论文标题
多孔元异质流的随机均质
Stochastic homogenization of multicontinuum heterogeneous flows
论文作者
论文摘要
我们考虑了多孔媒体应用中的多通用模型，该模型被描述为耦合流程方程的系统。不同的连续图之间的耦合取决于许多因素，其建模对于多孔媒体应用很重要。系数取决于粒子沉积，该粒子沉积在SDE的随机过程解中描述。随机过程被认为比流动运动快，我们引入了时空尺度以建模问题。我们的目标是传递时间和空间的极限，并找到相关的平均系统。这是一个平均启发性问题，其中平均是根据与快速运动和空间变量相关的不变度度量计算的。我们使用上一篇论文中开发的技术来对Continua之间的相互作用进行建模，并得出可以在许多应用程序中使用的平均模型问题。
We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media applications. The coefficients depend on particle deposition that is described in term of a stochastic process solution of an SDE. The stochastic process is considered to be faster than the flow motion and we introduce time-space scales to model the problem. Our goal is to pass to the limit in time and space and to find an associated averaged system. This is an averaging-homogenization problem, where the averages are computed in terms of the invariant measure associated to the fast motion and the spatial variable. We use the techniques developed in our previous paper to model the interactions between the continua and derive the averaged model problem that can be used in many applications.
