Modified upwind finite volume scheme with second-order Lagrange multiplier method for dimensionally reduced transport model in intersecting fractured porous media

Abstract

In this paper, a dimensionally reduced model is introduced to express the solute transport in the porous media containing with intersecting fractures, in which the fractures are treated as dimensionally reduced manifolds with respect to the dimensions of surrounding media. The transmission conditions can be used to describe the physical behavior of concentration and flux. We construct a hybrid-dimensional finite volume method involving BDF2 time discretization and modified upwind scheme for advection-dominated diffusion model. Fully space-time second-order convergence rate is deduced on the staggered nonuniform grids based on the error estimates of coupling terms. The numerical tests are presented to show that the proposed finite volume method can handle reduced model in porous media with multiple L-shaped, crossing and bifurcated fractures efficiently and flexibly. In addition, the Lagrange multiplier approach is developed to construct bound preserving schemes for dimensionally reduced advection-dominated diffusion model in intersecting fractured porous media.