A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Cairncross, Richard A.; Schunk, Peter Randall; Baer, Thomas A.; Rao, Rekha R.; Sackinger, P.A.

doi:10.1002/1097-0363(20000615)33:3<375::aid-fld13>3.3.co;2-f

Cited by 46 publications

(90 citation statements)

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“…In particular, it allows the size of the boundary deformation imposed at each sub-step to be controlled by the value of K. This iterative approach could be replaced by other non-linear extensions of the surface displacement, e.g. considering the volume mesh as a hyperelastic material, which might be more robust in the case of very large deformations (see a stricking example in Cairncross et al (2000), p. 382). Notice that each solution of (11) on the reference meshT h automatically yields a deformation which preserves the topology of the reference mesh, i.e.…”

Section: D-shape Registrationmentioning

confidence: 99%

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Guibert

McLeod

Caiazzo

et al. 2014

Medical Image Analysis

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Abstract3D computational fluid dynamics (CFD) in patient-specific geometries provides complementary insights to clinical imaging, to better understand how heart disease, and the side effects of treating heart disease, affect and are affected by hemodynamics. This information can be useful in treatment planning for designing artificial devices that are subject to stress and pressure from blood flow. Yet, these simulations remain relatively costly within a clinical context. The aim of this work is to reduce the complexity of patient-specific simulations by combining image analysis, computational fluid dynamics and model order reduction techniques. The proposed method makes use of a reference geometry estimated as an average of the population, within an efficient statistical framework based on the currents representation of shapes. Snapshots of blood flow simulations performed in the reference geometry are used to build a POD (Proper Orthogonal Decomposition) basis, which can then be mapped on new patients to perform reduced order blood flow simulations with patient specific boundary conditions. This approach is applied to a data-set of 17 tetralogy of Fallot patients to simulate blood flow through the pulmonary artery under normal (healthy or synthetic valves with almost no backflow) and pathological (leaky or absent valve with backflow) conditions to better understand the impact of regurgitated blood on pressure and velocity at the outflow tracts.The model reduction approach is further tested by performing patient simulations under exercise and varying degrees of pathophysiological conditions based on reduction of reference solutions (rest and medium backflow conditions respectively).

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Section: D-shape Registrationmentioning

confidence: 99%

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Guibert

McLeod

Caiazzo

et al. 2014

Medical Image Analysis

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“…Here the mesh movement is constrained by a number of parameters (one for each spine used), thus reducing the computational overhead in exchange for restricting the generality of the approach. More general ALE forms have also been widely used for free-surface problems, based upon maintaining mesh quality [115,116], Laplacian smoothing [129] or pseudo-solid deformation [33,144]. Other applications which have benefited from successful ALE algorithms include phase-change problems [123], viscous sintering [84,94,151] and the interaction of free surfaces with solid boundaries [4,133,145].…”

Section: Ale (Arbitrary Lagrangian Eulerian) Methodsmentioning

confidence: 99%

“…By summing (4.31) over i the c i satisfy 33) since the w i 's form a partition of unity and mass is conserved. (We note in passing that the local conservation principle (4.2) corresponds to choosing the w i to be the characteristic function in Ω(t).)…”

Section: Distributed Mass-conserving Velocitiesmentioning

confidence: 99%

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Baines

Hubbard

Jimack

2011

Commun. comput. phys.

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Abstract. This article describes a number of velocity-based moving mesh numerical methods for multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

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“…Elsewhere, the mesh moves in an arbitrary manner. An example of an ALE implementation can be found in [Sackinger, Schunk and Rao, 1996] for 2D and extended to 3D by [Cairncross et al, 2000]. This nodal mesh velocity is defined by differentiating the position of the nodes with respect to time.…”

Section: Dynamic Discretization Via Moving Meshmentioning

confidence: 99%

Multiscale models of nuclear waste reprocessing : from the mesoscale to the plant-scale.

Rao¹,

Brotherton²,

Domino³

et al. 2012

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Nuclear waste reprocessing and nonproliferation models are needed to support the renaissance in nuclear energy. This report summarizes an LDRD project to develop predictive capabilities to aid the next-generation nuclear fuel reprocessing, in SIERRA Mechanics, Sandia's high performance computing multiphysics code suite and Cantera, an open source software product for thermodynamics and kinetic modeling.Much of the focus of the project has been to develop a moving conformal decomposition finite element method (CDFEM) method applicable to mass transport at the water/oil droplet interface that occurs in the turbulent emulsion of droplets within the contactor. Contactor-scale models were developed using SIERRA Mechanics turbulence modeling capability. Unit operations occur at the column-scale where many contactors are connected in series. Population balance models 4 were developed to investigate placements and coupling of contactors at this scale. Thermodynamics models of the separation were developed in Cantera to allow for the prediction of distribution coefficients for various concentrations of surfactant and acid. Droplet-scale modeling was conducted in a microfluidic device and for verification of the algorithm. Extensive validation and discovery experiments were performed at the droplet and contactor-scales for both fluid dynamics and mass transport. 5 AcknowledgmentsThe authors would like to thank our mission specialist Veena Tikare for helping us develop the project, our reprocessing material balance expert Ben Cipiti for explaining the details of the reprocessing plant., Roger Pawlowski and Rich Schiek helped with the idea of a scalable network model, but were unable to continue with the project, though were very helpful in the first year of the work. We believe this type of work should be continued at Sandia. Paul Galambos and John Pflug supported our microfluidic experiments. Reviewers Randy Schunk and Lisa Mondy provided helpful feedback. Randy Schunk also helped with our droplet-scale modeling in a moving reference frame. The Aria Product Owners past and present, Amalia Black, Sheldon Tieszen, and Kim Mish, have been invaluable for keeping the project going despite the many other directions of Sierra Mechanics. We would like to thank the "Enabling Predictive Simulations" investment area of the LDRD program for funding this work. We would like to express our gratitude to the LDRD office for the extension given for receiving the final report due to the illness of the PI.6

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A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion

Cited by 46 publications

References 0 publications

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

Multiscale models of nuclear waste reprocessing : from the mesoscale to the plant-scale.

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