Discontinuous Galerkin Method for the Coupled Dual-Porosity-Navier-Stokes Model (Communications in Computational Physics, 2025)
In this paper, we extend the weighted discontinuous Galerkin finite element method (WDG) on polygonal grids for solving the dual-porosity-Navier-Stokesmodel. The Navier-Stokes model describes the free flow in conduits, while the dual-porosity model describes the fluid flow in a medium composed of matrix and microfractures. These two models are coupled through four physically meaningful interface conditions. We obtain the existence and local uniqueness of the solution, as wellas the optimal error estimate, under appropriate small data conditions that maintainphysical properties. Through numerical experiments, the advantages of the numericalmethod are verified, such as the optimal convergence rate of the numerical solution todifferent mesh types and numerical schemes, the performance of the classical upwindscheme combined with the Picard iteration method in handling small viscosity problems, the flow around a horizontal production wellbore with open-hole completion,the different application simulation of multistage hydraulic fractured horizontal wellbore with cased hole completion, as well as the simulation of fluid flow characteristicsaround macro-fractures.
Keywords: Dual porosity model; Navier-Stokes equations; Beavers-Joseph-Saffman interface condition; weighted discontinuous Galerkin methods; error estimate.