AJK2011-04001 A FULL EULERIAN FINITE DIFFERENCE METHOD FOR HYPERELASTIC PARTICLES IN FLUID FLOWS

ABSTRACT A full Eulerian finite difference method has been developed for solving a dynamic interaction problem between Newtonian fluid and hyperelastic material. It facilitates to simulate certain classes of problems, such that an initial and neutral configuration of a multi-component geometry converted from voxel-based data is provided on a fixed Cartesian mesh. A solid volume fraction, which has been widely used for multiphase flow simulations, is applied to describing the multicomponent geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for incompressible hyperelastic materials. The present Eulerian approach is confirmed to well reproduce the material deformation in the lid-driven flow and the particle-particle interaction in the Couette flow computed by means of the finite element method. It is applied to a Poiseuille flow containing biconcave neo-Hookean particles. The deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. INTRODUCTION Numerical simulations of Fluid-Structure Interaction (FSI) problems would make it possible to predict the effect of a medical treatment and help one decide the treatment strategy in clinical practice. In particular, a blood flow simulation is expected to contribute to assisting the surgical planning of a cardiovascular disease and a brain aneurysm. Recently, there are growing expectations for its applications along with a progress in imaging and computational technologies. It is also expected to contribute to the field of life science, such as in the understanding of the very essence of life and the demonstration of pathological mechanisms. It is of great importance to develop numerical techniques suitable for the characteristics of body tissues, which are flexible and complicated in shape, when attempting to rationalize and to generalize the fluidstructure coupled analyses. The expectations include the further understandings of the micro/mesoscopic behavior of the flexibly deformable Red Blood Cells (RBCs) in plasma useful for evaluating the macroscopic blood rheology, and the thrombosis formation as aggregation of platelets, of which th