Eulerian numerical modelling of fluid-structure interactions: application to the simulation of biological capsules in flow – CapsEulerianFSI

New semi-implicit schemes will be developed to simulate longer physical
times and implemented in the Notus code which is massively parallel and open source. We will therefore demonstrate that intensive
simulation is a powerful tool of understanding and design for such an application.

A first part is devoted to the development in the Notus code of the new Eulerian models of complete membrane elasticity developed by the coordinator. The numerical code was validated on 3D test cases of the relaxation of a prestressed sphere. A second part concerns the development of new semi-implicit schemes for the Eulerian fluid-structure interaction. Two approaches were tested: a semi-implication of the elastic force in the fluid equations and a semi-implication of the velocity in the transport equation. The first results on a simple test case of relaxation with a membrane model «variation of area« gives gains on the time step up to a factor of ten.

These semi-implicit schemes are currently being extended in the context of complete membrane models with shear. The next step will be to parallelize the code and show good scalability on hundreds and then thousands of processors for the linear systems involved in these semi-implicit schemes. The HPC modeling and simulation of capsules will then be based on the numerical code under development.

No publication at this stage of the project

A capsule is composed of a membrane, which is a closed surface with elastic properties protecting an internal fluid. The capsule size varies between a few millimeters and a few microns. In all the applications, capsules are immersed in an external fluid. They are used in many fields such as cosmetics, bioengineering or medicine. Many pathologies, like cancers and infections, can alter cell size and change their mechanical properties. Sorting cells according to their characteristics opens the way to detect and isolate infected cells. In addition to the financial cost, designing new microfluidic devices for each application is currently time consuming as it requires multiple experiments to find the optimal device. This is precisely the purpose of the present project, its goal is to develop an original HPC numerical tool for fluid-structure interaction to simulate the behavior of capsules in their environments, and to use it to design microfluidic systems dedicated to enrichment and sorting of capsules suspensions. In order to meet this objective, it is proposed to use completely Eulerian models of fluid / structure interaction that take into account the inertia, complex geometries and large deformations of the structure. However, two numerical locks have been identified for our application: increasing physical simulation time for fluid-structure interaction simulations when membrane stiffness is important and taking into account contacts in particle/particle and particle/walls interactions. In order to remove these locks, it is proposed to develop new semi-implicit schemes fully Eulerian and to implement Eulerian models of contacts.The numerical schemes will be implemented in the massively parallel, open-source code Notus developed in the I2M Laboratory of Bordeaux. It is also proposed in the project to enrich the capsule model with an elastic nucleus. This validated numerical tool will allow us to optimize microfluidic devices for enrichment and sorting of diluted or concentrated suspensions.