多孔介质中不可压缩不混溶多相流的变分方法
Incompressible immiscible multiphase flows in porous media: a variational approach
摘要：
我们将多孔介质中（N + 1）个不可压缩不混溶相的竞争运动描述为奇异能量在非负测度空间中的梯度流，该空间具有给定的质量和张量Wasserstein距离.我们证明了由极小化方案得到的近似的收敛性。约旦湾Kinder-lehrer \& F. Otto，SIAM J. Math. Anal，29（1）：1--17，1998]。这允许获得一个新的存在结果的物理上建立良好的系统的PDE组成的Darcy-Muskat定律为每个阶段，N毛细管压力关系，并由流体所占据的体积的约束。我们的研究不需要引入任何全球性或补充性压力。
英文摘要：
We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization schemè a la [R. Jordan, D. Kinder-lehrer \& F. Otto, SIAM J. Math. Anal, 29(1):1--17, 1998]. This allow to obtain a new existence result for a physically well-established system of PDEs consisting in the Darcy-Muskat law for each phase, N capillary pressure relations, and a constraint on the volume occupied by the fluid. Our study does not require the introduction of any global or complementary pressure.
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