An Edge-Based Method for the Incompressible Navier–Stokes Equations on Polygonal Meshes

Wright, Jeffrey; Smith, Richard W.

doi:10.1006/jcph.2001.6705

Cited by 60 publications

(31 citation statements)

References 23 publications

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“…The governing equations for the fluid given by equation (2.2) are solved using an in-house three-dimensional, unstructured, pressure-based finite volume solver [34,35] written in a rulebased framework [36]. The geometric conservation law [37] is satisfied [38].…”

Section: Numerical Modelsmentioning

confidence: 99%

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Kang

Shyy

2013

J. R. Soc. Interface.

164

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We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier-Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid-structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing-wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.

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Section: Numerical Modelsmentioning

confidence: 99%

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Kang

Shyy

2013

J. R. Soc. Interface.

164

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“…is evaluated using the trapezoidal rule in conjunction with a linear reconstruction [7,9,10] of the velocity based on the upwind value of v and it's gradient v∇. Sampling the edge mass ux, f e , at the edge midpoint yields…”

Section: Convective Uxmentioning

confidence: 99%

“…An implicit multi-stage time integrator is constructed that is GCL compliant to the precision of the arithmetic used in the computation and is shown to be second-order-accurate in time for an arbitrarily deforming mesh. As in Reference [7], the use of a staggered grid system eliminates the need for ad hoc modiÿcations to suppress a checkerboard pressure ÿeld as well as the need to prescribe a boundary condition for pressure. Other aspects of the basic method on ÿxed grids, as well as a brief discussion of other related edge-based ÿnite volume methods can be found in Reference [7].…”

Section: Introductionmentioning

confidence: 99%

“…As in Reference [7], the use of a staggered grid system eliminates the need for ad hoc modiÿcations to suppress a checkerboard pressure ÿeld as well as the need to prescribe a boundary condition for pressure. Other aspects of the basic method on ÿxed grids, as well as a brief discussion of other related edge-based ÿnite volume methods can be found in Reference [7]. Here, the method is ÿrst evaluated using several well-known unsteady incompressible Navier-Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem.…”

Section: Introductionmentioning

confidence: 99%

“…Here, a recently developed edge-based ÿnite volume method [7] for the incompressible Navier-Stokes equations is revised and extended to admit a time-dependent mesh. An implicit multi-stage time integrator is constructed that is GCL compliant to the precision of the arithmetic used in the computation and is shown to be second-order-accurate in time for an arbitrarily deforming mesh.…”

Section: Introductionmentioning

confidence: 99%

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An implicit edge‐based ALE method for the incompressible Navier–Stokes equations

Smith

Wright

2003

Numerical Methods in Fluids

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SUMMARYA new ÿnite volume method for the incompressible Navier-Stokes equations, expressed in arbitrary Lagrangian-Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is ÿrst evaluated using several well-known unsteady incompressible Navier-Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in

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A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

Şahin

2005

Numerical Methods in Fluids

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SUMMARYA new semi-staggered ÿnite volume method is presented for the solution of the incompressible NavierStokes equations on all-quadrilateral (2D)=hexahedral (3D) meshes. The velocity components are deÿned at element node points while the pressure term is deÿned at element centroids. The continuity equation is satisÿed exactly within each elements. The checkerboard pressure oscillations are prevented using a special ÿltering matrix as a preconditioner for the saddle-point problem resulting from second-order discretization of the incompressible Navier-Stokes equations. The preconditioned saddle-point problem is solved using block preconditioners with GMRES solver. In order to achieve higher performance FORTRAN source code is based on highly e cient PETSc and HYPRE libraries. As test cases the 2D=3D lid-driven cavity ow problem and the 3D ow past array of circular cylinders are solved in order to verify the accuracy of the proposed method.

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An Edge-Based Method for the Incompressible Navier–Stokes Equations on Polygonal Meshes

Cited by 60 publications

References 23 publications

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

An implicit edge‐based ALE method for the incompressible Navier–Stokes equations

A preconditioned semi‐staggered dilation‐free finite volume method for the incompressible Navier–Stokes equations on all‐hexahedral elements

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