Meshfree Generalized Multiscale Method for Parabolic Problem in Multicontinuum Media

This paper presents the Meshfree Generalized Multiscale Finite Element Method (MFGMsFEM) for solving parabolic problems in multicontinuum media. Multicontinuum models are widely used in various fields, such as petroleum engineering, hydrogeology, and biomechanics, to describe fluid flow in fractured porous materials. The proposed approach leverages the advantages of both mesh free methods and the Generalized Multiscale Finite Element Method (GMsFEM), allowing for efficient and accurate numerical modeling. The novelty of this work lies in the development of multiscale basis functions, constructed using both split and coupled strategies. Numerical experiments demonstrate the effectiveness of the method in capturing complex flow dynamics while significantly reducing computational costs compared to traditional fine-grid simulations. The results show that the coupled multiscale basis functions provide higher accuracy in modeling flow interactions within multicontinuum media.