Summary
This work deals with the decomposition of a vector fieldu intou=∇×ψ+∇φ. Non homogeneous boundary conditions on ψ or φ are investigated; applications to the computation of inviscid flows are given; finally a conforming finite element implementation is studied and tested.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
De Rham, G.: Varietes differentiables. Paris: Ed. Hermann 1960
Bernardi, C.: These de 3 eme cycle. Universite Paris VI, 1979
Bendali, A., Dominguez, J.M., Gallic, S.: A variational approach for the vector potential formulation of the Stokes and Navier-Stokes problems in three dimensional problems. Rapport interne No 95, Ecole Polytechnique, CMA (1983)
Lacor, C., Hirsch, C.: Rotational flow calculations in three dimensional blade passage. ASME report, 82-GT-316
Sokhey, J.S.: Transonic flow around axisymetric inlets including rotational flow effects. AIAA 18th meeting, Pasadena (1980)
Papaillon, N., Chaviaropoulos, P., Gianakoglou, K.: Numerical computation of 2-D rotational inviscid transonie flows, using the decomposition of the flow field into a potential and a rotational part, 7th ISABE Conf. Bejung, China, 1985
Amara, M.: Analyse de methodes d'elements finis pour des ecoulements transsoniques. These d'Etat, Universite Paris VI, Analyse Numerique (1983)
Dominguez, J.M.: Etude des equations de la Magnetohydrodynamique stationnaires et leur approximation par elements finis. These de Docteur Ingenieur, Universite Paris VI (1982)
Lions, J.L., Magenes, E.: Problemes aux limites non homogenes et applications, Vol. 1. Paris: Dunod 1968
Foias, C., Temam, R.: Remarques sur les equations de Navier-Stokes et phenomenes successifs de bifurcation. Ann. Sc. Norm. Super. Pisa, IV. Ser.V, 29–63 (1978)
El Dabaghi, F., Periaux, J., Pironneau, O., Poirier, G.: 3-D finite element solution of steady Euler transonic flow by stream vector correction, AIAA 7th computational fluid dynamics conference, AIAA-85-1532-CP, Cincinnati, Ohio, USA, 1985
Jameson, A.: A multi-grid scheme for transonic potential calculations on arbitrary grids. Proceedings of the AIAA 4th computational fluid dynamics conference, Williamsburg, Va., pp. 122–146, 1979
Jameson, A.: Numerical solutions of the euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA paper 81-1259, AIAA 14th fluid and plasma dynamics conference, Palo Alto, CA 1981
Bristeau, M.O., Glowinski, R., Pironneau, O., Periaux, J., Perrier, P.: On the numerical solution of nonlinear problems by least squares and finite element methods (I) Least square formulation and conjugate gradient solution of the continuous problems, pp. 619–657, 17/18. Amsterdam: North-Holland 1979
Pironneau, O.: On the transport-diffusion algorithm and its applications to the Navier-Stokes equations. Numer. Mathe.8, 309–332 (1982)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland 1978
Verfurth, R.: Error estimates for a mixed finite element approximation of the Stokes equations. R.A.I.R.O. (To appear)
Nedelec, J.C.: Mixed finite elements in R3. Numer. Math.35, 315–341 (1980)
Peetre, J.: Another approach to elliptic boundary problems. Pure Appl. Math. Sci.14, 711–731 (1961)
Dominguez, J.: Formulation en potentiel vecteur du système de Stokes dans un domaine deR 3. Rapport 83015 LAN, Université Paris 6, 1983
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dabaghi, F.E., Pironneau, O. Stream vectors in three dimensional aerodynamics. Numer. Math. 48, 561–589 (1986). https://doi.org/10.1007/BF01389451
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01389451