| NUMERICAL METHOD FOR THREE-DIMENSIONAL NONLINEAR CONVECTION-DOMINATED PROBLEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA |
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| 作者姓名： | 袎益让 杜宁 王文洽 程爱杰 韩玉笈 |
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| 作者单位： | Institute of Mathematics Shandong University，Jinan 250100，P. R. China，Institute of Mathematics，Shandong University，Jinan 250100，P. R. China，Institute of Mathematics，Shandong University，Jinan 250100，P. R. China，Institute of Mathematics，Shandong University，Jinan 250100，P. R. China，Physical Exploration Institute of Shengli Petroleum Administration，Dongying 257022，Shandong Province，P. R. China |
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| 基金项目： | Project supported by the Major State Basic Research Program of China (No.G1999032803)
the National Tackling Key Problems Program (No.20050200069)
the National Natural Science Foundation of China (Nos.10372052, 10271066)
the Doctoral Foundation of Ministry of Education of China (No.20030422047). |
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| 摘 要： | For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
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| 关 键 词： | 非线性受控对流 流体动力学 有限差分法 数字模拟 |
| 收稿时间： | 2004-10-18 |
| 修稿时间： | 2006-01-18 |
Numerical method for three-dimensional nonlinear convection-dominated problem of dynamics of fluids in porous media |
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| Professor Yi-rang Yuan,Ning Du,Wen-qia Wang,Ai-jie Cheng,Yu-ji Han.NUMERICAL METHOD FOR THREE-DIMENSIONAL NONLINEAR CONVECTION-DOMINATED PROBLEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA[J].Applied Mathematics and Mechanics(English Edition),2006,27(5):683-694. |
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| Authors: | Professor Yi-rang Yuan Ning Du Wen-qia Wang Ai-jie Cheng Yu-ji Han |
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| Institution: | 1. Institute of Mathematics, Shandong University, Jinan 250100, P. R. China
2. Physical Exploration Institute of Shengli Petroleum Administration, Dongying 257022, Shandong Province, P. R. China |
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| Abstract: | For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Fractional steps techniques are needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates are adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects. |
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| Keywords: | nonlinear convection-dominated dynamics of fluids upwind fractional steps finite difference method convergence numerical simulation |
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