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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

袁益让   

  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

袁益让. 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[J]. 系统科学与数学, 2009, 29(7): 947-961.

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
石油科学在有机地球化学、石油的生成、运移、聚集研究取得重大进展,在评价油气资源时,对盆地发育史尤其对流体流动规律和受热变化历史的计算是非常重要的.其数学模型是三维空间非线性偶合偏微分方程组的初边值问题.从实际出发,考虑了流体的压缩性和三维问题大规模科学与工程计算的特征, 提出了一类变网格交替方向特征有限元格式,应用变分形式、算子分裂、广义$L^2$投影、能量方法、负模估计、微分方程先验估计的理论和技巧,得到最佳阶$L^2$误差估计. 此方法已成功应用到油气资源评估数值模拟的生产实践中,成功解决了这一重要问题.
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.
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