Variational methods for the potential flow past an airfoil

Applicable Analysis

Volumn 65, Issue 1-2, 1997, Pages 153-182

  Hsiao, George C ^a   Marcozzit, Michael D ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNITED STATES MILITARY ACADEMY   (United States)

Author keywords

Boundary integral operators; Potential flows; Weak formulation

Indexed keywords

EID: 1842858150     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819708840556     Document Type: Article

References (36)

1. [I] G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge University Press, 1988.
2. H. Berger, G. Warnecke, and W.L. Wendland, Analysis of a FEM/BEM coupling method for transonic pow computations, Preprint 93-9, Mathematisches Institut A, Univ. Stuttgart, 1993.
3. M.S. Birman and G.E.Skvortsov, Square summability of the highest derivatives of the solutions of the Dirichlet problem in a domain with a piecewise smooth boundary, Izv. Vyss. Ucebn. Zaved. Matmatika, 50 (1962), pp. 11-21.
4. J. Chazarain and A. Piriou, Introduction to the Theory of Linear Partial Diflerential Equations, North-Holland, Amsterdam, 1982.
5. J.F. Ciavaldini, M. Pogu, and G. Tournemine, Existence and regularity of stream functions for subsonic flows past profiles with a sharp trailing edge, Arch. Rat. Mech. Anal., 93 (1986), pp. 1-14.
6. M. Costabel and E. Stephen, Curvature terms in the asymptotic expansions for solutions of boundary integral equations on curved polygons, J. Integral Equations, 5 (1983), pp. 353-371.
7. M. Costabel and E. Stephen, Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation, Banach Center, Warsaw, 1985.
8. M. Dauge and M. Pogu, Ecoulement de Juide parfait compressible dans un domain tridimensional pre'sentant une singubarite' conique. Condition de Kutta-Joukowski, Annales de la Facult6 des Sciences de Toulouse, 1988.
9. M. Dauge and M. Pogu, Existence et re'gularite' de la function potential pour des e'coulements subcritiques s'e'tablissant autour d'un corps d singularite' conique, Ann. Fac. des Sci. de'Toulouse, IX (1988))pp. 213-242.
10. M. Dauge and J.L. Steux, Problbme de Dirichlet pour le Laplacian dans un polygone curviligne, J. Diff. Equat., 70 (1987), pp. 93-113.
11. M. Dauge, J. Lubuma, and J. Nicaise, 'Coeficients des singubaritie's pour be problbme de Dirichtet sur un polygone, C.R. Acad. Sc. Paris 304 Se'rie I, 16 (1987))pp. 483-486.
12. M. Feistauer, Mathematical Methods in Fluid Dynamics, Pitman, New York, 1993.
13. M. Feistauer, J. Felcman, M. Rokyta, and Z. Vlkek, Finite-element solution of flow problems with trailing conditions, J. Comp. Appl. Math., 44 (1992), pp. 131-165.
14. G. Fichera, Linear elliptic equations of higher order in two independent variables and singular integral equations, with applications to anisotropic inhomogeneous elasticity, Partial Diff. Equat. and continuum Mech., edited by R.E.Langer, pp. 55-80, Madison, The University of Wisconsin Press 1961.
15. G.N. Gatica and G.C. Hsiao, On the coupled BEM and FEM for a nonlinear exterior Dirichlet problem in Bi2, Numer. Math., 61 (1992), pp. 171-214.
16. G.C. Hsiao, On the stability of integral equations of the first kind with logarithmic kernel, Arch. Rat. Mech. Anal., 7 (1986), pp. 179-192.
17. G.C. Hsiao, On boundary integral equations of the first kind, J. Comput. Math., 7 (1989), pp. 121-131.
18. G.C. Hsiao, The coupling of boundary element and finite element methods, Z. angew. Math. Mech., 70 (1990), pp. T493-T503.
19. G.C. Hsiao, On the progeny of Fichera's boundary integral method, Probemi Attuali Dell' Analisi E Della Fisica Matematica, edited by P.E. Ricci, pp. 127-144, Dipartimento di Roma, "La Sapianza", 1993.
20. G.C. Hsiao and R.C. MacCamy, Solution of boundary value problems by integral equations of the first kind, SIAM Review, 15 (1973), pp. 687-705.
21. G.C. Hsiao and M.D. Marcozzi, The coupling of boundary element and finite element methods for the potential pow past an airfoil, Center for the Mathematics of Waves, Univ. of Delaware, Technical Report No. 95-2.
22. G.C. Hsiao and W.L. Wendland, A finite element method for some integral equations of the first kind, J. Math. Anal. Appl., 58 (1977), pp. 449-481.
23. G.C. Hsiao and W.L. Wendland, Variational Methods for Boundary Integral Equations and Mathematical Foundations of Boundary Element Methods, Springer-Verlag, in prepation.
24. G.C. Hsiao, M.D. Marcozzi, and S. Zhang, An eficient computational method for the pow past an airfoil, Contemporary Math., 180 (1994), pp. 497-502.
25. K. Ibuki, Dirichlet problem for elliptic equations of the second order in a singular domain in Jl2, J. Math. Kyoto Univ., 14 (1974)) pp. 54-71.
26. K. Karamcheti, Principles of Ideal-Fluid Aerodynamics, Kreiger, 1980.
27. V.A. Kondratiev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskovkogo Mat. Obschetsva, 16 (1967), pp. 209-292 (and Transactions Moscow Mat. Soc., pp. 227-313).
28. A. Kufner and A.M. Sandig, Some Applications of Weighted Sobolev Spaces, BSB Tueber, Leipzig, 1987.
29. V.A. Maz'ya and B.A. Plamenevskii, On the coeficients in the asymptotes of the solutions of elliptic boundary value problems in a cone, Zap. Nauchn. Senin. Leningr. Otd. Mat. Inst. Steklova, 52 (1975), pp. 110-127 (and J. Sov. Math., 9 (1978), pp. 750-764).
30. V.A. Maz'ya and B.A. Plamenevskii, On the coeficients of the solutions of elliptic boundary value problems in domains with conical points, Math. Nachr., 76 (1977), pp. 29-60 (and Transl., 11, Am. Math. Soc., 123 (1984), pp. 57-88).
31. V.A. Maz'ya and B.A. Plamenevskii, Estimates in L, and in Holder classes, and the Miranda-Agmon maximum principle for the solutions of elliptic boundary value problems in domains with singular points on the boundary, Math. Nachr., 81 (1978), pp. 25-82.
32. K. Rektory, Variational Methods in Mathematics, Science and Engineering, D. Reidel, Praque, 1980.
33. M. Schiffer, Analytic theory of subsonic and supersonic Bows, Encylopedia of Physics, 9, pp. 1-161, Springer-Verlag, New York, 1960.
34. W.L. Wendland and C. Coclici, On the convergence of a coupled finite element-boundary element method for the transonic full potential pow, to appear.
35. D.V. Widder, The Laplace Transform, Princeton University Press, 1946.
36. S. Yon, J. Katz, and A. Plotkin, Effect of airfoil (trailing edge) thickness on the numerical solution of panel methods based on the dim'chlet boundary condition, AIAA Journal, 30 (1992), pp. 697-702.