Sharp-front problems arising from equations that tend toward a hyperbolic limit occur routinely in modeling transport phenomena in porous medium systems. Numerical methods to approximate hyperbolic conservation equations are mature for finite volume methods. However, irregularly shaped domains make finite element methods (FEMs) an attractive approach for many subsurface problems. For conforming FEM approaches, sharp fronts continue to pose a computational challenge. We build on recent work to develop and evaluate an entropy viscosity approach. Recent theoretical advancements have resulted in the formulation of entropy inequality equations for many porous medium problems, which we use to compute a physically-based entropy production rate for both linear and nonlinear species transport problems. The entropy production rate is in turn used to add dissipation to the approximation of the hyperbolic operator using an entropy-viscosity formulation. We demonstrate how existing, problem-specific theoretical results can be leveraged in a generic and efficient numerical method to create problem-specific dissipation functions.

通常，在对多孔介质系统中的传输现象进行建模时，通常会出现由趋于双曲线极限的方程式引起的尖锐前沿问题。对于有限体积方法，近似双曲守恒方程的数值方法已经成熟。但是，不规则形状的区域使有限元方法（FEM）成为解决许多地下问题的一种有吸引力的方法。对于一致的有限元方法，尖锐的前沿继续构成计算难题。我们以最近的工作为基础，以开发和评估熵粘度方法。最近的理论进步导致了许多多孔介质问题的熵不等式的公式化，我们用它们来计算线性和非线性物种迁移问题的基于物理的熵生产率。熵产生率又用于使用熵-粘度公式将耗散增加到双曲算子的近似值。我们演示了如何在通用且有效的数值方法中利用现有的，特定于问题的理论结果来创建特定于问题的耗散函数。