Abstract
This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in both L2 and H1 norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme.
Highlights
Managing the quality of groundwater resources is imperative today with the risks of environmental and industrial contamination
One of the most popular models is the coupled continuum pipeflow/Darcy (CCPF) model in which the conduits embedded in the continuum matrix are simplified into a network of one-dimensional pipes, see [2, 3, 4, 5, 11, 19]
The objective of this paper is to study CCPF model with the inclined pipe cube embedded in the porous media
Summary
Managing the quality of groundwater resources is imperative today with the risks of environmental and industrial contamination. The steady-state coupled continuum pipe-flow/Darcy (CCPF) model in Karst aquifers is given as follows. Liu et al used anisotropic finite element method and coupled finite element method to solve the same model as in [5] based on the horizontal pipe domain in [12] and [13], respectively. The second goal of this paper is to introduce the quasi-Wilson element to approximate the two-dimensional Darcy equation of CCPF model (1.1) and conforming finite element to solve the pipe-flow equation. The existence and uniqueness of the solution are obtained for the coupled approximation scheme based on the quasi-Wilson nonconforming finite element method for Darcy equation with conforming finite element method for pipe-flow equation. The approximation scheme using quasi-Wilson nonconforming element on anisotropic grid combined with conforming finite element method is carried out for the coupled CCPF model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
