多孔介质三相流中欠压缩激波的结构
Structure of undercompressive shock waves in three-phase flow in porous media
AI总结：
本文研究多孔介质三相流中的欠压缩激波，分别针对单位矩阵和毛细作用矩阵构造激波面，证明其结构相似并揭示毛细作用矩阵对 Riemann 问题解的影响。
摘要：
欠压缩激波是一类满足黏性剖面准则而非 Lax 不等式的特殊间断。这类激波可作为两个或更多守恒律方程组的解出现。本文针对两类扩散矩阵构造了欠压缩激波面。第一类是单位矩阵；第二类是毛细作用矩阵，它与由毛细压力引起的扩散效应的恰当建模相关。我们证明，对于不同扩散矩阵，欠压缩激波面的结构是相似的。我们还展示了毛细作用矩阵的选择如何影响 Riemann 问题的解。
英文摘要：
Undercompressive shocks are a special type of discontinuities that satisfy the viscous profile criterion rather than the Lax inequalities. These shocks can appear as a solution to systems of two or more conservation laws. This paper presents the construction of the undercompressive shock surface for two types of diffusion matrices. The first type is the identity matrix. The second one is the capillarity matrix associated with the proper modeling of the diffusive effects caused by capillary pressure. We show that the structure of the undercompressive surface for the different diffusion matrices is similar. We also show how the choice of the capillarity matrix influences the solutions to the Riemann problem.
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