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Solution of the axisymmetric inverse problem by higher‐order line doublets
Author(s) -
Zedan M. F.
Publication year - 1994
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650180406
Subject(s) - rotational symmetry , inverse , singularity , matrix (chemical analysis) , convergence (economics) , mathematical analysis , mathematics , order (exchange) , line (geometry) , distribution (mathematics) , gravitational singularity , node (physics) , geometry , physics , materials science , acoustics , composite material , finance , economics , economic growth
The axial singularity inverse method for designing bodies of revolution has been improved by using higher‐order doublet elements. The performance of the method for various element orders and other solution parameters is presented in detail. The results indicate that the method is generally more robust, less sensitive to insets and has a better‐conditioned coefficient matrix compared with the source method of the same order. The condition number of the matrix is shown to increase with the thickness of the body, the order of the method, the number of elements and the degree of stretching of the node distribution. In general, good performance is attained for most bodies even with ƒ r as low as 2 by using 10–12 second‐order doublet elements with insets greater than 0.02 L from rounded ends. Increasing the insets to 0.06 L appears to improve the accuracy of the method for most bodies but slows its convergence.