19 research outputs found
Systematic Stochastic Reduction of Inertial Fluid-Structure Interactions subject to Thermal Fluctuations
We present analysis for the reduction of an inertial description of
fluid-structure interactions subject to thermal fluctuations. We show how the
viscous coupling between the immersed structures and the fluid can be
simplified in the regime where this coupling becomes increasingly strong. Many
descriptions in fluid mechanics and in the formulation of computational methods
account for fluid-structure interactions through viscous drag terms to transfer
momentum from the fluid to immersed structures. In the inertial regime, this
coupling often introduces a prohibitively small time-scale into the temporal
dynamics of the fluid-structure system. This is further exacerbated in the
presence of thermal fluctuations. We discuss here a systematic reduction
technique for the full inertial equations to obtain a simplified description
where this coupling term is eliminated. This approach also accounts for the
effective stochastic equations for the fluid-structure dynamics. The analysis
is based on use of the Infinitesmal Generator of the SPDEs and a singular
perturbation analysis of the Backward Kolomogorov PDEs. We also discuss the
physical motivations and interpretation of the obtained reduced description of
the fluid-structure system. Working paper currently under revision. Please
report any comments or issues to [email protected]: 19 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1009.564
Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
We present approaches for the study of fluid-structure interactions subject
to thermal fluctuations. A mixed mechanical description is utilized combining
Eulerian and Lagrangian reference frames. We establish general conditions for
operators coupling these descriptions. Stochastic driving fields for the
formalism are derived using principles from statistical mechanics. The
stochastic differential equations of the formalism are found to exhibit
significant stiffness in some physical regimes. To cope with this issue, we
derive reduced stochastic differential equations for several physical regimes.
We also present stochastic numerical methods for each regime to approximate the
fluid-structure dynamics and to generate efficiently the required stochastic
driving fields. To validate the methodology in each regime, we perform analysis
of the invariant probability distribution of the stochastic dynamics of the
fluid-structure formalism. We compare this analysis with results from
statistical mechanics. To further demonstrate the applicability of the
methodology, we perform computational studies for spherical particles having
translational and rotational degrees of freedom. We compare these studies with
results from fluid mechanics. The presented approach provides for
fluid-structure systems a set of rather general computational methods for
treating consistently structure mechanics, hydrodynamic coupling, and thermal
fluctuations.Comment: 24 pages, 3 figure
Simulation-Based Design of Bicuspidization of the Aortic Valve
Objective: Severe congenital aortic valve pathology in the growing patient
remains a challenging clinical scenario. Bicuspidization of the diseased aortic
valve has proven to be a promising repair technique with acceptable durability.
However, most understanding of the procedure is empirical and retrospective.
This work seeks to design the optimal gross morphology associated with surgical
bicuspidization with simulations, based on the hypothesis that modifications to
the free edge length cause or relieve stenosis.
Methods: Model bicuspid valves were constructed with varying free edge
lengths and gross morphology. Fluid-structure interaction simulations were
conducted in a single patient-specific model geometry. The models were
evaluated for primary targets of stenosis and regurgitation. Secondary targets
were assessed and included qualitative hemodynamics, geometric height,
effective height, orifice area and prolapse.
Results: Stenosis decreased with increasing free edge length and was
pronounced with free edge length less than or equal to 1.3 times the annular
diameter d. With free edge length 1.5d or greater, no stenosis occurred. All
models were free of regurgitation. Substantial prolapse occurred with free edge
length greater than or equal to 1.7d.
Conclusions: Free edge length greater than or equal to 1.5d was required to
avoid aortic stenosis in simulations. Cases with free edge length greater than
or equal to 1.7d showed excessive prolapse and other changes in gross
morphology. Cases with free edge length 1.5-1.6d have a total free edge length
approximately equal to the annular circumference and appeared optimal. These
effects should be studied in vitro and in animal studies
Flagellum Pumping Efficacy in Shear-Thinning Viscoelastic Fluids
Microorganism motility often takes place within complex, viscoelastic fluid
environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In
such complex fluids, strains and stresses generated by the microorganism are
stored and relax across a spectrum of length and time scales and the complex
fluid can be driven out of its linear response regime. Phenomena not possible
in viscous media thereby arise from feedback between the "swimmer" and the
complex fluid, making swimming efficiency co-dependent on the propulsion
mechanism and fluid properties. Here we parameterize a flagellar motor and
filament properties together with elastic relaxation and nonlinear
shear-thinning properties of the fluid in a computational immersed boundary
model. We then explore swimming efficiency over this parameter space. One
exemplary insight is that motor efficiency (measured by the volumetric flow
rate) can be boosted vs.\ degraded by moderate vs.\ strong shear-thinning of
the viscoelastic environment.Comment: 15 pages, 8 figure
On the chordae structure and dynamic behaviour of the mitral valve
We develop a fluid-structure interaction (FSI) model of the mitral valve (MV) that uses an anatomically
and physiologically realistic description of the MV leaflets and chordae tendineae. Three different
chordae models — complex, “pseudo-fibre”, and simplified chordae — are compared to determine how
different chordae representations affect the dynamics of the MV. The leaflets and chordae are modelled as
fibre-reinforced hyperelastic materials, and FSI is modelled using an immersed boundary-finite element
(IB/FE) method. The MV model is first verified under static boundary conditions against the commercial
FE software ABAQUS, and then used to simulate MV dynamics under physiological pressure conditions.
Interesting flow patterns and vortex formulation are observed in all three cases. To quantify the highly
complex system behaviour resulting from FSI, an energy budget analysis of the coupled MV FSI model
is performed. Results show that the complex and pseudo-fibre chordae models yield good valve closure
during systole, but that the simplified chordae model leads to poorer leaflet coaptation and an unrealistic
bulge in the anterior leaflet belly. An energy budget analysis shows that the MV models with complex
and pseudo-fibre chordae have similar energy distribution patterns, but the MV model with the simplified
chordae consumes more energy, especially during valve closing and opening. We find that the complex
chordae and pseudo-fibre chordae have similar impact on the overall MV function, but that the simplified
chordae representation is less accurate. Because a pseudo-fibre chordal structure is easier to construct
and less computationally intensive, it may be a good candidate for modelling MV dynamics or interaction
between the MV and heart in patient-specific applications
Validation of Immersed Boundary Simulations of Heart Valve Hemodynamics against In Vitro 4D Flow MRI Data
The immersed boundary (IB) method is a mathematical framework for
fluid-structure interaction problems (FSI) that was originally developed to
simulate flows around heart valves. Validation of FSI simulations around heart
valves against experimental data is challenging, however, due to the difficulty
of performing robust and effective simulations, the complications of modeling a
specific physical experiment, and the need to acquire experimental data that is
directly comparable to simulation data. In this work, we performed physical
experiments of flow through a pulmonary valve in an in vitro pulse duplicator,
and measured the corresponding velocity field using 4D flow MRI (4-dimensional
flow magnetic resonance imaging). We constructed a computer model of this
pulmonary artery setup, including modeling valve geometry and material
properties via a technique called design-based elasticity, and simulated flow
through it with the IB method. The simulated flow fields showed excellent
qualitative agreement with experiments, excellent agreement on integral
metrics, and reasonable relative error in the entire flow domain and on slices
of interest. These results validate our design-based valve model construction,
the IB solvers used and the immersed boundary method for flows around heart
valves