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首页> 外文期刊>Computers & mathematics with applications >Solving a model for 1-D, three-phase flow vertical equilibrium processes in a homogeneous porous medium by means of a Weighted Essentially Non Oscillatory numerical scheme
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Solving a model for 1-D, three-phase flow vertical equilibrium processes in a homogeneous porous medium by means of a Weighted Essentially Non Oscillatory numerical scheme

机译：用加权基本非振荡数值格式求解均匀多孔介质中一维，三相流垂直平衡过程的模型

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摘要

Mathematical models of multi-phase flow are useful in some engineering applications like enhanced oil recovery, filtration of pollutants into subsurface, etc. In this work, we derive a mathematical model for the motion of one-dimensional three-phase flow in a porous medium under the condition of vertical equilibrium, which can be viewed as an extension of some two-phase flow models described in the literature. Our model involves a system of two partial differential equations in the form of viscous conservation laws, whose solutions may contain very sharp transitions. We show that a high-order/high resolution Weighted Essentially Non Oscillatory scheme is an appropriate tool to discretize the buoyancy flux and obtain a well resolved representation of the solution of the model. In addition, we show that the efficiency of the scheme may be improved by using Implicit-Explicit (IMEX) strategies, where the parabolic terms are handled by an implicit discretization.
机译：多相流的数学模型在某些工程应用中很有用，例如提高采油率，将污染物过滤到地下等。在这项工作中，我们导出了多孔介质中一维三相流运动的数学模型。在垂直平衡条件下，可以看作是文献中描述的某些两相流模型的扩展。我们的模型涉及一个由粘性守恒定律形式的两个偏微分方程组成的系统，其解可能包含非常尖锐的跃迁。我们表明，高阶/高分辨率加权基本非振荡方案是离散浮力通量并获得模型求解的良好解析表示的合适工具。此外，我们表明，通过使用隐式-显式（IMEX）策略可以提高该方案的效率，其中抛物线项由隐式离散化处理。

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