In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.
Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model
In this paper, we propose and analyze two stabilized mixed finite element methods for the dual‐porosity‐Stokes model, which couples the free flow region and microfracture‐matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea of partitioned time stepping, the four interface conditions, and the mass exchange terms in the dual‐porosity model, the second stabilized mixed finite element method is decoupled in two levels and allows a noniterative splitting of the coupled problem into three subproblems. Due to their superior conservation properties and convenience of the computation of flux, mixed finite element methods have been widely developed for different types of subsurface flow problems in porous media. For the mixed finite element methods developed in this article, no Lagrange multiplier is used, but an interface stabilization term with a penalty parameter is added in the temporal discretization. This stabilization term ensures the numerical stability of both the coupled and decoupled schemes. The stability and the convergence analysis are carried out for both the coupled and decoupled schemes. Three numerical experiments are provided to demonstrate the accuracy, efficiency, and applicability of the proposed methods.
more » « less- Award ID(s):
- 1722647
- PAR ID:
- 10459573
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Volume:
- 120
- Issue:
- 6
- ISSN:
- 0029-5981
- Page Range / eLocation ID:
- p. 803-833
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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