Hybrid Virtual Element Method For Solving Darcy Flow Problems In Porous Media With Fractures

In this paper,the mixed virtual element method(MVEM)based on polygonal mesh is used to discretize Darcy flow in fractured porous media.The fractures are considered as the interfaces between subdomains and two-dimensional fractures are regarded as one-dimensional interfaces.In this way,the dimension of fractures and the amount of calculation can be reduced.Because of the irregular shape of the fractures in reality,polygonal mesh generation is more convenient.In 2020,Fumagalli firstly applied MVEM to fracture problem [20].The lowest order Raviart-Thomas(RT)virtual element method was used to discretize the problem,but no theoretical analysis was given.They mainly considered applying MVEM to underground flow and other problems,numerical examples show that MVEM can deal with the strong change of permeability matrix robustly.In this paper,we consider the BrezziDouglas-Marini(BDM)virtual element and discuss the discrete problem in detail.The existence and uniqueness of the discrete problem are proved,the optimal convergence order of the error is obtained.In numerical experiments,we use two examples to verify the conclusion.