Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

Davis, Robert T.

doi:10.1017/s0022112072002265

Cited by 85 publications

(64 citation statements)

References 9 publications

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“…Indeed, as pointed out by Gresho, nearly thirty years ago Davis [17] formulated a streamfunctionvorticity method based on finite differences that implicitly discarded the need for any boundary conditions on vorticity. A little later, Barrett [2] and Campion-Renson and Crochet [7] independently also proposed streamfunction-vorticity methods, this time based on finite elements, in which no boundary condition is imposed on vorticity.…”

Section: Introductionmentioning

confidence: 99%

A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

Davies¹,

Carpenter

2001

Journal of Computational Physics

113

114

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Section: Introductionmentioning

confidence: 99%

A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

Davies¹,

Carpenter

2001

Journal of Computational Physics

113

114

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“…Davis [11] has shown that the viscous solution for ow past a parabola approaches the Blasius solution as → ∞. The reader is referred to References [11,9] for more details. The impact of the Prandtl transposition can be clearly seen as the roughness perturbations on the base geometry become embedded in the governing equations.…”

Section: Governing Equationsmentioning

confidence: 99%

A novel method for automated grid generation of ice shapes for local‐flow analysis

Ogretim

Huebsch

2004

Numerical Methods in Fluids

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SUMMARYModelling a complex geometry, such as ice roughness, plays a key role for the computational ow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local ow analysis over an aerodynamic surface. The ÿrst enhancement is use of the leading-edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors a ecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine-cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational ow ÿeld analysis around airfoils with ice roughness.

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“…The boundary conditions most frequently associated with (26), (27) come from the specification of the velocity vector u on the boundary S of a flow domain V. Since the velocity vector has Cartesian components (a$/ay, -a$/dx), we can determine from the specification of u the two conditions…”

Section: Applications To Two-dimensional Equationsmentioning

confidence: 99%

“…As we have already mentioned, the boundary conditions (28) pose a problem in the solution of (26), (27) in that two conditions are specified for J/ and none for 5. In previous sections it has been demonstrated how this overspecification can be overcome by the use of integral conditions of onedimensional character.…”

Section: Applications To Two-dimensional Equationsmentioning

confidence: 99%

Some uses of Green's theorem in solving the Navier–Stokes equations

Dennis

Quartapelle

1989

Numerical Methods in Fluids

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SUMMARYThis paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier-Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier-Stokes equations are considered: that in terms of the streamfunction and vorticity for two-dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two-dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two-dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two-dimensional flows in both of the mentioned formulations and a numerical illustration is given.

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Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

Cited by 85 publications

References 9 publications

A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

A Novel Velocity–Vorticity Formulation of the Navier–Stokes Equations with Applications to Boundary Layer Disturbance Evolution

A novel method for automated grid generation of ice shapes for local‐flow analysis

Some uses of Green's theorem in solving the Navier–Stokes equations

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