Computational Methods for Fluid Dynamics

Ferziger, Joel H.; Perić, Milovan

doi:10.1007/978-3-642-56026-2

Cited by 3,103 publications

(2,217 citation statements)

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“…For this reason, it is convenient to solve for the concentrations of membrane molecules at exactly the same points, because it facilitates coupling with the volume variables. Even though the points {r i } do not necessarily lie on S, our algorithm uses these points to approximate the solution of Eq (1) on S. We utilize a finite volume discretization scheme, which is used frequently in transport problems and guarantees that numerical errors do not violate mass conservation [18].…”

Section: Diffusion On a Curved Surfacementioning

confidence: 99%

“…The solution error relates to the truncation error through the equation [18], (6) The solution of Eq (6) can be written as a convolution of the truncation error with a smooth non-negative Green's function ψ, (7) The terms summed in (7) are significantly non-zero in the region of the size centered at the i-th node. For Dt>>h 2 , the sum in (7) contains a large number of terms with alternating signs, which makes it possible for the solution error to become convergent 2 .…”

Section: Convergence Studiesmentioning

confidence: 99%

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Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology

Novak

Gao

Choi

et al. 2007

Journal of Computational Physics

106

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An algorithm is presented for solving a diffusion equation on a curved surface coupled to diffusion in the volume, a problem often arising in cell biology. It applies to pixilated surfaces obtained from experimental images and performs at low computational cost. In the method, the Laplace-Beltrami operator is approximated locally by the Laplacian on the tangential plane and then a finite volume discretization scheme based on a Voronoi decomposition is applied. Convergence studies show that mass conservation built in the discretization scheme and cancellation of sampling error ensure convergence of the solution in space with an order between 1 and 2. The method is applied to a cellbiological problem where a signaling molecule, G-protein Rac, cycles between the cytoplasm and cell membrane thus coupling its diffusion in the membrane to that in the cell interior. Simulations on realistic cell geometry are performed to validate, and determine the accuracy of, a recently proposed simplified quantitative analysis of fluorescence loss in photobleaching. The method is implemented within the Virtual Cell computational framework freely accessible at www.vcell.org.

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Section: Diffusion On a Curved Surfacementioning

confidence: 99%

Section: Convergence Studiesmentioning

confidence: 99%

Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology

Novak

Gao

Choi

et al. 2007

Journal of Computational Physics

106

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“…a foot kick or arm movement in swimming), even with a very low magnitude [50,51]. Each action a swimmer performs will, therefore, perturb fluid flows, which will in turn induce changes in surrounding energy flows, providing new perceptual information about the performance environment.…”

Section: Fluid Perturbations From Swimmer's Movementmentioning

confidence: 99%

Individual–Environment Interactions in Swimming: The Smallest Unit for Analysing the Emergence of Coordination Dynamics in Performance?

et al. 2017

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Displacement in competitive swimming is highly dependent on fluid characteristics, since athletes use these properties to propel themselves. It is essential for sport scientists and practitioners to clearly identify the interactions that emerge between each individual swimmer and properties of an aquatic environment. Traditionally, the two protagonists in these interactions have been studied separately. Determining the impact of each swimmer's movements on fluid flow, and vice versa, is a major challenge. Classic biomechanical research approaches have focused on swimmers' actions, decomposing stroke characteristics for analysis, without exploring perturbations to fluid flows. Conversely, fluid mechanics research has sought to record fluid behaviours, isolated from the constraints of competitive swimming environments (e.g. analyses in two-dimensions, fluid flows passively studied on mannequins or robot effectors). With improvements in technology, however, recent investigations have focused on the emergent circular couplings between swimmers' movements and fluid dynamics. Here, we provide insights into concepts and tools that can explain these on-going dynamical interactions in competitive swimming within the theoretical framework of ecological dynamics. 3 Key points Swimming movements are characterised by continuous interactions between individuals and the aquatic environment: water is essential to progression, yet it also acts as a brake on swimmers' displacement.  Ecological dynamics is a theoretical framework that provides concepts and tools to investigate the continuous coupling of performers and the performance environment in swimming, providing an indivisible entity for analysis.  Key ideas in ecological dynamics (constraints and affordances) are highlighted to help coaches to design representative practice contexts for athletes that simulate competitive performance environments in swimming.4

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“…The methods proposed for the numerical representation of the interface, can be classified into two categories, namely the surface methods and the volume methods, see [11]. The surface methods consider the interface itself as an object, either explicitly or implicitly.…”

Section: An Overview On the Numerical Techniques For Simulating The Imentioning

confidence: 99%

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

Mousavi¹,

Kummer²,

Oberlack³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Computational Methods for Fluid Dynamics

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 3,103 publications

References 0 publications

Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology

Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology

Individual–Environment Interactions in Swimming: The Smallest Unit for Analysing the Emergence of Coordination Dynamics in Performance?

Level Set Method for Simulating the Interface Kinematics: Application of a Discontinuous Galerkin Method

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