ECOGEN is a receptacle of a story of diffuse-interface-method (DIM) theory that started in the late 90s. DIM summarizes more than 20 years of researches on multiphase flow1 modelling with the goal to develop mathematical models as well as their associated numerical methods.

What is a diffuse interface? In DIM theory, the interfaces between pure phases are captured as diffuse numerical regions, meaning that one goes continuously from one phase to another.

diffuse interface
1D extraction of the diffuse-interface region of a water droplet.

This way is possible thanks to a thermodynamics consistency. Then, the flow solution does no longer requires interface tracking algorithms: It becomes easy to simulate complex topological-shape evolutions between miscible or non-miscible fluids. Moreover, pressure waves (shock waves, acoustic waves) can propagate and interact properly in the whole flow.

The base research on DIM is now matured enough to propose ECOGEN, a numerical tool that can be largely cast and use to solve industrial as well as research multiphase flow problems. Hereafter are presented some recent applications involving different physical effects.

Physics of Shock

Shock waves can propagate in matter whatever its physical state: Gaseous, liquid or even solid. They can travel through interfaces or into a multiphase mixture of materials. Because ECOGEN is devoted to compressible, hyperbolic systems of equations, shock dynamics is included whatever the problem is.


The ability to treat cavitation problems is definitely one of the major assets of the diffuse-interface formulation. Now, thanks to consistent thermodynamics consideration, it is possible to intrinsically simulate interface appearance / disappearance between a liquid and its vapor without any specific algorithm for interface tracking.

Droplet fragmentation

The simulation of droplet fragmentation is of prime interest considering various industrial applications as well as for academic knowledge. The deformation of the droplet is a competition between surface tension and inertial forces (measured by the Weber number) that can lead to the creation of smaller droplets. Surface tension then determines the resulting droplet sizes.

1: The multiphase flows can involve pure phases but also mixture of phases.