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 multi-component 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.
- Fluids Engineering Division
A Full Eulerian Finite Difference Method for Hyperelasic Particles in Fluid Flows
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Sugiyama, K, Ii, S, Takeuchi, S, Takagi, S, & Matsumoto, Y. "A Full Eulerian Finite Difference Method for Hyperelasic Particles in Fluid Flows." Proceedings of the ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D. Hamamatsu, Japan. July 24–29, 2011. pp. 1561-1567. ASME. https://doi.org/10.1115/AJK2011-04001
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