The Upwind Finite Difference Method for Three-dimensional Moving Boundary Value Problem
三维动边值问题的迎风差分方法

The research of the three-dimensional compressible miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For a generic case of three-dimensional bounded region, the authors put forward a kind of upwind finite difference schemes and make use the calculus of variations, the change of variables and the theory of a priori estimates and techniques. Optimal order estimates in l2 norm are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, model numerical method and software development. Thus, the well-known problem is solved.