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 projection, energy method, negative norm estimate, the theory of prior estimates and techniques, optimal order estimates in 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.
YUAN Yirang. , {{custom_author.name_en}}.
The Characteristic Finite Element Alternating-Direction Method with Moving Meshes and Analysis for the Numerical Simulation of Oil-Gas Resources. Journal of Systems Science and Mathematical Sciences, 2009, 29(7): 947-961 https://doi.org/10.12341/jssms08433
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