Variational boundary integral approach for asymmetric impinging jets of arbitrary two-dimensional nozzle

Sung Sic Yoo, Wing Kam Liu, Do Wan Kim*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider asymmetric impinging jets issuing from an arbitrary nozzle. The flow is assumed to be two-dimensional, inviscid, incompressible, and irrotational. The impinging jet from an arbitrary nozzle has a couple of separated infinite free boundaries, which makes the problem hard to solve. We formulate this problem using the stream function represented with a specific single layer potential. This potential can be extended to the surrounding region of the jet flow, and this extension can be proved to be a bounded function. Using this fact, the formulation yields the boundary integral equations on the entire nozzle and free boundary. In addition, a boundary perturbation produces an extraordinary boundary integral equation for the boundary variation. Based on these variational boundary integral equations, we can provide an efficient algorithm that can treat with the asymmetric impinging jets having arbitrarily shaped nozzles. Particularly, the proposed algorithm uses the infinite computational domain instead of a truncated one. To show the convergence and accuracy of the numerical solution, we compare our solutions with the exact solutions of free jets. Numerical results on diverse impinging jets with nozzles of various shapes are also presented to demonstrate the applicability and reliability of the algorithm.

Original languageEnglish (US)
Pages (from-to)193-216
Number of pages24
JournalInternational Journal for Numerical Methods in Fluids
Issue number4
StatePublished - Oct 10 2018


  • arbitrary nozzle
  • free boundary
  • impinging jets
  • infinite computational domain
  • potential flow
  • variational boundary integral equations

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Computer Science Applications
  • Applied Mathematics

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