Numerical simulations of granular dam break: Comparison between discrete element, Navier-Stokes, and thin-layer models.

Granular flows occur in various contexts, including laboratory experiments, industrial processes, and natural geophysical flows. To investigate their dynamics, different kinds of physically based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microscopic scale to individually model each grain, Navier-Stokes models use a mesoscopic scale to consider elementary volumes of grains, and thin-layer models use a macroscopic scale to model the dynamics of elementary columns of fluids. In each case, the derivation of the associated equations is well-known. However, few studies focus on the extent to which these modeling solutions yield mutually coherent results. In this article, we compare the simulations of a granular dam break on a horizontal or inclined planes for the discrete model convex optimization contact dynamics (COCD), the Navier-Stokes model Basilisk, and the thin-layer depth-averaged model SHALTOP. We show that, although all three models allow reproducing the temporal evolution of the free surface in the horizontal case (except for SHALTOP at the initiation), the modeled flow dynamics are significantly different, and, in particular, during the stopping phase. The stresses measured at the flow's bottom, reflecting the flow dynamics, are in relatively good agreement, but significant variations are obtained with the COCD model due to complex and fast-varying granular lattices. Similar conclusions are drawn using the same rheological parameters to model a granular dam break on an inclined plane. This comparison exercise is essential for assessing the limits and uncertainties of granular flow modeling.

How cohesion controls the roughness of a granular deposit.

Cohesive granular materials often form clusters of grains, which alter their flowing properties. How these clusters form and evolve is difficult to visualize in the bulk of the material, and thus to model. Here, we use a proxy to investigate the formation of such clusters, which is the rough surface of a cohesive granular deposit. We characterize this roughness and show how it is related to the cohesion between beads. Specifically, the size of this roughness increases with the inter-particle cohesion, and the profile exhibits a self-affine behaviour, as observed for crack paths in the domain of fractography. In addition to providing a simple method to measure the inter-particle cohesion from macroscopic parameters, these results give better comprehension of the formation of clusters in cohesive granular materials.

Distribution of Flow in an Arteriovenous Fistula Using Reduced-Order Models.

The creation of a communication between an artery and a vein (arteriovenous fistula or AVF), to speed up the blood purification during hemodialysis of patients with renal insufficiency, induces significant rheological and mechanical modifications of the vascular network. In this study, we investigated the impact of the creation of an AVF with a zero-dimensional network model of the vascular system of an upper limb and a one-dimensional model around the anastomosis. We compared the simulated distribution of flow rate in this vascular system with Doppler ultrasound measurements. We studied three configurations: before the creation of the AVF, after the creation of the AVF, and after a focal reduction due to a hyper flow rate. The zero-dimensional model predicted the bounds of the diameter of the superficial vein that respects the flow constraints, assuming a high capillary resistance. We indeed highlighted the importance of knowing the capillary resistance as it is a decisive parameter in the models. We also found that the model reproduced the Doppler measurements of flow rate in every configuration and predicted the distribution of flow in cases where the Doppler was not available. The one-dimensional model allowed studying the impact of a venous constriction on the flow distribution, and the capillary resistance was still a crucial parameter.

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models.

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 > .95) with experimental blood pressure data.

Effects of Cross-Clamping on Vascular Mechanics: Comparing Waveform Analysis With a Numerical Model.

BACKGROUND: Immediate changes in vascular mechanics during aortic cross-clamping remain widely unknown. By using a numerical model of the arterial network, vascular compliance and resistance can be estimated and the time constant of pressure waves can be calculated and compared with results from the classic arterial waveform analysis. METHODS: Experimental data were registered from continuous invasive radial artery pressure measurements from 11 patients undergoing vascular surgery. A stable set of beats were chosen immediately before and after each clamping event. Through the arterial waveform analysis, the time constant was calculated for each individual beat and for a mean beat of each condition as to compare with numerical simulations. Overall proportional changes in resistance and compliance during clamping and unclamping were calculated using the numerical model. RESULTS: Arterial waveform analysis of individual beats indicated a significant 10% median reduction in the time constant after clamping, and a significant 17% median increase in the time constant after unclamping. There was a positive correlation between waveform analysis and numerical values of the time constant, which was moderate (ρ = 0.51; P = 0.01486) during clamping and strong (ρ = 0.77; P ≤ 0.0001) during unclamping. After clamping, there was a significant 16% increase in the mean resistance and a significant 23% decrease in the mean compliance. After unclamping, there was a significant 19% decrease in the mean resistance and a significant 56% increase in the mean compliance. CONCLUSIONS: There are significant hemodynamic changes in vascular compliance and resistance during aortic clamping and unclamping. Numerical computer models can add information on the mechanisms of injury due to aortic clamping.

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals.

This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a nonlinear Kelvin-Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin-Voigt model and the experimental measurements. We found that the viscoelastic relaxation time-defined by the ratio between the viscoelastic coefficient and the Young's modulus-is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high-frequency waves is clear especially at the peripheral sites.

Specific features of a stopped pipe blown by a turbulent jet: Aeroacoustics of the panpipes.

Flute-like instruments with a stopped pipe were widely used in ancient cultures and continue to be used in many musical expressions throughout the globe. They offer great flexibility in the input control parameters, allowing for large excursions in the flux and in the geometrical configuration for the lips of the instrumentalist. For instance, the transverse offset of the jet axis relative to the labium can be shifted beyond the operational limits found in open-open pipes, and the total jet flux can be increased up to values that produce highly turbulent jets while remaining on the first oscillating regime. Some of the fundamental aspects of the acoustics and hydrodynamics of this kind of instrument are studied, like the instability of the jet wave and the static aerodynamic balance in the resonator. A replica of an Andean siku has been created to observe, through the Schlieren flow visualization, the behavior of both excitation and resonator of the instrument.

The dicrotic notch analyzed by a numerical model.

Divergent concepts on the origin of the dicrotic notch are widespread in medical literature and education. Since most medical textbooks explain the origin of the dicrotic notch as caused by the aortic valve closure itself, this is commonly transmitted in medical physiology courses. We present clinical data and numerical simulations to demonstrate that reflected pressure waves could participate as one of the causes of the dicrotic notch. Our experimental data from continuous arterial pressure measurements from adult patients undergoing vascular surgery suggest that isolated changes in peripheral vascular resistance using an intravenous bolus of phenylephrine (a selective alpha 1-receptor agonist and thus a potent vasoconstrictor) modify the dicrotic notch. We then explore the mechanisms behind this phenomenon by using a numerical model based on integrated axisymmetric Navier-Stokes equations to compute the hemodynamic flow. Our model illustrates clearly how modifications in peripheral artery resistance may result in changes in the amplitude of the dicrotic notch by modifying reflected pressure waves. We believe that this could be a useful tool in teaching medical physiology courses.

Fluid friction and wall viscosity of the 1D blood flow model.

We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and experiments was achieved. For amplitude decrease, the effect of wall viscosity on the pulse wave has been shown as important as that of fluid viscosity.

Verification and comparison of four numerical schemes for a 1D viscoelastic blood flow model.

A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, monotonic upwind scheme for conservation law and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.

Time-domain simulation of flute-like instruments: comparison of jet-drive and discrete-vortex models.

This paper presents two models of sound production in flute-like instruments that allow time-domain simulations. The models are based on different descriptions of the jet flow within the window of the instrument. The jet-drive model depicts the jet by its transverse perturbation that interacts with the labium to produce sound. The discrete-vortex model depicts the jet as two independent shear layers along which vortices are convected and interact with the acoustic field within the window. The limit of validity between both models is usually discussed according to the aspect ratio of the jet W/h, with W the window length and h the flue channel height. The present simulations, compared with experimental data gathered on a recorder, allow to extend the aspect ratio criterion to the notion of dynamic aspect ratio defined as λ/h where λ is the hydrodynamic wavelength that now accounts for geometrical properties, such as W/h, as well as for dynamic properties, such as the Strouhal number. The two models are found to be applicable over neighboring values of geometry and blowing pressure.

Behaviour of silica nanoparticles in dermis-like cellularized collagen hydrogels.

A model of the fate of colloidal silica in the dermis was designed based on the diffusion of fluorescent silica nanoparticles through collagen hydrogels. The diffusion process was found to depend on particle size (10-200 nm) and surface charge, as well as on collagen concentration (1.5-5 mg mL-1). The presence of human dermal fibroblasts within the hydrogels also significantly impacted on the behaviour of the particles. In particular, the simultaneous monitoring of particulate and soluble forms of silica showed that both the hydrogel network and the cellular activity have a strong influence on the solubilization process of the silica particles, through a combination of surface sorption, uptake and intracellular dissolution. Interactions between silica and collagen in 3D environments also lower the cytotoxicity of 10 nm particles compared to traditional 2D cultures. The results emphasize the complexity of silica chemistry in living tissues and specifically indicate the need for further investigations of the in vivo behaviour of its soluble forms.

Experimental study on the pressure and pulse wave propagation in viscoelastic vessel tubes-effects of liquid viscosity and tube stiffness.

A pulse wave is the displacement wave which arises because of ejection of blood from the heart and reflection at vascular bed and distal point. The investigation of pressure waves leads to understanding the propagation characteristics of a pulse wave. To investigate the pulse wave behavior, an experimental study was performed using an artificial polymer tube and viscous liquid. A polyurethane tube and glycerin solution were used to simulate a blood vessel and blood, respectively. In the case of the 40 wt% glycerin solution, which corresponds to the viscosity of ordinary blood, the attenuation coefficient of a pressure wave in the tube decreased from 4.3 to 1.6 dB/m because of the tube stiffness (Young's modulus: 60 to 200 kPa). When the viscosity of liquid increased from approximately 4 to 10 mPa·s (the range of human blood viscosity) in the stiff tube, the attenuation coefficient of the pressure wave changed from 1.6 to 3.2 dB/m. The hardening of the blood vessel caused by aging and the increase of blood viscosity caused by illness possibly have opposite effects on the intravascular pressure wave. The effect of the viscosity of a liquid on the amplitude of a pressure wave was then considered using a phantom simulating human blood vessels. As a result, in the typical range of blood viscosity, the amplitude ratio of the waves obtained by the experiments with water and glycerin solution became 1:0.83. In comparison with clinical data, this value is much smaller than that seen from blood vessel hardening. Thus, it can be concluded that the blood viscosity seldom affects the attenuation of a pulse wave.

Regime change and oscillation thresholds in recorder-like instruments.

Based on results from the literature, a description of sound generation in a recorder is developed. Linear and non-linear analysis are performed to study the dependence of the frequency on the jet velocity. The linear analysis predicts that the frequency is a function of the jet velocity. The non-linear resolution provides information about limit cycle oscillation and hysteretic regime change thresholds. A comparison of the frequency between linear theory and experiments on a modified recorder shows good agreement except at very low jet velocities. Although the predicted threshold for the onset of the first regime shows an important deviation from experiments, the hysteresis of threshold to higher regimes is accurately estimated. Furthermore, a qualitative analysis of the influence of different parameters in the model on the sound generation and regime changes is presented.

One-dimensional model for propagation of a pressure wave in a model of the human arterial network: comparison of theoretical and experimental results.

Pulse wave evaluation is an effective method for arteriosclerosis screening. In a previous study, we verified that pulse waveforms change markedly due to arterial stiffness. However, a pulse wave consists of two components, the incident wave and multireflected waves. Clarification of the complicated propagation of these waves is necessary to gain an understanding of the nature of pulse waves in vivo. In this study, we built a one-dimensional theoretical model of a pressure wave propagating in a flexible tube. To evaluate the applicability of the model, we compared theoretical estimations with measured data obtained from basic tube models and a simple arterial model. We constructed different viscoelastic tube set-ups: two straight tubes; one tube connected to two tubes of different elasticity; a single bifurcation tube; and a simple arterial network with four bifurcations. Soft polyurethane tubes were used and the configuration was based on a realistic human arterial network. The tensile modulus of the material was similar to the elasticity of arteries. A pulsatile flow with ejection time 0.3 s was applied using a controlled pump. Inner pressure waves and flow velocity were then measured using a pressure sensor and an ultrasonic diagnostic system. We formulated a 1D model derived from the Navier-Stokes equations and a continuity equation to characterize pressure propagation in flexible tubes. The theoretical model includes nonlinearity and attenuation terms due to the tube wall, and flow viscosity derived from a steady Hagen-Poiseuille profile. Under the same configuration as for experiments, the governing equations were computed using the MacCormack scheme. The theoretical pressure waves for each case showed a good fit to the experimental waves. The square sum of residuals (difference between theoretical and experimental wave-forms) for each case was <10.0%. A possible explanation for the increase in the square sum of residuals is the approximation error for flow viscosity. However, the comparatively small values prove the validity of the approach and indicate the usefulness of the model for understanding pressure propagation in the human arterial network.

Modelling the human pharyngeal airway: validation of numerical simulations using in vitro experiments.

In the presented study, a numerical model which predicts the flow-induced collapse within the pharyngeal airway is validated using in vitro measurements. Theoretical simplifications were considered to limit the computation time. Systematic comparisons between simulations and measurements were performed on an in vitro replica, which reflects asymmetries of the geometry and of the tissue properties at the base of the tongue and in pathological conditions (strong initial obstruction). First, partial obstruction is observed and predicted. Moreover, the prediction accuracy of the numerical model is of 4.2% concerning the deformation (mean quadratic error on the constriction area). It shows the ability of the assumptions and method to predict accurately and quickly a fluid-structure interaction.

ENDOCOM : abdominal aortic aneurysm test bench for in vitro simulation.

An abdominal aortic aneurysm (AAA) is a dilatation of the aorta at the abdominal level, whose rupture is a life threatening complication. Recent treatment procedures of AAA consists in endovascular treatment with covered stent grafts. Despite improving design of these devices, this treatment is still associated with close to 25% of failure, due to persisting pressure into the excluded aneurysmal sac. The follow-up becomes thus crucial and demands frequent examinations (CT-scan, IRM) which are not so liable given the complications. In order to evaluate the post-operative period of an AAA treatment, we designed a communicative stent, comprising of an integrated pressure sensor. This paper presents the conception of a communicative sensor, the elaboration of a numerical model, and the development of an experimental testbench reproducing the aortic flux across an AAA and allowing the optimization and validation of the measurement principle.

Morphodynamic modeling of erodible laminar channels.

A two-dimensional model for the erosion generated by viscous free-surface flows, based on the shallow-water equations and the lubrication approximation, is presented. It has a family of self-similar solutions for straight erodible channels, with an aspect ratio that increases in time. It is also shown, through a simplified stability analysis, that a laminar river can generate various bar instabilities very similar to those observed in natural rivers. This theoretical similarity reflects the meandering and braiding tendencies of laminar rivers indicated by F. Métivier and P. Meunier [J. Hydrol. 27, 22 (2003)]. Finally, we propose a simple scenario for the transition between patterns observed in experimental erodible channels.