• Elena Gaburro, Inria Bordeaux, France
• Ilya Peshkov, University of Trento, Italy

The numerical simulation of fluid-structure-interaction problems and the accurate tracking of material interfaces are highly challenging topics of interest in many applications from naval and aerospace engineering to flows of biological fluids.

Numerical methods dealing with this type of problem can be divided into two big families. Namely, i) the sharp interface techniques, mostly based on adaptive geometries (grids) co-moving and co-deforming with the interfaces, and ii) the diffuse interface approaches which instead avoid any complex computational mesh management but rely on the model itself and treat the interface as a diffused zone with a rapid but smooth change of an interface variable (order parameter, mass or volume fraction, etc.).

In this mini-symposium, we will focus on the second family of methods. We will gather together the presentation of recent advances in i) the design of models that ameliorate the dynamics on both sides of the diffuse interface via a single system of partial differential equations, and ii) the corresponding development of new accurate and efficient numerical schemes able to reduce the numerical diffusion at those interfaces.

We will consider both reduced models valid under some simplifying hypothesis (e.g. motion of rigid solid bodies, full mechanical equilibrium, etc.) as well as advanced models with a complex physics inside the diffuse interface (mixture cells, surface tension, phase transition, mass transfer, non-equilibrium, etc.).
Special attention will be devoted to applications involving fluid-structure interaction problems which are usually considered in the sharp interface context.

KEYWORDS:
diffuse-interface methods, interface sharpening, compressible two-phase flow, multi-phase modelling, multimaterial flows, phase transition, surface tension, elasto-plastic solids, non-conservative hyperbolic systems, Finite Volume and Discontinous Galerkin schemes