In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space approximations. We use a finite-volume method for fine-scale approximation, and the nonlocal multicontinuum (NLMC) method is used to construct an accurate and physically meaningful coarse-scale approximation. The NLMC method is an accurate technique to develop a physically meaningful coarse scale model based on defining the macroscale variables. The multiscale basis functions are constructed in local domains by solving constraint energy minimization problems and projecting the system to the coarse grid. The resulting basis functions have exponential decay properties and lead to the accurate approximation on a coarse grid. We construct a fully Implicit time approximation for semi-discrete systems arising after fine-scale and coarse-scale space approximations. We investigate the stability of the two and three-level schemes for fully Implicit and Implicit-Explicit time approximations schemes for multicontinuum problems in fractured porous media. We show that combining the decoupling technique with multiscale approximation leads to developing an accurate and efficient solver for multicontinuum problems.

翻译：本文提出了一种高效解耦多连续介质问题的方法。为构建解耦格式，我们提出了一般形式的隐式-显式时间逼近，并针对细尺度与粗尺度空间逼近进行了研究。细尺度逼近采用有限体积法，而粗尺度逼近则利用非局部多连续介质（NLMC）方法构建精确且具有物理意义的粗尺度模型。NLMC方法是一种通过定义宏观变量来发展具有物理意义的粗尺度模型的高精度技术。多尺度基函数通过求解约束能量最小化问题并在局部域中构造，同时将系统投影至粗网格。所得基函数具有指数衰减特性，能够在粗网格上实现精确逼近。针对细尺度与粗尺度空间逼近后的半离散系统，我们构建了全隐式时间逼近格式。研究了裂缝性多孔介质中多连续介质问题的全隐式与隐式-显式时间逼近的二层及三层格式的稳定性。研究表明，将解耦技术与多尺度逼近相结合，能够为多连续介质问题开发出精确且高效的求解器。