gain great development. Similarly, ill-posed problem in the indirect problem's seek solution domain is extensive existence too. Ill-posed problem is put forward by Hadamard , who is a mathematician in France. It is aimed at partial differential equation's fixed solution problem. Tikhohov puts forward famous regularization theory toward ill-posed problem, through leas steady function, restrains effectively error in seek solution of indirect problem process, so makes the problem of seek solution stabilize. The focal point of indirect problem research is not to seek exact solution, but a generalized solution.In fact, water environment model and parameter is non-linearity and discomfort, and it has more than one solution. When we use the tradition method, we may not get the best solution. The tradition method has many limitations and problems in inversion parameter question. The modern optimizationalcalculation method is a global and concurrent method, include neural network method, genetic algorithm, analogue annealing method and homotopy parameter inversion method and so on. The method is widely used in the problem of water environment parameter model. It provide a new method for the indirect problem of environment model.The paper is based on the investigation and analysis of the forward and inversion method about environmental math model. It makes a general definition and application about the model indication. It also makes o deep analysis about the difficulty of the indirect problem, gives a summary about various method of it, and then compares the character and limitation of different methods. Now the direction of the method is given as follow:(l)Make water environmental model by the use of numerical method such as—finite difference method, finite element method, finite volume forward method, and then compare the three methods by an example. Finite volume forward method is the best one to dope out partial differential equation This method has a high definition and ingenuity.(2)Make one dimension perpendicular BOD—DO—temperature couple model and make a reveal of the regularity of the oxygen ,re-oxygenation consumption ratio and the thickness of BOD—DO at different temperatures.(3)By the study of the country point foundation analysis develop program(Gl 999045705) ((The formation of Miyu reservoir and it's upriver water environmental pollution's mechanism and deport and it's effect)) ,make a math model of the total phosphorus 3D—inversion and migration, gain a numerical answer ,draw a contour chart to prevent the pollution of the reservoir ,according to the above to choice the best program.(4) There have been expounded the couple theory of boundary element and finite element in the article. And this method researched now can exert the advantages both of boundary element and finite element and it can be more efficient in reducing the dimension of final coefficient matrix, increasing the precision of calculation and authentic degree of numerical modeling.