Two-phase flow benchmarks
The benchmarks in this section validate the fully coupled response of saturated porous media in numgeo. The porous material consists of a deformable solid skeleton and pore water. Depending on the selected element family, the primary variables are the solid displacement \(\boldsymbol{u}\), pore-water pressure \(p^w\), and/or water displacement \(\boldsymbol{U}\).
| Formulation | Primary variables | Typical application |
|---|---|---|
| \(u\)–\(p\) | solid displacement and pore-water pressure | consolidation and quasi-static coupled flow |
| \(u\)–\(U\) | solid and water displacement | dynamic problems in which relative fluid acceleration is important |
| \(u\)–\(p\)–\(U\) | solid displacement, pore-water pressure, and water displacement | mixed dynamic formulation retaining relative fluid acceleration |
The element labels encode the interpolation. For example, u8p4-sat uses eight nodes for solid displacement and four nodes for pore-water pressure, whereas u8p4u8-sat additionally uses eight nodes for water displacement. The suffix -sat denotes a fully saturated formulation and -red denotes reduced integration.
The following benchmarks are provided:
- Terzaghi one-dimensional consolidation: dissipation of an initially uniform excess pore-water pressure and comparison with the analytical consolidation solution.
- One-dimensional compression-wave propagation: dynamic response to a Heaviside surface load and assessment of the influence of relative fluid acceleration.
For complete element definitions, degrees of freedom, integration schemes, and recommendations, see the reference pages for \(u\)–\(p\) elements, \(u\)–\(U\) elements, and \(u\)–\(p\)–\(U\) elements.