In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for nodes whose subdomains contain fractures, and the explicit scheme is used for all others. In this way, it is possible to use a time step that is independent of the diffusion coefficient for fractures. Numerical results demonstrating high accuracy of calculations are presented.

翻译：本文提出了一种采用部分显式时间离散的多尺度方法。该方法针对裂隙介质中的过滤问题，利用部分显式时间格式：对子域包含裂隙的节点采用隐式格式，其余节点则采用显式格式。通过这种方式，时间步长可独立于裂隙的扩散系数进行选择。文中给出了数值计算结果，证明了该方法具有高精度。