A semi-implicit method for incompressible three-phase flow in porous media

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• 作者：Justin Dong ; Béatrice Rivière
• 关键词：Semi ; implicit ; Discontinuous Galerkin ; High order ; Heterogeneous permeability and porosity
• 刊名：Computational Geosciences
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：20
• 期：6
• 页码：1169-1184
• 全文大小：9,868 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Geotechnical Engineering
  Hydrogeology
  Soil Science and Conservation
  
• 出版者：Springer Netherlands
• ISSN：1573-1499
• 卷排序：20

文摘

In this paper, we present a semi-implicit method for the incompressible three-phase flow equations in two dimensions. In particular, a high-order discontinuous Galerkin spatial discretization is coupled with a backward Euler discretization in time. We consider a pressure-saturation formulation, decouple the pressure and saturation equations, and solve them sequentially while still keeping each equation implicit in its respective unknown. We present several numerical examples on both homogeneous and heterogeneous media, with varying permeability and porosity. Our results demonstrate the robustness of the scheme. In particular, no slope limiters are required and a relatively large time step may be taken.