A numerical model has been proposed to solve fluid flows with complex free surfaces in two and three space dimensions. The unknowns are the volume fraction of liquid in the whole cavity containing the fluid, the velocity and pressure in the liquid. A splitting algorithm is used to decouple advection phenomena to diffusion phenomena. Advection is solved using the forward characteristics method on a fine grid of rectangular cells. Diffusion is solved using simple finite elements on a tetrahedral mesh of the cavity.

The model has been successfully applied to mould filling situations. It can be modified in order to take into account the case when bubbles of gas are trapped into the liquid. The model has also been successfully extended to viscoelastic flows in complex domains. Complex experiments such as the stretching of a filament or jet buckling have been reproduced.

Mathematical and numerical analysis of simplified models have been performed.

Below is an example of non-Newtonian flows simulation with different physical properties.

Below is an example of S-shape cavitiy filling with bubble creation.

### Recent Publications

**A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows**;

*Computers & Fluids*. 2018-08-30. DOI : 10.1016/j.compfluid.2018.04.002.

**The Gaia-ESO Survey: dynamics of ionized and neutral gas in the Lagoon nebula (M 8)**;

*Astronomy & Astrophysics*. 2017. DOI : 10.1051/0004-6361/201730986.

**Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications**. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7950.

**From the free surface flow of a viscoelastic fluid towards the elastic deformation of a solid**;

*Comptes Rendus Mathematique*. 2016. DOI : 10.1016/j.crma.2016.02.001.

**An octree-based adaptive semi-Lagrangian free surface flow solver**. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7011.

**Applicability of Non-Destructive Examination to Iter TF Joints Nb3Sn**;

*IEEE Transactions on Applied Superconductivity*. 2015. DOI : 10.1109/TASC.2014.2361407.

**Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves**;

*International Journal For Numerical Methods In Fluids*. 2014. DOI : 10.1002/fld.3967.

**Numerical simulation of two-phase flow with interface tracking by adaptive Eulerian grid subdivision**;

*Mathematical And Computer Modelling*. 2012. DOI : 10.1016/j.mcm.2011.08.027.

**Modeling Viscoelastic Flows Using Reflected Stochastic Differential Equations**;

*Communications In Mathematical Sciences*. 2010.

**Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow**;

*Numerische Mathematik*. 2007. DOI : 10.1007/s00211-007-0085-y.

**Mathematical analysis of a simplified Hookean dumbbells model arising from viscoelastic flows**;

*Journal of Evolution Equations*. 2006. DOI : 10.1007/s00028-006-0251-1.

**Numerical simulation of 3D viscoelastic flows with free surfaces**;

*Journal of Computational Physics*. 2006. DOI : 10.1016/j.jcp.2005.11.013.

**Analysis and numerical simulation of viscoelastic flows**. Lausanne, EPFL, 2006. DOI : 10.5075/epfl-thesis-3490.

**Analysis of a one-dimensional free boundary flow problem**;

*Numerische Mathematik*. 2005. DOI : 10.1007/s00211-005-0619-0.

**Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas**;

*Journal of Computational Physics*. 2005. DOI : 10.1016/j.jcp.2004.09.009.

**Analysis and numerical simulation of free surface flows**. Lausanne, EPFL, 2004. DOI : 10.5075/epfl-thesis-2893.