• 论文 •

### 油气资源数值模拟的变网格交替方向特征有限元格式和分析

1. 山东大学数学研究所, 济南 250100
• 收稿日期:2007-11-19 修回日期:1900-01-01 出版日期:2009-07-25 发布日期:2009-07-25

YUAN Yirang. The Characteristic Finite Element Alternating-Direction Method with Moving Meshes and Analysis for the Numerical Simulation of Oil-Gas Resources[J]. Journal of Systems Science and Mathematical Sciences, 2009, 29(7): 947-961.

### The Characteristic Finite Element Alternating-Direction Method with Moving Meshes and Analysis for the Numerical Simulation of Oil-Gas Resources

YUAN Yirang

1. Institute of Mathematics, Shandong University, Jinan 250100
• Received:2007-11-19 Revised:1900-01-01 Online:2009-07-25 Published:2009-07-25

Petroleum science has made remarkable progress in organic geochemistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differential equations with initial-boundary value problems. In this paper, from actual conditions such as the effect of fluid
compressibility and the three-dimensional characteristic of large-scale
science-engineering computation, a characteristic finite element alternating-direction method with moving meshes is proposed. By using calculus of variations, operator-splitting, generalized $L^{2}$ projection, energy method, negative norm estimate, the theory of prior estimates and techniques, optimal order estimates in $L^{2}$ norm are derived to determine the error in the approximate solution. This method has been successfully applied to the numerical simulation of oil-gas resources evaluation.

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 [1] 张志跃. 三维热传导型半导体问题的交替方向特征有限元方法[J]. 系统科学与数学, 2002, 22(4): 395-405.