Fluid-structure interaction with applications in biomechanics

Hron, J.; Mádlík, Martin

doi:10.1016/j.nonrwa.2006.05.007

Cited by 27 publications

(28 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With this the uid problem is rewritten as one on the transformed domain ‡ (Figure 2). For this see arbitrary Lagrangian-Eulerian (ALE) methods [1][2][3] and deforming space-time ÿnite element formulations [4,5]. Both the partitioned and the transformation approach to the Euler-Lagrange discrepancy explicitly track the mesh and are generally referred to as interface tracking methods.…”

Section: Introductionmentioning

confidence: 99%

An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation

Dunne

2006

Numerical Methods in Fluids

112

View full text Add to dashboard Cite

SUMMARYWe propose an Eulerian framework for modelling uid-structure interaction (FSI) of incompressible uids and elastic structures. The model is based on an Eulerian approach for describing structural dynamics. This is achieved by tracking the movement of the initial positions of all 'material' points. In this approach the displacement appears as a primary variable in an Eulerian framework.Our approach uses a technique which is similar to the level set method in so far that it also tracks initial data, in our case the set of initial positions (IP), and from this determines to which 'phase' a point belongs. To avoid the occasional reinitialization of the initial position set we employ the harmonic continuation of the structure velocity ÿeld into the uid domain.By using the IP set for tracking the structure displacement, we can ensure that corners and edges of the uid-structure interface are preserved well.Based on this monolythic model of the FSI we apply the Dual Weighted Residual (DWR) method for goal-oriented a posteriori error estimation to stationary FSI problems.Examples are presented based on the model and for the goal-oriented local mesh adaptation.

show abstract

Section: Introductionmentioning

confidence: 99%

An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation

Dunne

2006

Numerical Methods in Fluids

112

View full text Add to dashboard Cite

show abstract

“…Hron and Turek [40] and Hron and Mádlík [41] stated that the monolithic approach which treated the problem as a single continuum with coupling automatically takes care of the internal interface. This gets rid of the problematic interface treatment when the fluid and structure are solved separately.…”

Section: Monolithic Approachmentioning

confidence: 99%

“…second-order time stepping scheme as well as the same finite elements for fluid and structure should be utilized. Hron and Turek [40] and Hron and Mádlík [41] applied different types of discretization in space and time. They solved the simplified two-dimensional examples with finite element and CrankNicolson for the space and time discretization, respectively.…”

Section: Monolithic Approachmentioning

confidence: 99%

Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Tang

Amin

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

Some numerical approaches to solve fluid structure interaction problems in blood flow are reviewed. Fluid structure interaction is the interaction between a deformable structure with either an internal or external flow. A discussion on why the compliant artery associated with fluid structure interaction should be taken into consideration in favor of the rigid wall model being included. However, only the Newtonian model of blood is assumed, while various structure models which include, amongst others, generalized string models and linearly viscoelastic Koiter shell model that give a more realistic representation of the vessel walls compared to the rigid structure are presented. Since there exists a strong added mass effect due to the comparable densities of blood and the vessel wall, the numerical approaches to overcome the added mass effect are discussed according to the partitioned and monolithic classifications, where the deficiencies of each approach are highlighted. Improved numerical methods which are more stable and offer less computational cost such as the semi-implicit, kinematic splitting, and the geometrical multiscale approach are summarized, and, finally, an appropriate structure and numerical scheme to tackle fluid structure interaction problems are proposed.

show abstract

“…The resulting linear subproblems are then solved by the GMRES method with preconditioning by a geometric multigrid method with block-ILU smoothing. This approach is well known, we omit its details and refer to the relevant literature, e.g., [25], [21], or [16].…”

Section: Solution Of the Algebraic Systemsmentioning

confidence: 99%

Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation

Dunne

Rannacher

2006

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Abstract. We propose a general variational framework for the adaptive finite element approximation of fluid-structure interaction problems. The modeling is based on an Eulerian description of the (incompressible) fluid as well as the (elastic) structure dynamics. This is achieved by tracking the movement of the initial positions of all 'material' points. In this approach the deformation appears as a primary variable in an Eulerian framework. Our approach uses a technique which is similar to the Level Set method in so far that it also tracks initial data, in our case the set of Initial Positions, and from this determines to which 'phase' a point belongs. To avoid the need for reinitialization of the initial position set, we employ the harmonic continuation of the structure velocity field into the fluid domain. Based on this monolithic model of the fluid-structure interaction we apply the dual weighted residual method for goal-oriented a posteriori error estimation and mesh adaptation to fluid-structure interaction problems. Results from nonstationary examples are presented.

show abstract

Fluid-structure interaction with applications in biomechanics

Cited by 27 publications

References 32 publications

An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation

An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation

Some Numerical Approaches to Solve Fluid Structure Interaction Problems in Blood Flow

Adaptive Finite Element Approximation of Fluid-Structure Interaction Based on an Eulerian Variational Formulation

Contact Info

Product

Resources

About