The numerical solution of the Navier-Stokes equations for laminar, incompressible flow past a parabolic cylinder

Botta, E. F. F.; Dijkstra, D.; Veldman, Arthur

doi:10.1007/bf01535240

Cited by 18 publications

(13 citation statements)

References 6 publications

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“…* =@y * ¡0 at the wall (x * ¿0; y * = 0). This result is similar to that of Botta and Dijkstra [8], which was also obtained based on the Navier-Stokes equations. This non-zero gradient, @!…”

Section: Results For the Ow ÿEldsupporting

confidence: 89%

“…It is noted that the in uence of the expansion order m on the leading coe cient A is small. The present results for this coe cient agree very well with the value calculated by Botta and Dijkstra [8], with a di erence being less than 0.6%. In comparison, the result from the Blasius solution is about 12.5% smaller than the present values.…”

Section: Development Of the Boundary Layer Owsupporting

confidence: 90%

“…In contrast to A, the results obtained for B (= 12 A 2 ) vary in a wider range with varying expansion orders m. Nevertheless, the e ect of this variation on the skin friction is not of [34] 1.128 -Dean [35] 0.796 -Davies [36] 0.779 -Yoshizawa [37] 0.748 0.044 Botta and Dijkstra [8] 0 signiÿcance, considering that the total contribution of the second term is minor at Re x 60:1, according to the quantitative evaluation discussed above.…”

Section: Development Of the Boundary Layer Owmentioning

confidence: 58%

“…Substituting Equation (10) into Equation (8), one obtains the following equation for the function f i (Â) in the case i = ∈ {−1; 0; 1},…”

Section: Local Expansion Around the Leading Edgementioning

confidence: 99%

“…One of them is the conformal transformation. For example, Botta and Dijkstra [8] successfully applied this technique to treat the leading-edge singularity of a semi-inÿnite plate. Nevertheless, a suitable transformation is not always available in practice.…”

Section: Introductionmentioning

confidence: 98%

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A combined analytical–numerical method for treating corner singularities in viscous flow predictions

Shi

Breuer

Durst

2004

Numerical Methods in Fluids

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SUMMARYA combined analytical-numerical method based on a matching asymptotic algorithm is proposed for treating angular (sharp corner or wedge) singularities in the numerical solution of the Navier-Stokes equations. We adopt an asymptotic solution for the local ow around the angular points based on the Stokes ow approximation and a numerical solution for the global ow outside the singular regions using a ÿnite-volume method. The coe cients involved in the analytical solution are iteratively updated by matching both solutions in a small region where the Stokes ow approximation holds. Moreover, an error analysis is derived for this method, which serves as a guideline for the practical implementation. The present method is applied to treat the leading-edge singularity of a semi-inÿnite plate. The e ect of various in uencing factors related to the implementation are evaluated with the help of numerical experiments. The investigation showed that the accuracy of the numerical solution for the ow around the leading edge can be signiÿcantly improved with the present method. The results of the numerical experiments support the error analysis and show the desired properties of the new algorithm, i.e. accuracy, robustness and e ciency. Based on the numerical results for the leading-edge singularity, the validity of various classical approximate models for the ow, such as the Stokes approximation, the inviscid ow model and the boundary layer theory of varying orders are examined. Although the methodology proposed was evaluated for the leading-edge problem, it is generally applicable to all kinds of angular singularities and all kinds of ÿnite-discretization methods.

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Section: Results For the Ow ÿEldsupporting

confidence: 89%

Section: Development Of the Boundary Layer Owsupporting

confidence: 90%