Local and parallel finite element methods for the mixed Navier–Stokes/Darcy model

Abstract

In this paper, the mixed Navier–Stokes/Darcy problem which describes a fluid flow filtrating through porous media is considered. Based on two-grid discretizations, two local and parallel finite element algorithms for solving this mixed model are proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the local and parallel finite element algorithms.

Keywords:

• Navier–stokes equations
• Darcy's law
• decoupling
• two-grid discretization
• parallel finite element method

2010 AMS Subject Classifications:

• 35M30
• 65N12
• 65N30
• 76D05
• 76S05

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Subsidized by NSFC [grant number 11171269] and the Ph.D. Programs Foundation of Ministry of Education of China [grant number 20110201110027].