Explicit coupling schemes for incompressible fluid-structure interaction – EXIFSI

We propose to tackle the challenge through two angles of attack that build on two novel explicit coupling paradigms. A major ingredient in the stability of these schemes is that the artificial interface power, generated by the time splitting, can be controlled by the numerical dissipation of the coupling (not the physical dissipation nor the numerical dissipation of the time-marching in each sub-system).

The ground-breaking nature of the explicit coupling schemes developed will be demonstrated in selected problems, involved in the mathematical modeling of blood flows, e.g: blood-vessel interaction, flow-valve interaction and ventricular flows with flow-valve interaction.

Computer based simulations in patient-specific geometries can provide valuable information to physicians in order to enhance therapy planing. Such simulations can also be a major ingredient in the design/optimization of medical devices. Moreover, it is worth noting that there is emerging interest among the bioengineering community in improving clinical diagnosis through model personalization (e.g., solving inverse problems by coupling clinical data and vascular fluid-structure interaction models). This clearly demands further developments of efficient numerical methods for the direct problem, which is precisely the main concern of this project.

The project results will be presented to the communities of applied mathematicians and bio-engineers, through common publications In peer reviewed journals and communications in renowned international conferences. News on the different activities within the project, benchmark information and publications are available in the project web site. The organization of a summer school on unfitted meshes methods is planed.

Incompressible fluid-structure interaction problems, i.e., mathematical models that describe the interaction of a deformable structure with an internal or surrounding incompressible fluid flow, are among the most widespread multi-physics problems. Their numerical simulation is of major interest in practically all the engineering fields, from the aeroelasticity of bridge decks and parachutes, to naval hydrodynamics and the biomechanics of blood and airflow. The separate simulation of either an elastic structure in large displacements or incompressible flow in fixed domains is rather well established. Yet, making both models interact via efficient numerical methods is a permanent challenge in scientific computing and numerical analysis. In fact, besides the increasing complexity of the models (contacting structures, active mechanics, porous media, etc.), there is also an emerging interest in addressing inverse problems (e.g., to improve clinical diagnosis via personalized fluid-structure models) which definitely calls for efficient numerical methods. Nowadays, numerical simulations of these multi-physics systems are obtained at the expense of efficiency. They are much more computationally onerous than solving two independent fluid and structure problems. This indicates that, in terms of efficiency, the coupling scheme does not fully exploits the maturity of the numerical methods for each of the sub-systems, which is a major obstacle. The basic principle of this proposal is that, to guarantee efficiency, the coupling scheme must allow a decoupled time-marching of the fluid and the structure. This is a particularly challenging problem in numerical analysis since fluid incompressibility generally makes standard decoupling schemes unstable. The scientific objective is thus to marry decoupling with stability and accuracy.