Incorporation of subscale processes into enhanced constitutive relationships on the meso- and macroscale

在SPIII中，我们打算分析宏观尺度的非均匀性对两相流过程的影响，基于模拟和分析实验室实验，和模拟的两相流过程中人工生成的结构。重点是量化宏观动态效应和滞后过程。相应地，数值求解的守恒方程将得到推广，即. G.结合MUFTE-UG的滞后模块和动态毛细管压力饱和关系。在第二种方法中，我们计划将随机放大方法应用于由动态毛细管压力-饱和度关系扩展的理查兹方程。

Within SPIII we intend to analyse the influence of macroscale heterogeneities on two-phase flow processes based on simulations and analysis of laboratory experiments, and simulations of two-phase flow processes in artificially generated structures. Emphasis is put on quantifying macroscale dynamikc effects and hysteresis processes. Accordingly, the numerically solved conservation equations will be extended, e. g. combining the hysteresis module of MUFTE-UG with a dynamic capillary pressuresaturation relationship. In a second approach we plan to apply a stochastic upscaling method to the RICHARDS equation extended by the dynamic capillary pressure-saturation relationship.