多维多孔介质中气水流动的有限体积格式收敛性
Convergence of a Finite Volume Scheme for Gas Water Flow in a Multi-Dimensional Porous Media
AI总结：
针对多孔介质中可压缩不混溶气水流动，提出一种有限体积格式，并在二维或三维情形下证明了其收敛性，其中气体密度依赖于全局压力。
摘要：
考虑多孔介质中水-气流动的经典模型。由质量守恒得到的退化耦合方程组通常在油藏模拟中通过有限体积格式近似。这些格式的收敛性质仅对不可压缩流体已知。本章讨论多孔介质中可压缩不混溶流动的有限体积格式的构造和收敛性分析。与不可压缩流体相比，可压缩流体需要更强大的技术。我们给出了在二维或三维多孔介质中收敛的新结果，仅需修改气体密度依赖于全局压力。
英文摘要：
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence properties of these schemes are only known for incompressible fluids. This chapter deals with construction and convergence analysis of a finite volume scheme for compressible and immiscible flow in porous media. In comparison with incompressible fluid, compressible fluids requires more powerful techniques. We present a new result of convergence in a two or three dimensional porous medium and under the only modification that the density of gas depends on global pressure.
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