van R Raoul Loon

A fluid-structure interaction method with solid-rigid contact for heart valve dynamics

A computational method is proposed for problems where fluid-structure interaction is combined with solid-rigid contact. This combination is particularly important for the dynamics and impact of heart valves. The Navier-Stokes equation in an Eulerian setting is coupled to a Neo-Hookean solid model using a Lagrangian description. A fictitious domain method extended with a local mesh adaptation algorithm provides the required flexibility with respect to the motion and deformation of the valve. In addition, it ensures the solids ability of sustaining pressures present in the fluid. Making use of the fact that the fluid and solid mesh are not required to be connected conformingly, it is shown that the model can be extended with a contact algorithm without introducing meshing complications near the contact surfaces.

Fluid-solid mixtures and electrochemomechanics: the simplicity of Lagrangian mixture theory

Today, the focus of physical scientists is shifting more to biology than ever before. A biological tissue is typically an ionised porous medium saturated with a solution of ions and neutral solutes. Because classical porous media theories do not account for ionisation, the present paper addresses this issue. The characteristic pore size in most biological applications is close to the molecular level and hence below the Debye-Hueckel scale. Not only pressure gradients and concentration gradients, but electrical gradients as well are intimately linked to fluid flow, ion flow and deformation.