Geodesic
Transonic flow calculation via finite elements
Applications of Mathematics, Tome 33 (1988) no. 4, pp. 296-321
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Using new results based on a convenient entropy condition, two types of algorithms for computing transonic flows are constructed. A sequence of solutions of the linearised problem with a posteriori control is constructed and its convergence to the physical solution of transonic flow in some special situations is proved. This paper contains also numerical results and their analysis for the case of flow past NACA 230012 airfoil. Some numerical improvements of the general algorithms, based on our practical experience with this problem, are also included.
Using new results based on a convenient entropy condition, two types of algorithms for computing transonic flows are constructed. A sequence of solutions of the linearised problem with a posteriori control is constructed and its convergence to the physical solution of transonic flow in some special situations is proved. This paper contains also numerical results and their analysis for the case of flow past NACA 230012 airfoil. Some numerical improvements of the general algorithms, based on our practical experience with this problem, are also included.
DOI : 10.21136/AM.1988.104311
Classification : 65N30, 76-08, 76H05, 76M99
Keywords: finite elements; entropy condition; transonic flow; a posteriori control; NACA 230012 airfoil 
@article{10_21136_AM_1988_104311,
     author = {Klou\v{c}ek, Petr and M\'alek, Josef},
     title = {Transonic flow calculation via finite elements},
     journal = {Applications of Mathematics},
     pages = {296--321},
     year = {1988},
     volume = {33},
     number = {4},
     doi = {10.21136/AM.1988.104311},
     mrnumber = {0949251},
     zbl = {0657.76057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104311/}
}
TY  - JOUR
AU  - Klouček, Petr
AU  - Málek, Josef
TI  - Transonic flow calculation via finite elements
JO  - Applications of Mathematics
PY  - 1988
SP  - 296
EP  - 321
VL  - 33
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104311/
DO  - 10.21136/AM.1988.104311
LA  - en
ID  - 10_21136_AM_1988_104311
ER  - 
%0 Journal Article
%A Klouček, Petr
%A Málek, Josef
%T Transonic flow calculation via finite elements
%J Applications of Mathematics
%D 1988
%P 296-321
%V 33
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104311/
%R 10.21136/AM.1988.104311
%G en
%F 10_21136_AM_1988_104311
Klouček, Petr; Málek, Josef. Transonic flow calculation via finite elements. Applications of Mathematics, Tome 33 (1988) no. 4, pp. 296-321. doi: 10.21136/AM.1988.104311

[1] M. Feistauer J. Nečas: On the solvability of transonic potential flow problems. Zeitschrift für Analysis und ihre Anwendungen, Bd. 4(4) 1985, 305-329. | MR

[2] J. Mandel J. Nečas: Convergence of finite elements for transonic potential flow. Preprint, Charles University, Prague, May 1986. | MR

[3] G. Poirier: Traitements numeriques en elements finis de la condition d'entropie des equations transsoniques. These, L'universite et Marie Curie, 1981.

[4] E. Polak: Computational methods in optimization. Academic Press, New York, 1971. | MR

[5] R. Glowinski: Numerical methods for nonlinear variational problems. New York, Berlin, Heidelberg, Tokyo, 1984. | MR | Zbl

[6] J. Nečas I. Hlaváček: Mathematical theory of elastic and elastico-plastic bodies: An introduction. Elsevier North-Holland, Inc., 1981. | MR

Cité par Sources :