On the treatment of the Kutta-Joukowski condition in transonic flow computations

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 79, Issue 8, 1999, Pages 507-534

  Coclici, C A ^a   Wendland, W L ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Boundary elements; Finite elements; Generalized analytic functions; Kutta Joukowski condition and stress intensity factor; Transonic full potential equation

Indexed keywords

EID: 33748045479     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/(SICI)1521-4001(199908)79:8<507::AID-ZAMM507>3.0.CO;2-B     Document Type: Article

References (52)

1. ADAMS, R. A.: Sobolev spaces. Academic Press, Boston 1978.
2. BABUŠKA, I.; AZIZ, A. K.: Survey lectures on the mathematical foundations of the finite element method. In: AZIZ, A. K. (ed.): The mathematical foundation of the finite element method with applications to partial differential equations. Academic Press, New York 1972, pp. 3-359.
3. BASSANINI, P.; CASCIOLA, C. M.; LANCIA, M. R.; PIVA, P.: On the removal of the trailing edge singularity in 3D flows. In: MORINO, L.; WENDLAND, W. L. (eds.): Boundary integral methods for nonlinear problems. Kluwer Acad. Publ., Dordrecht, Holland, 1997, pp. 1-7.
4. BASSANINI, P.; CASCIOLA, C. M.; LANCIA, M. R.; PIVA, R.: On the trailing edge singularity and Kutta condition for 3D flows. Eur. J. Mech. B/Fluids 15 (1996), 809-830.
5. BECKER, E. B.; CAREY, G. F.; ODEN, J. T.: Finite elements. Vol. VI: Fluid mechanics. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1984.
6. BERGER, H.: Finito-Element-Approximationen für transsonische Strömungen. Doctoral Thesis, Universität Stuttgart, Germany, 1989.
7. BERGER, H.: A convergent finite element formulation for transonic flows. Numer. Math. 56 (1989), 425-447.
8. BERGER, H.; FEISTAUER, M.: Analysis of the finite element variational crimes in the numerical approximation of transonic flow. Math. Comp. 61 (1993), 493-521.
9. BERGER, H.; WARNECKE, G.; WENDLAND, W. L.: Finite Element-Berechnungen für transsonische Strömungen unter Berücksichtigung verschiedener Fernfeldrandbedingungen. In: Strömungen mit Ablösungen, DGLR-Bericht 88-05. Bonn 1988, pp. 233-242.
10. BERGER, H.; WARNECKE, G.; WENDLAND, W. L.: Finite elements for transonic potential flows. Numer. Meth. Part. Diff. Eqns. 6 (1990), 17-42.
11. BERGER, H.; WARNECKE, G.; WENDLAND, W. L.: Analysis of a FEM/BEM coupling method for transonic flow computations. Math. Comp. 66 (1997), 1407-1440.
12. BERS, L.: Existence and uniqueness of subsonic flow past a given profile. Commun. Pure Appl. Math. 7 (1954), 441-504.
13. BERS, L.: Mathematical aspects of subsonic and transonic gas dynamics. In: Surveys in Applied Mathematics III. Wiley, New York 1958.
14. BLUM, H.: Numerical treatment of corner and crack singularities. In: STEIN, E.; WENDLAND, W. L. (eds.): Finite element and boundary element techniques from mathematical and engineering point of view. CISM Courses and Lectures No. 301. Springer-Verlag, Vienna-New York 1987, pp. 171-211.
15. BOJARSKI, B.: Subsonic flow of compressible fluid. In: The Mathematical Problems in Fluid Mechanics. Institute of Basic Technical Problems, Polish Academy of Sciences, Warsaw 1967, pp. 9-31.
16. BOJARSKI, B.: Homeomorphic solutions of Beltrami systems. Dokl. Akad. Nauk 102 (1955), 661-664.
17. BOJARSKI, B.: Generalized solutions of a system of differential equations of the first order, of elliptic type, with discontinuous coefficients. Matem. Sbornik 43 (1957), 451-503.
18. BRISTEAU, M. O.; GLOWINSKI, R.; PERIAUX, J.; PERRIER, P.; PIRONNEAU, O.; POIRIER, G.: Application of optimal control and finite element methods to the calculation of transonic flows and incompressible flows. In: HUNT, B. (ed.): Numerical Methods in Applied Fluid Dynamics. Academic Press, New York 1980, pp. 203-312.
19. BRISTEAU, M. O.; GLOWINSKI, R.; PERIAUX, J.; PERRIER, P.; PIRONNEAU, O.; POIRIER, G.: On the numerical solution of nonlinear problems in fluid dynamics by least squares and finite element methods. II. Application to transonic flow simulations. Comput. Methods Appl. Mech. Engrg. 51 (1985), 363-394.
20. CHAPLYGIN, S. A.: On gas jets. Scientific memoirs, Imperial University of Moskow, Mathematical-Physical Section 21 (1902), 1-21 (English Translation, National Advisory Committee for Aeronautics, Technical Memo No. 1063, 1944).
21. CARLEMAN, T.: Sur les systèmes linéaires aux dérivées partielles du premier ordre à deux variables. Comptes Rendus des Séances de l'Académie des Sciences, Paris 18 (1933), 471-474.
22. CIARLET, P. G.: The finite element method for elliptic problems, North-Holland, Amsterdam 1978.
23. CIAVALDINI, J. F.; POGU, M.; TOURNEMINE, G.: Existence and regularity of stream functions for subsonic flows past profiles with a sharp trailing edge. Arch. Rat. Mech. Anal. 93 (1986), 1-14.
24. COSTABEL, M.: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19 (1988), 613-626.
25. DJAOUA, M.: A method of calculation of lifting flows around two-dimensional corner-shaped bodies. Math. Comp. 36 (1981), 405-425.
26. FEISTAUER, M.; FELCMAN, J.; ROKYTA, M.; Vlášek, Z.: Finite-element solution of flow problems with trailing edge conditions. J. Comp. Appl. Math. 44 (1992), 131-165.
27. FEISTAUER, M.; NEČAS, J.: On the solvability of transonic potential flow problems. Z. Anal. Anw. 4 (1985), 305-329.
28. FEISTAUER, M.; ŽENÍŠEK, A.: Finite element solution of nonlinear elliptic problems. Numer. Math. 50 (1987), 451-475.
29. FRANKL, F. I.; KELDYSH, Y: Die äussere Neumann'sche Aufgabe für nichtlincare elliptische Differentialgleichungen mit Anwendung auf die Theorie der Flügel im kompressiblen Gas. Bull. Acad. Sci., URSS 12 (1934), 561-607.
30. GATICA, G. N.; HSIAO, G. C.: The coupling of boundary element and finite element methods for a nonlinear exterior boundary value problem. Numer. Math. 61 (1992), 171-214.
31. GLOWINSKI, R.; PIRONNEAU, O.: On the computation of transonic flows. In: FUJITA, H. (ed.): Funct. Anal. and Num. Anal., Jap. Soc. Prom. Sci., Tokyo-Kyoto 1978, pp. 143-173.
32. GÖHNER, U.; WARNECKE, G.: A shock indicator for adaptive transonic flow computations. Numer. Math. 66 (1994), 423-448.
33. GÖHNER, U.; WARNECKE, G.: A second order finite difference error indicator for adaptive transonic flow computations. Numer. Math. 70 (1995), 129-161.
34. GRISVARD, P.: Elliptic problems in nonsmooth domains. Pitman Publ., London 1985.
35. HSIAO, G. C.; MARCOZZI, M. D.; ZHANG, S.: An efficient computational method for the flow past an airfoil. Contemporary Math. 180 (1994), 497-502.
36. HSIAO, G. C.; KOPP, P.; WENDLAND, W. L.: Some applications of a Galerkin-collocation method for boundary integral equations of the first kind. Math. Methods Appl. Sci. 6 (1984), 280-325.
37. HSIAO, G. C.; WENDLAND, W. L.: A finite element method for an integral equation of the first kind. J. Math. Anal. Appl. 58 (1977), 449-481.
38. JAENICKE, J.: Über lineare Randwertprobleme der Systeme von zwei linearen partiellen Differentialgleichungen erster Ordnung vom elliptischen Typus. Doctoral Thesis, Technische Universität Berlin, Germany, 1957.
39. KEYFITZ, B. L.; WARNECKE, G.: The existence of viscous profiles and admissibility for transonic shocks. Commun. Part. Diff. Eqns. 16 (1991), 1197-1221.
40. LEHMAN, R. S.: Developments at an analytic corner of solutions of elliptic partial differential equations. J. Mathematics and Mechanics 8 (1959), 727-760.
41. LEROUXÉ, M. N.: Résolution numérique du problème du potential dans le plan par une méthode variationelle d'éléments finis. Doctoral Thesis, University of Rennes, 1974.
42. MANDEL, J.; NEČAS, J.: Convergence of finite elements for transonic potential flows. SIAM J. Numer. Anal. 24 (1987), 985-996.
43. MORAWETZ, C. S.: Non-existence of transonic flow past a profile III. Commun. Pure Appl. Math. 17 (1964), 357-367.
44. MORAWETZ, C. S.: On a weak solution for a transonic flow problem. Commun. Pure Appl. Math. 38 (1985), 797-818.
45. r-1,q est compact pour tout q < 2. Math. Pure Appl. 60 (1981), 309-322.
46. NAZAROV, S. A.; PLAMENEVSKY, B. A.: Elliptic problems in domains with piecewise smooth boundaries. Walter de Gruyter, Berlin-New York 1994.
47. MUSKHELISHVILI, N. I.: Singular integral equations. Noordhoff, Groningen 1953.
48. NEČAS, J.: Compacité par entropie et écoulements de fluides. Lecture Notes Université de Charles et E.N-S., Masson, Paris 1989.
49. VEKUA, I. N.: Generalized analytic functions. Pergamon Press, New York 1952.
50. WARNECKE, G.: Admissibility of solutions to the Riemann problems for systems of mixed type - transonic small disturbance theory. In: KEYFITZ, B. L.; SHEARER, M. (eds.): Nonlinear evolution equations that change type. IMA-Series Volume 27, Springer-Verlag, New York 1990, pp. 258-284.
51. WENDLAND, W. L.: Elliptic systems in the plane. Pitman Publ., London 1979.
52. ZIEREP, J.: Theoretische Gasdynamik. Braun, Karlsruhe 1976.