带动态毛细管压力的两相流模型有限体积格式的能量耗散与稳定性
Energy dissipation and stability of a finite-volume scheme for two-phase flow models with dynamic capillary pressure
AI总结：
本文针对多孔介质中带动态毛细管压力的非饱和两相流，提出隐式欧拉有限体积格式，证明其离散解的存在唯一性等性质，通过二维实验展示动态毛细管压力的作用。
AI中文摘要：
本文提出并分析了一种用于退化伪抛物型交叉扩散方程的隐式欧拉有限体积格式，该系统描述了多孔介质中具有动态毛细管压力的非饱和两相流混合物的动力学。该数值格式基于两点通量近似，可保持能量结构、确保总质量守恒，并保证水饱和度的严格正性与有界性，这些性质依赖于为非线性分量精心选取的平均函数。文中证明了离散解的存在性、唯一性及额外的网格一致有界性，二维空间的数值实验展示了动态毛细管压力的作用效果。
英文摘要：
An implicit Euler finite-volume scheme for degenerate pseudo-parabolic cross-diffusion equations is proposed and analyzed. The system describes the dynamics of an unsaturated two-phase flow mixture with dynamic capillary pressure in a porous medium. The numerical scheme is based on a two-point flux approximation that preserves the energy structure, ensures the conservation of total mass, and guarantees strict positivity and boundedness of the water saturation. These properties rely on carefully selected mean functions for the nonlinear components. The existence and uniqueness of a discrete solution and additional mesh-uniform bounds are proved. Numerical experiments in two space dimensions illustrate the effects of the dynamic capillary pressure.
