Flow of a non-Newtonian fluid on an inclined plane (CROCO computation)
These animations represent the flow of fluids to threshold under the action of their own weight. Areas where shear in non-zero are shaded in gray, and areas where the fluid behaves as a solid are shown in white.
This calculation combines the processing of convective terms by the method of characteristics with a discretization of the diffusive terms by the finite element method.
For further information :
- Vola D., Boscardin L., Latché J.C. (2003). Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results. Journal of Computational Physics, 187, 2003
- Latché J.-C., Vola D. (2004) Analysis of the Brezzi-Pitkaranta stabilized Galerkin scheme for creeping flows of Bingham fluids. SIAM Journal of Numerical Analysis, 42, 3, 1208-1225
- Vola D., Babik F., Latché J.-C. (2004) On a numerical strategy to compute gravity currents of non-Newtonian fluids, Journal of Computational Physics, 201, 397-420
Bubble crossing a liquid/liquid interface 
This figure represents a snapshot of a bubble crossing a liquid/liquid interface. The blue area is occupied by the denser fluid, the green area is occupied by the less dense fluid, and the red area is occupied by the gas.
The flow is modeled by a diffuse interface approach (Cahn-Hilliard model). Discretization in space is performed by a finite element method using dynamic local refinement techniques to create a finer mesh in the neighborhood of the interfaces (CHARMS method).
For further information :
• Boyer F., Lapuerta C. (2006) Study of a Three Component Cahn-Hilliard Flow Model Mathematical Modeling and Numerical Analysis, 40, 2, 653-687
Dam-break flow
A fluid is initially confined by an impermeable wall. When the wall is removed, it flows out under the effect of its own weight on a substrate peppered with obstacles. The flow is governed by the Saint-Venant equations. The discretization of the diffusion terms is performed by a linear finite element method, while the convection terms are processed by finite volumes, with control cells centered on the nodes of the mesh, and the flows are obtained by solving elementary Riemann problems.
