An adaptive method for treat number-sequences occurring in lifting surface calculations. (English) Zbl 0541.76079
In lifting surface calculations, assessment of convergence characteristics of number-sequences is a difficult task. A formulation is proposed here to achieve automatically and without iteration a specified accuracy. This saves computation time, and may be termed an ’adaptive method’. A new method of chordwise quadrature, ’TrTr-NONEQ’, is presented as a model. This model indicates that the general formulation is reasonable. In addition, TrTr-NONEQ exhibits many advantages over other current methods such as those of Wagner, Gauss and Cunningham.
MSC:
| 76G25 | General aerodynamics and subsonic flows |
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
Keywords:
lifting surface calculations; convergence characteristics of number- sequences; adaptive method; chordwise quadratureReferences:
| [1] | Terazawa, K., Mathematics for Scientists and Engineers (1970), Iwanami: Iwanami Tokyo, (in Japanese). |
| [2] | S. Ando and D.H. Lee, An automatic adaptive numerical method for lifting surface theories, submitted to AIAA J.; S. Ando and D.H. Lee, An automatic adaptive numerical method for lifting surface theories, submitted to AIAA J. · Zbl 0547.76014 |
| [3] | Wagner, S., On the singularity method of subsonic lifting-surface theory, J. Aircraft, 6, 6, 549-558 (1969) |
| [4] | Hildebrand, F. B., Introduction to Numerical Analysis (1956), McGraw-Hill: McGraw-Hill New York · Zbl 0070.12401 |
| [5] | Ninomiya, I., Improvements of adaptive Newton-Cotes quadrature method, J. Inform. Process., 3, 3, 162-170 (1980) |
| [6] | Lee, D. H.; Asami, K.; Ando, S., Comparative study between various quadratures of chordwise integrals for subsonic lifting surfaces, J. Japan Soc. Aeronautical & Space Sci., 31, 348, 43-52 (1983), (in Japanese). |
| [7] | Cunningham, A. M., An effective steady subsonic collocation method for solving lifting-surface problems, J. Aircraft, 8(3), 168-176 (1971) |
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