Journal of Computational Physics
A three-dimensional computational method for blood flow in the heart. II. contractile fibers
Journal of Computational Physics
A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Computational investigations in vascular disease
Computers in Physics
A numerical method for solving incompressible viscous flow problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
An adaptive version of the immersed boundary method
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
A fluid-structure interaction method with solid-rigid contact for heart valve dynamics
Journal of Computational Physics
Design principles for bounded higher-order convection schemes - a unified approach
Journal of Computational Physics
An iterative matrix-free method in implicit immersed boundary/continuum methods
Computers and Structures
On computational issues of immersed finite element methods
Journal of Computational Physics
Partitioned block-Gauss-Seidel coupling for dynamic fluid-structure interaction
Computers and Structures
An enhanced Immersed Structural Potential Method for fluid-structure interaction
Journal of Computational Physics
Hi-index | 31.45 |
In this paper, a new fluid-structure interaction immersed computational methodology, based upon the original Immersed Boundary Method (IBM) [1] is outlined with the final aim of modelling cardiovascular phenomena, specifically, heart valve related problems. The principal characteristic of such immersed techniques is the representation of any deformable or rigid body immersed within an incompressible viscous flow field as a momentum forcing source in the Navier-Stokes equations. A number of shortcomings within the immersed formulation still require further investigation and improvement, including the excessive numerical diffusion caused by the interpolation/spreading process, the need to include realistic viscoelastic composite constitutive models describing more accurately the nature of cardiovascular tissues and also the need to capture more effectively stresses developed at the fluid-structure interface. By following the same philosophy as the original IBM, a more sophisticated formulation is derived in this paper, the ''Immersed Structural Potential Method (ISPM)''. The method introduced presents an alternative approach to compute the equivalent fluid-structure interaction forces at the fluid mesh, accounts for a sophisticated viscoelastic fibre-reinforced constitutive model to better describe the mechanics of cardiovascular tissues and utilises a novel time-integration methodology for the computation of the deformation gradient tensor which ensures compliance with the incompressibility constraint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of this new methodology.