Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 196-205.
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(Institute of Mathematics, Shandong University, Jinan 250100)
Online:
Published:
Abstract:
The software for oilgas transport and accumulation is to describe the history of oilgas transport accumulation in basin evolution. It is of great value in rational evaluation of prospecting and defines oil deposit location. The mathematical model can be described as a coupled system of nonlinear partial differential equations with initialboundary value problems. This thesis, from actual conditions such as the effects of gravitation, buoyancy, capillary pressure and the three-dimensional characteristic of largescale scienceengineering computation, puts forward a kind of characteristic finite element alternatingdirection schemes, this is, by dividing it into three continuous one-dimensional problems. By making use tensor product algorithm、negative norm estimate and theory of prior estimates. Optimal order estimates in L2 norm are derived for the error in approximate solutions.
Key words: Ｔｈｒｅｅｄｉｍｅｎｓｉｏｎａｌ, Ｔｒａｎｓｐｏｒｔａｃｃｕｍｕｌａｔｉｏｎ, Ｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｓ, Ｃｈａｒａｃｔｅｒｉｓｔｉｃｆｉｎｉｔｅｅｌｅｍｅｎｔｓ, Ａｌｔｅｒｎａｔｉｎｇｄｉｒｅｃｔｉｏｎ, ＯｐｔｉｍａｌｏｒｄｅｒｅｓｔｉｍａｔｅｓｉｎL２
CLC Number:
Yuan Yirang. The alternating birection schemes and numerical analysis for three dimensional transport accumulation (oil and water)[J].Acta mathematica scientia,Series A, 1999, 19(2): 196-205.
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１ ＵｎｇｅｒｅｒＰ．Ｂａｓｉｎｅｖａｌｕａｔｉｏｎｂｙｉｎｔｅｇｒａｔｅｄ２ｄｉｍｅｎｓｉｏｎａｌｍｏｄｅｌｉｎｇｏｆｈｅａｔｔｒａｎｓｆｅｒ，ｆｌｕｉｄｆｌｏｗ，ｈｙｄｒｏｃａｒｂｏｎｇｅｎｅｒａｔｉｏｎａｎｄｍｉｇｒａｔｉｏｎ．ＡＡＰＧＢｕｌｌ，１９９０，７４（３）：３０９－３３５ ２ ＤｏｕｇｌａｓＪＪｒ．Ｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｍｅｔｈｏｄｓｆｏｒｔｗｏｐｈａｓｅｉｎｃｏｍｐｒｅｓｓｉｂｉｃｆｌｏｗｉｎｐｏｒｏｕｓｍｅｄｉａ．ＳＩＡＭ ＪＮｕｍｅｒＡｎａｌ，１９８３，２０（４）：６８１－６９６ ３ 袁益让．三维动边值问题的特征混合元方法和分析．中国科学（Ａ 辑），１９９６，２６（１）：１１－２２ ４ ＤｏｕｇｌａｓＪＪｒ，ＲｕｓｓｅｌｌＴ Ｆ．Ｎｕｍｅｒｉｃａｌｍｅｔｈｏｄｓｆｏｒｃｏｎｖｅｃｔｉｏｎｄｏｍｉｎａｔｅｄｄｉｆｆｕｓｉｏｎｐｒｏｂｌｅｍｓｂａｓｅｄｏｎｃｏｍｂｉｎｉｎｇｔｈｅｍｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓｗｉｔｈｆｉｎｉｔｅｅｌｅｍｅｎｔｏｒｆｉｎｉｔｅｄｉｆｆｅｒｅｎｃｅｐｒｏｃｅｄｕｒｅｓ．ＳＩＡＭＪＮｕｍｅｒＡｎａｌ，１９８２，１９（５）：８７１－ ８８５ ５ ＥｗｉｎｇＲＥ，ＲｕｓｓｅｌｌＴＦ，ＷｈｅｅｌｅｒＭ Ｆ．Ｃｏｎｖｅｒｇｅｎｃｅａｎａｌｙｓｉｓｏｆａｎａｐｐｒｏｘｉｍａｔｉｏｎｏｆｍｉｓｃｉｂｌｅｄｉｓｐｌａｃｅｍｅｎｔｉｎｐｏｒｏｕｓｍｅｄｉａｂｙｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｓａｎｄａｍｏｄｉｆｉｅｄｍｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓ．ＣｏｍｐＭａｔｈＩｎＭｅｃｈａｎｄＥｎｇ，１９８４，４７：７３－９２ ６ ＤｏｕｇｌａｓＪＪｒ，ＹｕａｎＹｉｒａｎｇ．Ｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｏｆｉｍｍｉｓｃｉｂｌｅｆｌｏｗｉｎｐｏｒｏｕｓｍｅｄｉａｂａｓｅｄｏｎｃｏｍｂｉｎｅｄｔｈｅｍｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓｗｉｔｈｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｐｒｏｃｅｄｕｒｅ．ＴｈｅＩＭＡｖｏｌｕｍｅｓＩｎ ＭａｔｈａｎｄＩｔ＇ｓＡｐｐｌｉｃａｔｉｏｎ，１９８６，１１：１１９－ １３１ ７ ＫｒｉｓｈｎａｍａｃｈａｒｉＳＶ，ＨａｙｅｓＬＪ，ＲｕｓｓｅｌｌＴＦ．Ａｆｉｎｉｔｅｅｌｅｍｅｎｔａｌｔｅｒｎａｔｉｎｇｄｉｒｅｃｔｉｏｎｍｅｔｈｏｄｃｏｍｂｉｎｅｄｗｉｔｈａｍｏｄｉｆｉｅｄｍｅｔｈｏｄｏｆｃｈａｒａｃｔｅｒｉｓｔｉｃｓｆｏｒｃｏｎｖｅｃｔｉｏｎｄｉｆｆｕｓｉｏｎｐｒｏｂｌｅｍｓ．ＳＩＡＭＪＮｕｍｅｒＡｎａｌ，１９８９，２６（６）：１４６２－１４７３ ８ ＲａｖｉａｒｔＰＡ，ＴｈｏｍａｓＪＭ．Ａ ｍｉｘｅｄｆｉｎｉｔｅｅｌｅｍｅｎｔｍｅｔｈｏｄｆｏｒ２ｎｄｏｒｄｅｒｅｌｌｉｐｔｉｃｐｒｏｂｌｅｍｓ．Ｉｎ：ＭａｔｈｅｍａｔｉｃａｌＡｓｐｅｃｔｓｏｆｔｈｅＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄ，Ｒｏｍｅ，１９７５．Ｂｅｒｌｉｎ：ＳｐｒｉｎｅｒＶｅｒｌａｇ，１９７７．２９２－３１５ ９ ＦｅｒｎａｎｄｅｓＲＩ，ＦａｉｒｗｅａｔｈｅｒＧ．ＡｎａｌｔｅｒｎａｔｉｎｇｄｉｒｅｃｔｉｏｎＧａｌｅｒｋｉｎｍｅｔｈｏｄｆｏｒａｃｌａｓｓｏｆｓｅｃｏｎｄｏｒｄｅｒｈｙｐｅｒｂｏｌｉｃｅｑｕａｔｉｏｎｓｉｎｔｗｏｓｐａｃｅｖａｒｉａｂｌｅｓ．ＳＩＡＭＪＮｕｍｅｒＡｎａｌ，１９９１，２８（５）：１２６５－１２８１ １０ ＤｅｎｄｙＪＥ，ＦａｉｒｗｅａｔｈｅｒＧ．ＡｌｔｅｒｎａｔｉｎｇＤｉｒｅｃｔｉｏｎＧａｌｅｒｋｉｎｍｅｔｈｏｄｓｆｏｒｐａｒａｂｏｌｉｃａｎｄｈｙｐｅｒｂｏｌｉｃｐｒｏｂｌｅｍｓｏｎｒｅｃｔａｎｇｕｌａｒｐｏｌｙｇｏｎｓ．ＳＩＡＭＪＮｕｍｅｒＡｎａｌ，１９７５，１２（２）：１４４－１６３ １１ ＢｉｅｚｚｉＦ．Ｏｎｔｈｅｅｘｉｓｔｅｎｃｅ，ｕｎｉｑｕｅｎｅｓｓａｎｄａｐｐｒｏｘｉｍａｔｉｏｎｏｆｓａｄｄｌｅｐｏｉｎｔｐｒｏｂｌｅｍｓａｒｉｓｉｎｇｆｒｏｍＬａｇｒａｎｇｉａｎｍｕｌｔｉｐｌｉｅｒｓ．Ｒ ＡＩＲ Ｏ，ＡｎａｌＮｕｍｅｒ，１９７４，９（２）：１２９－１５１ １２ ＷｈｅｅｌｅｒＭ Ｆ．ＡｐｒｉｏｒL2ｅｒｒｏｒｅｓｔｉｍａｔｅｓｆｏｒＧａｌｅｒｋｉｎａｐｐｒｏｘｉｍａｔｉｏｎｓｔｏｐａｒａｂｏｌｉｃｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ．ＳＩＡＭＪＮｕｍｅｒＡｎａｌ，１９７３，１０（４）：７２３－７５９
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