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Center for Data and Simulation Science

Fluid-Structure Interaction Benchmark

CDS members associated with the benchmark: Prof. Dr Axel Klawonn

Stress distributions in walls of in vivo arteries (transmural stresses) are a major factor driving, e.g., arteriosclerosis and arteriogenesis. To compute the stress distributions, fluid-structure interaction (FSI) simulations of blood flow and arterial wall are used. In sufficiently large arteries, the blood is typically modeled using the Navier-Stokes equations, and in the past, the deformation of arterial walls was mostly described using linear elastic material models. However, it turns out that linear material models are not sufficient to obtain realistic deformations and stress distributions over the whole physiological load range of a heartbeat. Instead, sophisticated nonlinear structural models, which have been developed and adapted to experiments, lead to more realistic results.

Therefore, a fluid-structure interaction benchmark, which puts emphasis on the nonlinearity of the arterial wall model, was introduced in

  • Daniel Balzani, Simone Deparis, Simon Fausten, Davide Forti, Alexander Heinlein, Axel Klawonn, Alfio Quarteroni, Oliver Rheinbach, and Jörg Schröder, “Numerical Modeling of Fluid-Structure Interaction in Arteries with Anisotropic Polyconvex Hyperelastic and Anisotropic Viscoelastic Material Models at Finite Strains”, Int. J. Numer. Methods Biomed. Eng (IJNMBE), 2015. Published online December 7, 2015, http://dx.doi.org/10.1002/cnm.2756.

In this paper, anisotropic, polyconvex hyperelastic and viscoelastic arterial wall models are used to simulate aa initialization phase and several heartbeats of fluid-structure interaction in a section of an idealized coronary artery. It includes mesh convergence and parameter sensibility studies, and compares discretizations of different orders. The solver environment used for the simulations combines the FEM software packages LifeV and FEAP, which provide the nonlinear models for the fluid and a nonlinear, polyconvex, anisotropic model for the structure, in a monolithic coupling algorithm.

The benchmark was set up in a joint DFG-SNF project on Fluid-Structure Interaction of Arterial Walls and Blood Flow with the groups of Daniel Balzani, Simone Deparis, Alfio Quarteroni, Oliver Rheinbach, and Jörg Schröder.

The settings of the simulations can be found in the aforementioned publication, and the meshes can be found here.