Abstract
This paper presents a new stabilized finite element method for the Darcy-Stokes equations also known as the Brinkman model of lubrication theory. These equations also govern the flow of incompressible viscous fluids through permeable media. The proposed method arises from a decomposition of the velocity field into coarse/resolved scales and fine/ unresolved scales. Modelling of the unresolved scales corrects the lack of stability of the standard Galerkin formulation for the Darcy-Stokes equations. A significant feature of the present method is that the structure of the stabilization tensor τ appears naturally via the solution of the fine-scale problem. The issue of arbitrary combinations of pressure-velocity interpolation functions is addressed, and equal-order combinations of C° interpolations are shown to be stable and convergent.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 665-681 |
| Number of pages | 17 |
| Journal | International Journal for Numerical Methods in Fluids |
| Volume | 54 |
| Issue number | 6-8 |
| DOIs | |
| State | Published - Jul 20 2007 |
Keywords
- Arbitrary pressure-velocity interpolations
- Brinkman model
- Multiscale finite elements
- Stabilized methods
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics