Integral representation in the hodograph plane of compressible flow
Authors:
Erik B. Hansen and George C. Hsiao
Journal:
Quart. Appl. Math. 61 (2003), 73-88
MSC:
Primary 35Q35; Secondary 35A08, 35C15, 35R35, 76N99
DOI:
https://doi.org/10.1090/qam/1955224
MathSciNet review:
MR1955224
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Compressible flow is considered in the hodograph plane. The linearity of the equation determining the stream function is exploited to derive a representation formula involving boundary data only, and a fundamental solution to the adjoint equation. For subsonic flow, an efficient algorithm for computing the fundamental solution is developed.
L.Morino, Boundary integral equations in aerodynamics, Appl. Mech. Rev., 46, no. 8, 445–466, 1983
- C. Pozrikidis, Boundary integral and singularity methods for linearized viscous flow, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1992. MR 1156495
- K. Oswatitsch, Die Geschwindigkeitsverteilung bei lokalen Überschallgebieten an flachen Profilen, Z. Angew. Math. Mech. 30 (1950), 17–24 (German, with French and Russian summaries). MR 34180, DOI https://doi.org/10.1002/zamm.19500300102
- Klaus Oswatitsch (ed.), Symposium transsonicum, Springer-Verlag, Berlin, 1964 (German). International Union of Theoretical and Applied Mechanics, Aachen, Sept. 3-7, 1962. MR 0195346
- Klaus Oswatitsch (ed.), Symposium transsonicum, Springer-Verlag, Berlin, 1964 (German). International Union of Theoretical and Applied Mechanics, Aachen, Sept. 3-7, 1962. MR 0195346
- M. J. Lighthill, The hodograph transformation in transsonic flow. I. Symmetrical channels, Proc. Roy. Soc. London Ser. A 191 (1947), 323–341. MR 23682, DOI https://doi.org/10.1098/rspa.1947.0118
- M. J. Lighthill, The hodograph transformation in transsonic flow. II. Auxiliary theorems on the hypergeometric functions $\psi _n(\tau )$, Proc. Roy. Soc. London Ser. A 191 (1947), 341–351. MR 23396, DOI https://doi.org/10.1098/rspa.1947.0119
- M. J. Lighthill, The hodograph transformation in transsonic flow. III. Flow round a body, Proc. Roy. Soc. London Ser. A 191 (1947), 352–369. MR 23683, DOI https://doi.org/10.1098/rspa.1947.0120
- Ehud Shimborsky, Variational methods applied to the study of symmetric flows in Laval nozzles, Comm. Partial Differential Equations 4 (1979), no. 1, 41–77. MR 514719, DOI https://doi.org/10.1080/03605307908820091
Erik B. Hansen, Stokes flow down a wall into an infinite pool, J. Fluid Mech. 178, 243–256,
- Erik B. Hansen and Mark A. Kelmanson, Steady, viscous, free-surface flow on a rotating cylinder, J. Fluid Mech. 272 (1994), 91–107. MR 1289110, DOI https://doi.org/10.1017/S0022112094004398
- Richard von Mises, Mathematical theory of compressible fluid flow, Academic Press, Inc., New York, N.Y., 1958. Applied mathematics and mechanics. Vol. 3. MR 0094996
S. Nocilla, Sull’esistenza di flussi transonici continui attorne a profili alari ad arco cerchio, Atti della Academia delle Scienzi di Torino, 94, 796–822, 1960
R. Courant and D. Hilbert, Methods in Mathematical Physics, Interscience Publishers, New York, 1962, Vol. II, p. 336
- John Crank, Free and moving boundary problems, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1984. MR 776227
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 9th printing, 1970, pp. 562–564
W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, Springer, Wien, 5th ed., 1973, p. 148
L.Morino, Boundary integral equations in aerodynamics, Appl. Mech. Rev., 46, no. 8, 445–466, 1983
C. Pozrikidis, Boundary Integral and Singular Methods for Linearized Viscous Flow, Cambridge University Press, Cambridge, 1992
K. Oswatitsch, Die Geschwindigkeitverteilung bei lokalen Überschallgebiete an flachen Profilen, Z. Angew. Math. Mech., 30, 17–24, 1950
Symposium Transsonicum, K. Oswatitsch, Ed., Springer, Berlin, 1964
Symposium Transsonicum II, K. Oswatitsch and D. Rues, Eds., Springer, Berlin, 1976
M. J. Lighthill, The hodograph transformation in trans-sonic flow. I. Symmetric channels, Proc. Roy. Soc. London Ser. A 191, 323–341, 1947
M. J. Lighthill, The hodograph transformation in trans-sonic flow. II. Auxiliary theorems on the hypergeometric functions ${\psi _n}\left ( \tau \right )$, Proc. Roy. Soc. London Ser. A 191, 341–351, 1947
M. J. Lighthill, The hodograph transformation in trans-sonic flow. III. Flow round a body, Proc. Roy. Soc. London Ser. A 191, 352–369, 1947
E. Shimborsky, Variational methods applied to the study of symmetric flows in Laval nozzles, Comm. Partial Differential Equations 4, 41–77, 1979
Erik B. Hansen, Stokes flow down a wall into an infinite pool, J. Fluid Mech. 178, 243–256,
Erik B. Hansen and Mark A. Kelmanson, Steady, viscous, free-surface flow on a rotating cylinder, J. Fluid Mech. 272, 91–107, 1994
R. V. Mises, Mathematical Theory of Compressible Fluid Flow, Academic Press, New York, 1958, p. 251
S. Nocilla, Sull’esistenza di flussi transonici continui attorne a profili alari ad arco cerchio, Atti della Academia delle Scienzi di Torino, 94, 796–822, 1960
R. Courant and D. Hilbert, Methods in Mathematical Physics, Interscience Publishers, New York, 1962, Vol. II, p. 336
J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, 1984, chapter 2
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 9th printing, 1970, pp. 562–564
W. Gröbner and N. Hofreiter, Integraltafel, Zweiter Teil, Bestimmte Integrale, Springer, Wien, 5th ed., 1973, p. 148
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35Q35,
35A08,
35C15,
35R35,
76N99
Retrieve articles in all journals
with MSC:
35Q35,
35A08,
35C15,
35R35,
76N99
Additional Information
Article copyright:
© Copyright 2003
American Mathematical Society
