Hyperbolic Methods for Surface and Field Grid Generation

Chan, William

doi:10.1201/9781420050349.ch5

Cited by 15 publications

(14 citation statements)

References 18 publications

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“…(6)- (9). The basic elements of pattern formation for a gas bubble expanding into a Newtonian fluid in a radial Hele-Shaw cell are well understood from experiment [30], theory [3,37] and careful numerical simulation [21].…”

Section: Simulation Of the Saffman-taylor Instabilitymentioning

confidence: 99%

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A moving overset grid method for interface dynamics applied to non-Newtonian Hele–Shaw flow

Fast

Shelley

2004

Journal of Computational Physics

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Section: Simulation Of the Saffman-taylor Instabilitymentioning

confidence: 99%

“…6). Hyperbolic grid generation [9] is often used to produce such grids around complicated geometries. In the present case, a simpler approach can be used.…”

Section: Body Fitted Grid Generationmentioning

confidence: 99%

A moving overset grid method for interface dynamics applied to non-Newtonian Hele–Shaw flow

Fast

Shelley

2004

Journal of Computational Physics

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“…This value can be used in the construction of the system of linear equations. However, the smoothness of the grid can be enhanced by taking a weighted average of the volume computed for the neighbouring vertices, as [36] …”

Section: Cell Volume and Grid Spacingmentioning

confidence: 99%

“…Following the method first proposed by Kinsey et al [98] for 2D hyperbolic grids and later on extended by Chan [36,39] to 3D hyperbolic grids, the partial derivative with respect to ζ is discretized using an implicit weighted average method. After approximate factorization and the introduction of numerical dissipation to both the implicit part as well as the right hand side, the discrete equations read…”

Section: Spatial Discretizationmentioning

confidence: 99%

“…A significant contribution to developing the concept of zipper grids -used for the accurate evaluation of surface integrals -was done by Chan [37]. Chan also carried out much research on the subject of hyperbolic grid generation [36,39]. That work was based on the work of Steger [176,177], who introduced the concept of hyperbolic grid generation.…”

Section: Introductionmentioning

confidence: 99%

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O a method for simulation-based wind turbine blade design

Jongsma¹

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SummaryW ind turbines are an important means for the production of renewable energy. This energy, commonly referred to as wind energy, is produced by extracting the kinetic energy from the wind and to subsequently convert it, usually via a rotational motion, to electrical energy. Wind conditions vary from one site to another and the design of a horizontal axis wind turbine depends on these local wind conditions. One of the important aspects of the design of a wind turbine concerns the aerodynamic shape of the rotor blades. The research presented in this thesis focusses on the development of a computational method that can be used for aerodynamic shape optimization.Other aspects -apart from the aerodynamic shape of a wind turbine rotor bladeare also important in the design of a wind turbine, for instance the structural design of the blade. To take this multidisciplinary character of wind turbine design into account, one of the aims of the research presented in this thesis has been that the aerodynamic shape optimization method seamlessly fits into the design process. Moreover, the optimization method is required to be efficient and fully automatic.A suitable method for the parametrization of the wind turbine blade geometry has been investigated. This investigation lead to the choice to use a non-uniform rational basis spline (NURBS) surface for representing the aerodynamic shape of the wind turbine blade. Such a description of the parametrization of the geometry is compatible with computer aided design methods, which eases the incorporation of the aerodynamic shape optimization method in the multidisciplinary design process. A model optimization problem has been considered to determine the relation between the number of design variables that is required to sufficiently accurately represent the design space for solving an aerodynamic shape optimization problem to the number of design variables that is required to realize an accurate NURBS representation of an aerodynamic shape. For the purpose of obtaining a NURBS surface representation of a wind turbine rotor blade, a fitting procedure has been developed. The accuracy of the resulting fit for two representative wind turbine blades is presented. It has been found that sufficient accuracy can be achieved with a NURBS surface described by 13 chordwise sections with 13 control points each.In the present research, objective functions are considered for which the evaluation requires the solution of partial differential equations that govern flow: the Euler equations. Since only for very particular flow configurations an analytical solution of these equations can be found, an approximate solution is computed by solving the discretized equations. Solving the discretized Euler equations requires the discretization of the whole flow domain. During the optimization procedure, the geometry of the rotor blade adapts, i Summary requiring a discrete representation of the new flow domain. To accommodate the change in shape during the optimization, a hyperbolic grid generation me...

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Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

Amini-Afshar

Bingham

2017

Applied Ocean Research

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Hyperbolic Methods for Surface and Field Grid Generation

Cited by 15 publications

References 18 publications

A moving overset grid method for interface dynamics applied to non-Newtonian Hele–Shaw flow

A moving overset grid method for interface dynamics applied to non-Newtonian Hele–Shaw flow

O a method for simulation-based wind turbine blade design

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

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