GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Computer Methods in Applied Mechanics and Engineering
SIAM Journal on Numerical Analysis
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
Journal of Computational Physics
A hybrid method to study flow-induced deformation of three-dimensional capsules
Journal of Computational Physics
A full Eulerian finite difference approach for solving fluid-structure coupling problems
Journal of Computational Physics
Journal of Computational Physics
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In this paper, the dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. To describe the elastic deformation, an evolution equation for the Eulerian Almansi strain tensor is derived. A constitutive equation is thus constructed for an incompressible ''Neo-Hookean'' elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. The displacement field does not appear in this formulation. A monolithic finite element solver which uses Arbitrary Lagrangian-Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed by two non-dimensional parameters: Reynolds number (Re) and Capillary number (Ca, which is defined as the ratio of the viscous force to the elastic force). In the Stokes flow regime and when Ca is small (Ca