Sommario
Si riformula in termini generali il metodo della funzione di Green per estenderlo al caso di equazioni vettoriali e non lineari. In particolare si ricavano le espressioni della formula di Green e della rappresentazione integrale della soluzione per le equazioni di Navier Stokes non stazionarie. Si ottengono le soluzioni fondamentali in forma chiusa sia per il caso di fluidi comprimibili che incomprimibili. Si discutono infine brevemente i lati positivi ed i possibili limiti della metodologia illustrata.
Summary
The Green's function method is reformulated in general terms to treat vector unsteady and nonlinear equations. The particular expressions of the adjoint linear operator, the Green's formula and the integral representation of the solution are derived for unsteady Navier Stokes equations. The appropriate fundamental solutions for incompressible and for certain compressible flows have been obtained in closed form. Both the positive features and the possible limits of the method are briefly outlined.
This is a preview of subscription content, log in via an institution to check access.
References
Rizzo F.J.,An Integral Equation approach to boundary value problems of classical elastostatics, Q. Appl. Math., 25, 83–95.
Cruse T.A., 1969.Numerical Solutions in three dimensional elastostatics, Int. J. Solids Structures, 5, 1259–1274.
Youngren G.K., Acrivos A., 1975,Stokes flow past a particle of arbitrary shape: a numerical method of solution, J. Fluid Mech., 69, 337–403.
Tseng K.,Morino L., 1982,Non linear Green's function method for unsteady transonic flows, in Nixon D. (ed.), Transonic Aerodynamics, vol. 81 of Progress in Astronautics and Aeronautics.
Bush M.B., Tanner R.I., 1983,Numerical Solution of viscous flows using integral equation method, Int. J. Num. Meth. in Fluids, 3, 71.
Ma S., Graziani G., Piva R., 1984,A boundary-integral equation method for free surface viscous flows, Meccanica, 19, 4.
Swedlow J.L., Cruse T.A., 1971,Formulation of boundary integral equations for three-dimensional elasto-plastic flow, Int. J. Solids Structures, 7, 1673–1683.
Greenberg M.D., 1971,Application of Green's Functions in Science and Engineering, Prentice Hall.
Lanczos C., 1961,Linear Differential Operators, Van Nostrand.
Ladyzhenskaya O.A., 1963,The Mathematical Theory of Viscous Incompressible Flow. Gordon & Beach.
Stakgold I., 1967,Boundary Value Problems of Mathematical Physics. MacMillan.
Truesdell C., 1953,Precise Theory of the absorption and dispertion of forced plane infinitesimal waves according to the Navier-Stokes equations, J. Rational Mechanics and Analysis, 2, 643–741.
Hunt F.V., 1972,Propagation of sound in fluids, Am. Ins. Phys. Handb., Sec. 3, 37–68, McGraw-Hill.
Sandri G., 1984, private communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Piva, R., Morino, L. Vector green's function method for unsteady Navier-Stokes equations. Meccanica 22, 76–85 (1987). https://doi.org/10.1007/BF01556905
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01556905