渗流耦合系统动边值问题特征差分方法及其应用

Characteristic Finite Difference Method and Application for Moving Boundary Value Problem of the Coupled System

油气运移、聚集史软件的功能是重建盆地发育中油气资源运移、聚集的历史,它对合理评估油气资源的勘探和开发有重要的价值.其数学模型是一组多层对流扩散耦合系统的动边值问题.提出一类特征差分格式,得到最佳阶误差估计结果.对这一领域的模型分析、数值方法和软件研制均有重要的理论和实用价值.

The coupled system of multilayer dynamics of fluids in porous media is to describe the history of off-gas transport and aceumulation in basin evolution. It is of great value in rational evaluation of prospeething and exploiting off-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. A kind of characteristic finite difference schemes was put forward, from which optimal order estimates in norm was derived for the error in the approximate soluaons. The research is important both theoretically and practically for the model analysis in the field, for model numerical method and for software development.