• Corpus ID: 239016900

A reduced unified continuum formulation for vascular fluid-structure interaction

  title={A reduced unified continuum formulation for vascular fluid-structure interaction},
  author={Ingrid S. Lan and Ju Liu and Weiguang Yang and Alison L. Marsden Stanford University and Stanford and Usa and Southern University of Science and Technology and Shenzhen and People's Republic of China},
We recently derived the unified continuum and variational multiscale formulation for fluid-structure interaction (FSI) using the Gibbs free energy as the thermodynamic potential. Restricting our attention to vascular FSI, we now reduce this formulation in arbitrary Lagrangian-Eulerian (ALE) coordinates by adopting three common modeling assumptions for the vascular wall. The resulting semi-discrete formulation, referred to as the reduced unified continuum formulation, achieves monolithic… 
Numerical investigation of abdominal aortic aneurysm hemodynamics using the reduced unified continuum formulation for vascular fluid-structure interaction
We recently demonstrated the reduction of the unified continuum and variational multiscale formulation to a computationally efficient fluid-structure interaction (FSI) formulation via three sound


A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction.
  • Ju Liu, A. Marsden
  • Physics, Computer Science
    Computer methods in applied mechanics and engineering
  • 2018
The results indicate that the proposed modeling and numerical methodologies constitute a promising technology for biomedical and engineering applications, particularly those necessitating incompressible models.
A hybrid variational Allen-Cahn/ALE scheme for the coupled analysis of two-phase fluid-structure interaction
We present a novel partitioned iterative formulation for modeling of fluid-structure interaction in two-phase flows. The variational formulation consists of a stable and robust integration of three
An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics.
We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed in [41] and smooth generalizations of the Taylor-Hood element based
An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves.
This paper develops a geometrically flexible technique for computational fluid-structure interaction (FSI) that directly analyzes a spline-based surface representation of the structure by immersing it into a non-boundary-fitted discretization of the surrounding fluid domain, and introduces the term "immersogeometric analysis" to identify this paradigm.
Stable loosely-coupled-type algorithm for fluid-structure interaction in blood flow
A novel loosely coupled-type algorithm for fluid-structure interaction between blood flow and thin vascular walls that is based on a time-discretization via operator splitting which is applied, in a novel way, to separate the fluid sub- problem from the structure elastodynamics sub-problem.
Isogeometric fluid-structure interaction: theory, algorithms, and computations
We present a fully-coupled monolithic formulation of the fluid-structure interaction of an incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary
A coupled momentum method for modeling blood flow in three-dimensional deformable arteries
Abstract Blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel. Moreover, wave propagation phenomena in the cardiovascular system can only be
Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit
Over the last decade, the numerical simulation of incompressible fluid-structure interaction has been a very active research field and the subject of numerous works. This is due, in particular, to
Added-mass effect in the design of partitioned algorithms for fluid-structure problems
A simplified model representing the interaction between a potential fluid and a linear elastic thin tube is considered, which reproduces propagation phenomena and takes into account the added-mass effect of the fluid on the structure, which is known to be source of numerical difficulties.