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Medientyp: E-Artikel Titel: Treatment of Neumann boundaries in the complex variable boundary element method Beteiligte: Sato, Kozo; Watanabe, Yusuke Erschienen: Wiley, 2004 Erschienen in: Communications in Numerical Methods in Engineering Sprache: Englisch DOI: 10.1002/cnm.654 ISSN: 1069-8299; 1099-0887 Schlagwörter: Applied Mathematics ; Computational Theory and Mathematics ; General Engineering ; Modeling and Simulation ; Software Entstehung: Anmerkungen: Beschreibung: <jats:title>Abstract</jats:title><jats:p>For potential flow, the complex variable boundary element method (CVBEM) is formulated in terms of the velocity potential Φ and the stream function Ψ. In actual flow problems, Φ and ∂Φ/∂n are given along Dirichlet and Neumann boundaries, respectively. In the CVBEM, the Neumann‐type condition ∂Φ/∂n is not directly handled, and, instead, Ψ is used to define Neumann boundaries. Owing to this discrepancy, numerical difficulties are raised along Neumann boundaries. The current study addresses two such difficulties: (1) multiple Neumann boundaries and (2) branch cuts across Neumann boundaries. The first problem is due to the fact that Ψ along multiple boundaries cannot be specified <jats:italic>a priori</jats:italic>, and the second problem is due to the discontinuous jump inherent in Ψ for sink/source singularities. To overcome these difficulties, a new formulation of the CVBEM to solve for the unknown Ψ values and a proper way of branch‐cut placement are proposed, and these techniques are verified against example problems. Copyright © 2004 John Wiley & Sons, Ltd.</jats:p>