Fluid Mechanics Research Articles

Moving-boundary problems solved by adaptive radial basis functions

The objective of this paper is to present an alternative approach to the conventional level set methods for solving two-dimensional moving-boundary problems known as the passive transport. Moving boundaries are associated with time-dependent problems and the position of the boundaries need to be determined as a function of time and space. The level set method has become an attractive design tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations. In the present approach, the moving interface is captured by the level set method at all time with the zero contour of a smooth function known as the level set function. A new approach is used to solve a convective transport equation for advancing the level set function in time. This new approach is based on the asymmetric meshless collocation method and the adaptive greedy algorithm for trial subspaces selection. Numerical simulations are performed to verify the accuracy and stability of the new numerical scheme which is then applied to simulate a bubble that is moving, stretching and circulating in an ambient flow to demonstrate the performance of the new meshless approach.

Anomalous flow behavior in nanochannels: A molecular dynamics study

We report molecular dynamics simulations of flow of water in nanochannels with a range of surface wettability characteristics (hydrophobic to strongly hydrophilic) and driving forces (pressures). Our results show apparently anomalous behavior. At low pressures, the rate is higher in nanochannels with hydrophilic surfaces than that with hydrophobic surfaces; however, with high pressure driven flow we observe opposite trends. This apparently anomalous behavior can be explained on the basis of molecular thermodynamics and fluid mechanics considerations. Understanding such behavior is important in many nanofluidic devices such as nanoreactors, nanosensors, and nanochips that are increasingly being designed and used.

A computer-controlled apparatus for micrometric drop deposition at liquid surfaces

A low-cost, automated apparatus has been used to perform micrometric deposition of small pendant drops onto a quiet liquid surface. The approach of the drop to the surface is obtained by means of discrete, micron-scale translations in order to achieve deposition at adiabatically zero velocity. This process is not only widely used in scientific investigations in fluid mechanics and thermal sciences but also in engineering and biomedical applications. The apparatus has been designed to produce accurate deposition onto the surface and minimize the vibrations induced in the drop by the movement of the capillary tip. Calibration tests of the apparatus have shown that a descent of the drop by discrete translational steps of approximately 5.6 microm and duration of 150-200 ms is sufficient to minimize its penetration depth into the liquid when it touches the surface layer and reduce to a level of noise the vibrations transmitted to it by the translation of the dispenser. Different settings of the experimental setup can be easily implemented for use in a variety of other applications, including deposition onto solid surfaces, surface tension measurements of pendant drops, and wire bonding in microelectronics.

Transient growth and why we should care about it

The phrases ‘transient growth’ and ‘non-normality’ have become common parlance in fluid mechanics nowadays. We present these ideas with a simple two-dimensional system, to enable the reader to look for transient growth, as a trigger for nonlinear behaviour to set in, in a variety of situations probably having nothing to do with fluid mechanics. The article is aimed at undergraduate students of science, engineering, finance, etc., and the material is based completely on the excellent books of Trefethen and Embree, and Schmid and Henningson [1,2].

Thermal Wave Based on the Thermomass Model

In times comparable to the characteristic time of the energy carriers, Fourier’s law of heat conduction breaks down and heat may propagate as waves. Based on the concept of thermomass, which is defined as the equivalent mass of phonon gas in dielectrics, according to the Einstein’s mass-energy relation, the phonon gas in the dielectrics is described as a weighty, compressible fluid. Newton mechanics has been applied to establish the equation of state and the equation of motion for the phonon gas as in fluid mechanics, because the drift velocity of a phonon gas is normally much less than the speed of light. The propagation velocity of the thermal wave in the phonon gas is derived directly from the equation of state for the phonon gas, rather than from the relaxation time in the Cattaneo–Vernotte (CV) model (Cattaneo, C., 1948, “Sulla Conduzione Del Calore,” Atti Semin. Mat. Fis. Univ. Modena, 3, pp. 83–101; Vernotte, P., 1958, “Paradoxes in the Continuous Theory of the Heat Equation,” C. R. Acad. Bulg. Sci., 246, pp. 3154–3155). The equation of motion for the phonon gas gives rise to the thermomass model, which depicts the general relation between the temperature gradient and heat flux. The linearized conservation equations for the phonon gas lead to a damped thermal wave equation, which is similar to the CV-wave equation, but with different characteristic time. The lagging time in the resulting thermal wave equation is related to the wave velocity in the phonon gas, which is approximately two orders of magnitude larger than the relaxation time adopted in the CV-wave model for the lattices. A numerical example for fast transient heat conduction in a silicon film is presented to show that the temperature peaks resulting from the thermomass model are much higher than those resulting from the CV-wave model. Due to the slower thermal wave velocity in the phonon gas, by as much as one order of magnitude, the damage due to temperature overshooting may be more severe than that expected from the CV-wave model.

Hydrodynamic effects on fast monohulls or catamarans travelling through the critical speed in shallow water

The speed of linear waves in shallow water approaches a constant value as the wavelength becomes large relative to the water depth. For ships travelling in shallow water, this speed is known as the `critical speed' and acts as a barrier, similar to the speed of sound for aeroplanes. The possibility of travelling at transcritical and supercritical speeds is discussed for existing monohull and catamaran ships. We explore the predicted linearised flow around a ship as it approaches the critical speed, and the singularities that result. Experimental results show the actual flow patterns that occur at ship speeds close to the critical speed, for monohulls or catamarans, in open water or confined channels. References Ang, W. T. 1993 Nonlinear sinkage and trim for a slender ship in shallow water of finite width . Internal report, University of Adelaide. Chen, X. N. 1999 Hydrodynamics of wave-making in shallow water . Ph.D. thesis, University of Stuttgart. Chen, X. N., Sharma, S. D. and Stuntz, N. 2003 Wave reduction by S-Catamaran at supercritical speeds. Journal of Ship Research 47 , No. 1, pp. 1--10. Constantine, T. 1960 On the movement of ships in restricted waterways. Journal of Fluid Mechanics 9 , pp. 247--256. doi:10.1017/S0022112060001080 Dand, I. W., Dinham-Peren, T. A. and King, L. 1999 Hydrodynamic aspects of a fast catamaran operating in shallow water. Proceedings, Hydrodynamics of High Speed Craft , London, November 1999. Gourlay, T. P. 2000 Mathematical and Computational Techniques for Predicting the Squat of Ships . Ph.D. thesis, University of Adelaide. Gourlay, T. P. 2001 The supercritical bore produced by a high-speed ship in a channel. Journal of Fluid Mechanics 434 , pp. 399--409. doi:10.1017/S002211200100372X Gourlay, T. P. and Tuck, E. O. 2001 The maximum sinkage of a ship. Journal of Ship Research 45 , No. 1, pp. 50--58. Gourlay, T. P., Duffy, J. T. and Forbes, A. 2005 The bore produced between the hulls of a high-speed catamaran in shallow water. International Journal of Maritime Engineering 147 , Part A3, pp. 1--8. Gourlay, T. P. 2006 A simple method for predicting the maximum squat of a high-speed displacement ship. Marine Technology 43 , No. 3, pp. 146--151. Gourlay, T. P. 2008 Sinkage and trim of a fast displacement catamaran in shallow water. Journal of Ship Research 52 , No. 3, pp. 175--183. Graff, W., Kracht, A. and Weinblum, G. 1964 Some extensions of D. W. Taylor's standard series. Trans. SNAME 72 , 374--401. Huang, D. B., Sibul, O. J., Webster, W. C., Wehausen, J. V., Wu, D. M. and Wu, T. Y. 1982 Ships moving in the transcritical speed range. Proceedings, Conference on Behaviour of Ships in Restricted Waters, Varna , Vol. II, pp. 1--10. Insel, M. 1990 An investigation into the resistance components of high speed catamarans. Ph.D. thesis, Department of Ship Science, University of Southampton. Lea, G. K. and Feldman, J. P. 1972 Transcritical flow past slender ships. Proceedings, 9th Symposium on Naval Hydrodynamics , ONR, Washington D.C., p1527. Mei, C. C. 1976 Flow around a thin body moving in shallow water. Journal of Fluid Mechanics 77 , pp. 737--751. doi:10.1017/S0022112076002863 Michell, J. H. 1898 The wave resistance of a ship. Philosophical Magazine 45 , pp. 106--123. Mueller-Graf, B. 1995 General resistance aspects of advanced fast marine vehicles. Proceedings, Design of Advanced Fast Marine Vehicles , September, Glasgow. Newman, J. N. 1977 Marine Hydrodynamics , MIT Press. Stoker, J. J. 1957 Water Waves . Interscience. Tuck, E. O. Shallow water flows past slender bodies. Journal of Fluid Mechanics 26 , pp. 81--95. doi:10.1017/S0022112066001101 Tuck, E. O. 1974 One-dimensional flows as slender-body problems, with applications to ships moving in channels. Proceedings, Workshop on Slender Body Theory , Ann Arbor. University of Michigan Report NAME 164, pp. 27--35.

Uniform convergence for complex diffusion equation via a probabilistic approach and application

Motivated by the well-posedness theory in fluid mechanics, we investigate the question of uniform convergence of solutions to the following heat equation perturbed with a complex-valued potential and a small positive parameter: We introduce a class of potentials allowing a full representation of uε by the so-called Feynman–Kac integral in the Wiener space. We show that this ansatz provides an asymptotic expansion of uε as ε tends to zero as well as a uniform control of \documentclass{article}\usepackage{amssymb}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}$\|\nabla u^{\varepsilon}(t,\cdot)\|_{L^{2}({\mathbb{R}}^{d})}$\end{document} for small times. The proof is carried out by the stationary phase method for the Wiener measure introduced by Ben Arous in (Stochastics 1988; 25:125–153) and essentially applied in the context of the semi-classical approximation of solutions to the Schrödinger equation (J. Funct. Anal. 1996; 137:243–280). At last, we prove as an application a uniform local existence result for inhomogeneous rotating fluid problem in the frame of anisotropic Sobolev spaces. Copyright © 2010 John Wiley & Sons, Ltd.

Unsteady Mixed Convection in a Vented Enclosure Partially Filled with Two Non-Darcian Porous Layers

Mixed convection in a ventilated rectangular cavity with a horizontal strip occupied by two media of different permeability is studied by using the finite-volume method. The effect of the parameters that govern the problem, the Reynolds number (200–500), the Richardson number (0.1–10), the Darcy number (1.E–6–1.E–2), permeability ratio (0.01–100), aspect ratio of the cavity (1–1.5), and direction of flow with or against gravity, is investigated. From the numerical results, the influence of Darcy and Reynolds numbers on the fluid mechanics can be inferred. When the cold fluid flow is descending, the fluid–porous medium heat transfer increases because the hotter fluid is located in the upper zones of the cavity. As the aspect ratio (height/width) increases from 0.67 to 1.5, both the Nusselt number (7.5 < Nu < 27) and the friction coefficient increase. The friction coefficient on the walls is greater when Re = 500 and Ri = 10 in the two directions of flow. As the Darcy number increases, the velocity gradients increase near the walls, causing an increase of the friction coefficient (0 < Cf Re < 47).

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

This numerical study focuses on the use of the Modal Identification Method to build reduced models for problems of heat convection and diffusion. The principle is to minimize a cost function based on the difference between the outputs (velocity and/or temperature) of a detailed model and the outputs of a reduced one. The reduced model structure is defined from the partial differential equations governing fluid mechanics and heat transfer in the physical system. In this paper, an advection–diffusion problem is studied: forced heat convection is considered with an incompressible, stationary, laminar 2D flow. Physical properties of the fluid are temperature independent, hence velocity is independent of temperature. The system under consideration is a channel flow over a backward-facing step with a time-varying heat flux density applied upstream of the step. Three types of reduced models have been investigated: steady fluid mechanics only, unsteady heat transfer for a given constant Reynolds number, and unsteady heat transfer for any constant Reynolds number within the range [100:800]. In this last case, the thermal reduced model is weakly coupled to the fluid reduced one. Results show that reduced models fit very well with detailed ones, and allow a large decrease of computing time.

Dynamics of isolated vortices in shallow flows

Turbulent shallow flows are characterized by large-scale strongly two-dimensional vortex structures that are triggered and grow under the kinematic and dynamic conditions of shallowness. Shallow mixing layers, wakes and jets are prominent examples in hydro-environmental and geophysical flows, in which a series of such vortex structures, interacting with each other, are generated by continuous forcing. Isolated turbulent shallow vortices are key elements in the fluid mechanics of such shallow flows. Experimental investigations on two types of shallow vortices generated by instantaneous forcing have been conducted: the single forced vortex that evolves into a tri-polar vortex system, and the vortex couple (dipole). Scaling of the vorticity transport equation shows that the gradual spin-down of these vortices is governed by the bottom friction acting at the base of the vortex flow. A simple spin-down model is in good agreement with the observed data with different regimes for the initial turbulent stage and the final laminar stage. It is argued that the turbulent stage is of direct relevance for actual hydro-environmental and geophysical flows. Hence, laboratory experimentation must be performed at a sufficiently large scale to capture a Reynolds-invariant regime.

Unsteady conjugate mixed convection phase change of a power law non-Newtonian fluid in a square cavity

Transient phase change of a power law non-Newtonian fluid inside an inner thin walled container caused by external mixed convection in a square cavity has been analyzed numerically. Air was chosen as external cooling fluid and modified non-Newtonian water as the phase change fluid. Fluid mechanics and conjugate convective heat transfer, described in terms of continuity, linear momentum and energy equations, were predicted by using the finite volume method. Solidification was treated in terms of a phase change function varying linearly with temperature. The effect of the external Reynolds number, for Re = 200 and 1000 on solidification was studied along the influence of the non-Newtonian power law index ( n = 0.5, n = 1.0). Results for the time evolution of streamlines, isotherms and freezing curves are analyzed. The effect of the Reynolds number on streamlines of the external fluid is remarkable, principally near the region close to the internal water filled container. Differences between cooling and freezing times are found for Newtonian ( n = 1.0) and non-Newtonian modified ( n = 0.5) water.

Computational fluid dynamics (CFD) models in the learning process of Hydraulic Engineering

AbstractIn this article, we show the ability to use sophisticated computational fluid dynamics (CFD) models as simple and useful tools in the learning process for Fluid Mechanics and Hydraulic Engineering topics. Specifically, we present a comparison between results obtained for a controlled layout simulated both by physical and computational models. This particular experience is based on a Venturi tube. In the laboratory of the Multidisciplinary Center for Fluid Modeling (CMMF), we have implemented a suitable assembly to simulate different Venturi‐related phenomena and to take measurements in an intrusion flow forced by the pressure field into the perforated Venturi tube. The same geometry has been reproduced using a CFD code, and both pressure and velocity values have been compared. By doing this comparison, we first provide awareness to our students about the importance of calibration, then show them the agreement between measured and computed values, and finally design a methodology for students to visualize pressure and velocity fields by means of a number of graphical displays of the results. This approach has revealed itself to be a powerful tool for them to understand the intricacies of hydraulic topics. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 252–260, 2010; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20248

Dr Olivier Coussy, Scientist and Engineer of the Mechanics and Physics of Porous Materials (1953–2010)

Dr Olivier Coussy, Scientist and Engineer of the Mechanics and Physics of Porous Materials (1953–2010)

A contribution for thermoeconomic modelling: A methodology proposal

This work presents a thermoeconomic optimization methodology for the analysis and design of energy systems. This methodology involves economic aspects related to the exergy conception, in order to develop a tool to assist the equipment selection, operation mode choice as well as to optimize the thermal plants design. It also presents the concepts related to exergy in a general scope and in thermoeconomics which combines the thermal sciences principles (thermodynamics, heat transfer, and fluid mechanics) and the economic engineering in order to rationalize energy systems investment decisions, development and operation. Even in this paper, it develops a thermoeconomic methodology through the use of a simple mathematical model, involving thermodynamics parameters and costs evaluation, also defining the objective function as the exergetic production cost. The optimization problem evaluation is developed for two energy systems. First is applied to a steam compression refrigeration system and then to a cogeneration system using backpressure steam turbine.

CMP pad wear and polish-rate decay modeled by asperity population balance with fluid effect

An important task in chemical–mechanical polishing (CMP) is to determine when the pad should be changed or reconditioned. A model which can predict the pad asperity probability distribution function (PDF) during polishing and conditioning is valuable for this purpose. Previous work has been done without incorporating fluid mechanics into the model in L.J. Borucki, J. Eng. Math. 43 (2002) 105–114, but that will overestimate the pad wear because the fluid reduces the load applied on the individual asperities. This work models the wear of pad asperities and polish-rate decay in CMP by coupling the population balance model with fluid mechanics. Modeling results with and without fluid effect are compared. Polish-rate model results are compared with experimental data in D. Stein et al., J. Electron. Mater. 25 (10) (1996) 1623–1627, and the results agree with experimental results for both cases by using different wear rate coefficients to fit experimental data. A lesser wear rate coefficient must be used to fit Stein’s data for the fluid case compared to the case without fluid. The wear rate of the pad is calculated from the rate of change of the pad–wafer separation distance during polishing because only asperities above this distance will be in contact and worn down and that portion will be piled up at the pad–wafer separation distance on the PDF curve of the pad asperities. The PDF evolution model results with fluid show much less pad wear compared to the case without fluid. Also if fluid is neglected, pad–wafer separation distance will continue to drop until it is zero, while for the fluid case, it will eventually reach a dynamic steady-state with no pad wear indicating that the load is entirely supported by the fluid. Accurate predicting the interface gap (pad wear) is critical for controlling both mechanical and chemical removal rate and within wafer non-uniformity (WIWNU). These results show that fluid is an important factor which needs to be included into the model in predicting the interface gap and surface profile evolution of the pad during polishing and conditioning.

Darboux Transformation and Soliton Solutions for a Variable-Coefficient Modified Kortweg-de Vries Model from Fluid Mechanics, Ocean Dynamics, and Plasma Mechanics

This paper is to investigate a variable-coefficient modified Kortweg-de Vries (vc-mKdV) model, which describes some situations from fluid mechanics, ocean dynamics, and plasma mechanics. By the Ablowitz–Kaup–Newell–Segur procedure and symbolic computation, the Lax pair of the vc-MKdV model is derived. Then, based on the aforementioned Lax pair, the Darboux transformation is constructed and a new one-soliton-like solution is obtained as well. Features of the one-soliton-like solution are analyzed and graphically discussed to illustrate the influence of the variable coefficients in the solitonlike propagation.

The harmonic mean renormalises random diffusion across a spatial multigrid

Most methods for modelling dynamics posit just two time scales: a fast and a slow scale. But many applications, such as the diffusion in a random media considered here, possess a wide variety of space-time scales. Consider the microscale diffusion on a one dimensional lattice with arbitrary diffusion coefficients between adjacent lattice points. I develop a slow manifold approach to model the diffusion, with some rigorous support, on a lattice that is coarser by a factor of four: the coarser scale effective diffusion coefficients are the harmonic mean of fine scale coefficients. Then iterating the analytic mapping of random diffusion from the finer grid to the coarser grid generates a hierarchy of models on a spatial multigrid across a wide range of space-time scales, all with rigorous support. The one step harmonic mean renormalises to harmonic means for the effective diffusion coefficients across the entire hierarchy. References Todd Arbogast and Kirsten J. Boyd. Subgrid upscaling and mixed multiscale finite elements. SIAM J. Numer. Anal., 44:1150--1171, 2006. doi:10.1137/050631811. Achi Brandt. General highly accurate algebraic coarsening. Elect. Trans. Num. Anal., 10:1--20, 2000. http://www.emis.ams.org/journals/ETNA/vol.10.2000/pp1-20.dir/pp1-20.html. Achi Brandt. Multiscale scientific computation: review 2001. In T. F. Chan T. J. Barth and R. Haimes, editors, Multiscale and Multiresolution Methods: Theory and Applications, pages 1--96. Springer--Verlag, Heidelberg, 2001. Achi Brandt. Methods of systematic upscaling. Technical report, Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, March 2006. http://wisdomarchive.wisdom.weizmann.ac.il:81/archive/00000398/. William L. Briggs, Van Emden Henson, and Steve F. McCormick. A multigrid tutorial, second edition. SIAM, 2nd edition, 2001. J. Carr. Applications of centre manifold theory, volume 35 of Applied Math. Sci. Springer--Verlag, 1981. J. Dolbow, M. A. Khaleel, and J. Mitchell. Multiscale mathematics initiative: A roadmap. Report from the 3rd DoE workshop on multiscale mathematics. Technical report, Department of Energy, USA, http://www.sc.doe.gov/ascr/mics/amr, December 2004. Weinan E, Bjorn Engquist, Xiantao Li, Weiqing Ren, and Eric Vanden-Eijnden. The heterogeneous multiscale method: A review. Technical report, http://www.math.princeton.edu/multiscale/review.pdf, 2004. B. Engquist and P. E. Souganidis. Asymptotic and numerical homogenization. Acta Numerica, 17:147--190, 2008. Martin J. Gander and Andrew M. Stuart. Space-time continuous analysis of waveform relaxation for the heat equation. SIAM Journal on Scientific Computing, 19(6):2014--2031, 1998. Y. A. Kuznetsov. Elements of applied bifurcation theory, volume 112 of Applied Mathematical Sciences. Springer--Verlag, 1995. Tony MacKenzie and A. J. Roberts. Holistic discretisation ensures fidelity to dynamics in two spatial dimensions. Technical report, http://arxiv.org/abs/0904.0855v1, 2009. G. A. Pavliotis and A. M. Stuart. Multiscale methods: averaging and homogenization, volume 53 of Texts in Applied Mathematics. Springer, 2008. A. J. Roberts. Simple and fast multigrid solution of Poisson's equation using diagonally oriented grids. ANZIAM J., 43(E):E1--E36, July 2001. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/465. A. J. Roberts. Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. In Rowena Ball and Nail Akhmediev, editors, Nonlinear dynamics from lasers to butterflies, volume 1 of Lecture Notes in Complex Systems, chapter 7, pages 257--313. World Scientific, 2003. A. J. Roberts. Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation. Technical report, http://arxiv.org/abs/0811.0688, 2008. A. J. Roberts. Normal form transforms separate slow and fast modes in stochastic dynamical systems. Physica A, 387:12--38, 2008. A. J. Roberts. Model dynamics across multiple length and time scales on a spatial multigrid. Multiscale Modeling and Simulation, 7(4):1525--1548, 2009. G. Samaey, I. G. Kevrekidis, and D. Roose. The gap-tooth scheme for homogenization problems. SIAM Multiscale Modeling and Simulation, 4:278--306, 2005. doi:10.1137/030602046. G. Samaey, A. J. Roberts, and I. G. Kevrekidis. Equation-free computation: an overview of patch dynamics, chapter 8, pages 216--246. Oxford University Press, 2010.

Maximum-Likelihood Parameter Estimation for the Thin-Shell Quasi-Newtonian Model for a Laboratory Blown Film Extruder

While most plastic films are manufactured by blown film extrusion, their first-principles modeling has remained substantially more challenging than for most other chemical engineering unit operations due to its combination of heat transfer, crystallization, and non-Newtonian fluid mechanics. This paper applies maximum-likelihood parameter estimation to characterize the convective heat transfer characteristics from measured spatial radii and temperature profiles for a laboratory-scale blown film process extruding a linear low density polyethylene (LLDPE) polymer. The Pearson and Petrie thin-film extrusion model incorporates (i) a quasi-Newtonian constitutive relation for the effect of temperature and crystallization on the viscosity of the polymer and (ii) a spatial variation of the heat transfer coefficient that is qualitatively consistent with turbulent flow simulations reported in the literature. A single heat transfer expression fit the experimental conditions for a cooling air flow rate of 1.5 m/s, wh...

Correlating data: examples from turbulent wall layers

Flow fields in fluid mechanics often contain regions where different physical events occur. The relative size of the regions changes as a parameter is varied. Correlating field data, either physical or DNS calculation experiments, in these situations can be aided by using ideas from matched asymptotic expansions from applied mathematics. A second situation is when two slightly different processes occur in the same spatial region. For this case, a two-term asymptotic expansion is needed. This article discusses how composite expansions and the common part matching behavior are useful in correlating data.

Partitioned Fluid–Solid Coupling for Cardiovascular Blood Flow: Validation Study of Pressure-Driven Fluid-Domain Deformation

The Karlsruhe Heart Model (KaHMo) is a patient-specific simulation tool for a three-dimensional blood flow evaluation inside the human heart. Whereas KaHMo MRT is based on geometry movement identified from MRT data, KaHMo FSI allows the consideration of structural properties and the analysis of FSI. Previous investigations by Oertel et al. have shown the ability of KaHMo to gain insight into different intra-ventricular fluid mechanics of both healthy and diseased hearts. However, the in vivo validation of the highly dynamic cavity flow pattern has been a challenging task in recent years. As a first step, the focus of this study is on an artificial ventricular experiment, derived from real heart anatomy. Fluid domain deformation and intra-ventricular flow dynamics are enforced by an outer surface pressure distribution. The pure geometrical representation of KaHMo MRT can now be complemented by constitutive properties, pressure forces, and interaction effects using KaHMo FSI's partitioned code-coupling approach. For the first time, fluid domain deformation and intra-ventricular flow of KaHMo FSI has been compared with experimental data. With a good overall agreement, the proof of KaHMo's validity represents an important step from feasibility study toward patient-specific analysis.