Decoupled bound-preserving algorithms for compressible Darcy-Brinkman flow with advection-diffusion transport problem in fractured media

Abstract

A coupling of compressible Darcy-Brinkman flow and advection-diffusion transport problem is considered in fractured media. Treating the fracture as hyperplane, we obtain a two-layer reduced coupled model and the whole considered media is divided into low dimensional fracture-interfaces and surrounding high dimensional subdomains. To improve efficiency, two decoupled algorithms are constructed to solve the reduced coupled model. One decoupled algorithm is proposed based on interpolating vectors as inner boundaries and the other is constructed by interpolating scalars as iterative terms. By using both algorithms, the models in each subdomain are solved in parallel. The BDF2 formula and modified upwind scheme are employed to maintain the accuracy. For advection-diffusion model, we develop a novel bound-preserving scheme to keep the concentration within [0,1] combined with finite volume method by the Lagrange multiplier approach. The accuracy and efficiency of the proposed algorithms are verified by numerical experiments including three-dimensional case and benchmark testing.