YUAN Yi-rang, LI Chang-feng, YANG Cheng-shun, HAN Yu-ji. Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values[J]. Applied Mathematics and Mechanics, 2009, 30(11): 1281-1294. doi: 10.3879/j.issn.1000-0887.2009.11.003
Citation: YUAN Yi-rang, LI Chang-feng, YANG Cheng-shun, HAN Yu-ji. Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values[J]. Applied Mathematics and Mechanics, 2009, 30(11): 1281-1294. doi: 10.3879/j.issn.1000-0887.2009.11.003

Upwind Finite Difference Method for Miscible(Oil and Water) Displacement Problem With Moving Boundary Values

doi: 10.3879/j.issn.1000-0887.2009.11.003
  • Received Date: 2009-02-21
  • Rev Recd Date: 2009-09-10
  • Publish Date: 2009-11-15
  • The research of the miscible (oil and water) displacement problem with moving boundary values is of great value to the history of oil-gas transport and accumulation in basin evolution, as well as to the rational evaluation in prospecting and exploiting oil-gas resources. The mathematical model can be described as a coupled system of nonlinear partial differential equations with moving boundary values. For the two-dimensional bounded region, the upwindfinite difference schemes were put forward. Some techniques, such as calculus of variations, change of variables, theory of a priori estimates and techniques were adopted. Optmial orderestmiates are derived for the errors in approximate solutions. The research is important both theoretically and practically for model analysis in the field, for model numerical method and for software development.
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