Skip to main content
Log in

Distributions of sources and normal dipoles over a quadrilateral panel

  • Published:
Journal of Engineering Mathematics Aims and scope Submit manuscript

Summary

The potential due to a distribution of sources or normal dipoles on a flat quadrilateral panel is evaluated for the cases where the density of the singularities is constant, linear, bilinear, or of arbitrary polynomial form. The results in the first two cases are consistent with those derived previously, but the present derivation is considered to be simplified. In particular, the constant dipole distribution is derived from a geometric argument which avoids direct integration; this derivation applies more generally on a curvilinear panel bounded by straight edges.

Also presented are multipole expansions for the same potentials, suitable for use when the distance to the field point is substantially larger than the panel dimensions. Algorithms are derived to evaluate the coefficients in these expansions to an arbitrary order.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. HessJ.L. and SmithA.M.O.,Calculation of non-lifting potential flow about arbitrary three-dimensional bodies, Report No. E.S. 40622, Douglas Aircraft Company, Inc., Long Beach, CA (1962).

    Google Scholar 

  2. HessJ.L. and SmithA.M.O., Calculation of non-lifting potential flow about arbitrary three-dimensional bodies,J. Ship Res. 8, 2 (1964) 22–44.

    Google Scholar 

  3. HessJ.L. and SmithA.M.O., Calculation of potential flow about arbitrary bodies,Progress in Aero. Sci. 8 (1966) 1–138.

    Google Scholar 

  4. YeungR.W.,A singularity-distribution method for free-surface flow problems with an oscillating body, Report No. NA 73–6, College of Eng'g., Univ. of Cal., Berkeley (1973). (See also Bai, K.J., and Yeung, R.W., Numerical solutions to free-surface flow problems,Proc. 10th Symp. Naval Hydro. (1974) 631–633).

    Google Scholar 

  5. WebsterW.C., The flow about arbitrary three-dimensional smooth bodies,J. Ship Res. 19, 4 (1975) 206–218.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Newman, J.N. Distributions of sources and normal dipoles over a quadrilateral panel. J Eng Math 20, 113–126 (1986). https://doi.org/10.1007/BF00042771

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00042771

Keywords

Navigation