Résolution des équations d'Euler compressibles par une méthode variationnelle en éléments finis : schémas aux différences décentrées pour la résolution des équations de Navier-Stokes incompressibles
Thèses d'Orsay, no. 244 (1989) , 190 p. 
@phdthesis{BJHTUP11_1989__0244__P0_0,
     author = {Bruneau, Charles-Henri},
     title = {R\'esolution des \'equations {d'Euler} compressibles par une m\'ethode variationnelle en \'el\'ements finis : sch\'emas aux diff\'erences d\'ecentr\'ees pour la r\'esolution des \'equations de {Navier-Stokes} incompressibles},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud Centre d'Orsay},
     number = {244},
     year = {1989},
     language = {fr},
     url = {http://www.numdam.org/item/BJHTUP11_1989__0244__P0_0/}
}
TY  - BOOK
AU  - Bruneau, Charles-Henri
TI  - Résolution des équations d'Euler compressibles par une méthode variationnelle en éléments finis : schémas aux différences décentrées pour la résolution des équations de Navier-Stokes incompressibles
T3  - Thèses d'Orsay
PY  - 1989
IS  - 244
PB  - Université de Paris-Sud Centre d'Orsay
UR  - http://www.numdam.org/item/BJHTUP11_1989__0244__P0_0/
LA  - fr
ID  - BJHTUP11_1989__0244__P0_0
ER  - 
%0 Book
%A Bruneau, Charles-Henri
%T Résolution des équations d'Euler compressibles par une méthode variationnelle en éléments finis : schémas aux différences décentrées pour la résolution des équations de Navier-Stokes incompressibles
%S Thèses d'Orsay
%D 1989
%N 244
%I Université de Paris-Sud Centre d'Orsay
%U http://www.numdam.org/item/BJHTUP11_1989__0244__P0_0/
%G fr
%F BJHTUP11_1989__0244__P0_0
Bruneau, Charles-Henri. Résolution des équations d'Euler compressibles par une méthode variationnelle en éléments finis : schémas aux différences décentrées pour la résolution des équations de Navier-Stokes incompressibles. Thèses d'Orsay, no. 244 (1989), 190 p. http://numdam.org/item/BJHTUP11_1989__0244__P0_0/

[1] C.S. Morawetz, A uniqueness theorem for Frankl's problem, Comm. Pure Appl. Math. 7 (1954) 697-703. | MR | Zbl | DOI

[2] A.K. Aziz and S.H. Leventhal, Numerical solution of linear partial differential equations of elliptic-hyperbolic type, Numerical Solution of Partial Differential Equations III SYNSPADE (1975) 55-87. | MR | Zbl

[3] A.G. Deacon and S. Osher, A finite element method for a boundary value problem of mixed type, SIAM J. Numer. Anal. 16 (1979) 756-778. | MR | Zbl | DOI

[4] B. Engquist and S. Osher, Stable and entropy satisfying approximations for transonic flow calculations, Math. Comp. 34 (1980) 45-75. | MR | Zbl | DOI

[5] A. Jameson, Numerical solution of nonlinear partial differential equations of mixed type, Numerical Solution of Partial Differential Equations III SYNSPADE (1975) 275-307. | MR | Zbl

[6] K.O. Friedrichs, Symmetric positive differential equations, Comm. Pure Appl. Math. 11 (1958) 333-418. | MR | Zbl | DOI

[7] P.D. Lax and R.S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math. 13 (1960) 427-455. | MR | Zbl | DOI

[8] R.S. Phillips and L. Sarason, Singular symmetric positive first order differential operators, J. Math. Mech. 15 (2) (1966) 235-271. | MR | Zbl

[9] Ph. G. Ciarlet, Conforming and non conforming finite element methods for solving the plate problem, Conference on the Numerical Solution of Differential Equations, Dundee, 1973, Lecture Notes in Mathematics 363 (1973) 21-31. | MR | Zbl | DOI

[10] M. Crouzeix and P. A. Raviart, Conforming and non conforming finite element methods for solving the stationary Stokes equations, RAIRO Anal. Numer. R3 (1973) 33-76. | MR | Zbl | Numdam

[11] Ch. Bruneau, Résolution de l'équation de Tricomi par des méthodes variationnelles en éléments finis, Thèse de 3ème cycle, Université de Paris-Sud, Orsay, France, 1980.

[12] P. Lascaux and P. Lesaint, Some non conforming finite elements for solving the plate bending problem, RAIRO Inform. Theor. 9 (1975) 9-54. | MR | Zbl | Numdam

[13] M.R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, Nat. Bur. Standards J. Res. 49 (1952) 409-436. | MR | Zbl | DOI

[14] D.S. Kershaw, The incomplete Cholesky conjugate gradient method for the iterative solutions of systems of linear equations, J. Comp. Phys. 26 (1978) 43-65. | MR | Zbl | DOI

[15] J. Cea, Optimisation. Thèorie et Algorithmes (Dunod, Paris, 1971). | MR | Zbl

[1]. H. Viviand, "Pseudo-unsteady methods for transonic flow computations", 7th Int. Conf. on Num. Meth. in Fluids Dynamics", W.C. Reynolds and R.W. Mac Cormack editors, Springer-Verlag, Stanford, 1980, p. 44. | MR

[2]. A. Jameson, "Acceleration of transonic potential flow calculations on arbitrary meshes by the multiple grid method", A.I.A.A. 4th Comp. Fluid Dyn. Conf., Williamsburg, 1979, pp. 122-146.

[3]. J.J. Chattot, "Méthode variationnelle pour les problèmes hyperboliques et mixtes du premier ordre", Computing Methods in Applied Sciences & Engineering, R. Glowinski, J.L. Lions editors, North-Holland Publishing Company, 1980. | MR | Zbl

[4]. J.J. Chattot, J. Guiu-Roux, J. Laminie, "Numerical solution of a first order conservation equation by a least square method", to appear in Int. J. Num. Meth. in Fluids. | Zbl

[5]. Ch.H. Bruneau, "A non conforming method for solving a least-square formulation of Tricomi's problem", to appear in Computer Methods in Applied Mechanics and Engineering. | Zbl

[6]. J.J. Chattot, J. Guiu-Roux, J. Laminie, "Finite element calculation of steady transonic flow in nozzles using primitive variables", 7th Int. Conf. on Num. Meth. in Fluids Dynamics, W.C. Reynolds and R.W. Mac Cormack editors, Springer-Verlag, Stanford, 1980, p. 107.

|1|. Chattot, J.J., Guiu-Roux, J., and Laminie, J., Résolution numérique d'une équation de conservation par une approche variationnelle, Proc. 6th ICNMFD, Tbilissi, USSR, June 20-25, 1978. Lecture Notes in Physics, 90, Springer-Verlag, 1979. | MR

|2|. Chattot, J.J., Guiu-Roux, J., and Laminie, J., Finite element calculation of steady transonic flow in nozzles using primary variables, Proc. 7th ICNMFD, Stanford and NASA/Ames, USA, June 23-27, 1980, Lecture Notes in Physics, 141, Springer-Verlag, 1981.

|3|. Chattot, J.J., Guiu-Roux, J., and Laminie, J., Numerical solution of à first- order conservation equation by a least square method, Int. Journal for Num. Meth. in Fluids, vol. 2, 209-219, 1982. | Zbl | DOI

|4|. Habashi, W.G., and Hafez, M.M., Finite element method for transonic cascade flows, AIAA/SAE/ASME 17th Joint Propulsion Conference, Colorado Spring, USA, July 27-29, 1981, AIAA paper n° 81-1472.

|5|. Rizzi, A., and Viviand, H., Numerical methods for the computation of inviscid transonic flows with shock waves, a GAMM Workshop, (Notes on numerical fluid Mechanics, vol. 3), Vieweg, 1981. | Zbl | MR

[1] J.J. Chattot, M. Boschiero and C. Koeck, Méthodes numériques de prédiction de l'aérodynamique des missiles, AGARD-CP-336, feb. 1983.

[2] C. Koeck and J.J. Chattot, Computation of three-dimensional Vortex flows past wings using the Euler equations and a multiple-grid scheme, Proceedings 9th Int. Conf. Meth. in Fluid Dyn., June 25-29, 1984, CEN Saclay, France, Springer-Verlag. | Zbl

[3] M.D. Salas, Recent developments in transonic Euler flow over a circular cylinder, Proceedings 10th IMACS World Congress, Aug. 8-13, 1982, Montréal, Canada, Vol. 1, p. 175-177.

[4] C.H. Bruneau, J.J. Chattot, J. Laminie and J. Guiu-Roux, Finite element least square method for solving full steady Euler equations in a plane nozzle. Proceedings 8th Int. Conf. Meth. in Fluid Dyn., June 28-July 2, 1982, Aachen, Germany, Springer-Verlag.

[1] Ch.H. Bruneau, J.J. Chattot, J. Laminie, R. Temam : Numerical solutions of the Euler equations with separation by a finite element method. 9th ICNMFD Saclay 1984, Lecture Notes in Physics n° 218, Springer-Verlag. | Zbl

[2] Ch.H. Bruneau, J.J. Chattot, J. Laminie, J. Guiu-Roux : Finite element least square method for solving full steady Euler equations in a plane nozzle. 8th ICNMFD Aachen 1982, Lecture Notes in Physics n° 170, Springer-Verlag.

[3] S.H. Chang, G.M. Johnson : An embedding method for the steady Euler equations. J. Comp. Phys., n° 63, 1986. | MR | Zbl

[4] Ch. Koeck : Computation of three dimensional flow using the Euler equations and multiple-grid scheme. Int. J. Num. Meth. Fluids n° 5, 1985. | Zbl | DOI

1. A. Rizzi and Ch. J. Purcell, 'On the computation of transonic leading-edge vortices using the Euler equations', J. Fluid Mech., 181, 163-195 (1987). | Zbl | DOI

2. O. A. Kandil, A. H. Chuang and J. M. Shifflette, 'Finite-volume Euler and Navier-Stokes solvers for three-dimensional and conical vortex flows over delta wings', AIAA Paper 87-0041, 1987. | DOI

3. R. W. Newsome, 'Euler and Navier-Stokes solutions for flow over a conical delta wing', AIAA J. 24, 552-561 (1986). | Zbl | DOI

4. Ch. H. Bruneau, J. J. Chattot, J. Laminie and R. Temam, 'Numerical solutions of the Euler equations with separation by a finite element method', 9th ICNMFD, Saclay ; Lecture Notes in Physics 218, 1984, pp. 121-126. | Zbl

5. Ch. H. Bruneau, J. J. Chattot, J. Laminie and R. Temam, 'Computation of vortex flows past a flat plate at high angle of attack', 10th ICNMFD, Beijing ; Lecture Notes in Physics 264, 1986, pp. 134-140.

6. G. W. Hedstrom, 'Non reflecting boundary conditions for nonlinear hyperbolic systems', J. Comput. Phys., 30, 222-237 (1979). | MR | Zbl | DOI

7. J. Cullum and R. A. Willoughby, 'Computing eigenvalues of very large symmetric matrices-an implementation of a Lanczos algorithm with no reorthogonalization', J. Comput. Phys., 44, 329-358 (1981). | MR | Zbl | DOI

[1] Ch.H. Bruneau, J.J. Chattot, J. Laminie and R. Temam, Computation of vortex flow past a flat plate at high angle of attack, 10th ICNMFD, Beijing, 1986, Lecture Notes in Physics 264.

[2] Ch.H. Bruneau, J. Laminie and J.J. Chattot, Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady Euler equations, to appear in Int. J. Num. Meth. in Fluids. | MR | Zbl

[3] K. Powell, E. Murman, E. Perez and J. Baron, Total pressure loss in vortical solutions of the conical Euler equations, AIAA paper 85-1701. | DOI

[4] C. Koeck, Computation of three-dimensional flow using the Euler equations and a multiple-grid scheme, Int. J. Num. Meth. in Fluids, 5, 1985. | Zbl | DOI

[5] L.E. Eriksson and A. Rizzi, Computation of vortex flow around wings using the Euler equations, 4th GAMM Conf. on Num. Meth. in Fluid Mech., 1981. | Zbl

[1] Ch.-H. Bruneau, J.J. Chattot, J. Laminie and J. Guiu-Roux, Finite element least-squares method for solving full steady Euler equations in a plane nozzle, 8th ICNMFD, Aachen 1982, Lecture Notes in Physics 170.

[2] Ch.-H. Bruneau, J. Laminie and J.J. Chattot, Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady Euler equations, to appear in Int. J. for Num. Meth. in Fluids. | MR | Zbl

[3] Workshop on hypersonic flows for reentry problems, Antibes, 1990.

[4] G.H. Golub and G.A. Meurant, Résolution numérique des grands systèmes linéaires, Ecole d'Eté d'Analyse Numérique, CEA-EDF-INRIA, 1983. | MR | Zbl

[5] 7th International Conference of finite element methods in flow problems, Huntsville, 1989.

[6] P. Rebuffet, Aérodynamique Expérimentale, Tomes I and II, Dunod, 1966.

[7] P. Diringer, Calcul d'ondes de choc détachées, La Recherche Aéronautique 88, 1962.

[8] V. Selmin and L. Quartapelle, Finite element solution to the Euler equations, 10th ICNMFD, Beijing 1986, Lecture Notes in Physics 264.

[9] K. Khalfallah and A. Lerat, Communication to Hermes Meeting, Rome 1988.

[10] A. Lerat and J. Sides, Efficient solution of the steady Euler equations with a centered implicit method, Numerical Methods for Fluid Dynamics, Oxford, 1988. | MR | Zbl

[11] K. Khalfallah and A. Lerat, Correction d'entropie pour des schémas numériques approchant un système hyperbolique, C. R. Acad. Sc. Paris, 308, II, n° 9, 1989. | MR | Zbl

[1] M. Fortin, R. Peyret et R. Temam, Résolution numérique des équations de Navier-Stokes pour un fluide incompressible, J. Mécanique, 10, 1971, p. 357-390. | MR | Zbl

[2] K. Gustafson et K. Halasi, Vortex dynamics of cavity flows, J. Comput. Phys., 64, 1986, p. 279-319. | MR | Zbl | DOI

[3] S. P. Vanka, Block-implicit multigrid solution of Navier-Stokes equations in primitive variables, J. Compt. Phys., 65, 1986, p. 138-158. | MR | Zbl | DOI

[4] U. Ghia, K. N. Ghia et C. T. Shin, High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comput. Phys., 48, 1982, p. 387-411. | Zbl | DOI

[5] R. Schreiber et J. B. Keller, Driven cavity flows by efficient numerical techniques, J. Comput. Phys., 49, 1983, p. 310-333. | Zbl | DOI

[6] R. Peyret et T. D. Taylor, Computational methods for fluid flow, Springer, 1983. | MR | Zbl | DOI

[7] F. Thomasset, Implementation of finite element methods for Navier-Stokes equations, Springer, 1981. | MR | Zbl | DOI

[8] A. Brandt et N. Dinar, Multigrid solutions to elliptic flow problems, Numerical Methods for Partial Differential Equations, V. Parter éd., Madison, 1978, p. 53-147. | MR | Zbl

[9] C. H. Bruneau et C. Jouron, An efficient scheme for solving steady incompressible Navier-Stokes equations, en préparation. | Zbl

[1] M. Fortin, R. Peyret and R. Temam, J. Mécanique 10, 357 (1971). | MR

[2] F. Thomasset, Implementation of finite element methods for Navier-Stokes equations (Springer-Verlag, New York Heidelberg Berlin, 1981). | MR | Zbl | DOI

[3] R. Peyret and T.D. Taylor, Computational methods for fluid flow. (Springer-Verlag, New York Heidelberg Berlin, 1983). | MR | Zbl | DOI

[4] A. Fortin, M. Fortin and J.J. Gervais, J. Comput. Phys. 70, 295 (1987). | Zbl

[5] P. Constantin, C. Foias and R. Temam, Attractors representing turbulent flows, Memoirs of A.M.S. 53, 314 (1985). | MR | Zbl

[6] P. Le Quere and T. Alziary De Roquefort, J. Comput. Phys. 57, 210 (1985). | Zbl

[7] J. Shen, Thesis, University of Paris-Sud, Orsay, 1987 (unpublished).

[8] R. Schreiber and H.B. Keller, J. Comput. Phys. 49, 310 (1983). | Zbl

[9] S.P. Vanka, J. Comnut. Phys. 65, 138 (1986). | MR | Zbl

[10] U. Ghia, K.N. Ghia and C.T. Shin, J. Comput. Phys. 48, 387 (1982). | Zbl

[11] H.K. Moffatt, J. Fluid Mech. 18, 1 (1964). | Zbl | DOI

[12] K. Gustafson and R. Leben, Applied. Math, and Comput. 19, 89 (1986). | Zbl

[13] K. Gustafson and K. Halasi, J. Comput. Phys. 70, 271 (1987). | Zbl

[14] L.B. Zhang, Thesis, University of Paris-Sud, Orsay, 1987 (unpublished).

[15] A. Brandt and N. Dinar, in Proceedings of an Advanced Seminar Conducted bv the Mathematical Research Center. The University of Wisconsin-Madison, 1978, edited by S.V. Parter (Academic Press, 1979) p. 53.

[16] W. Hackbusch, Multigrid Methods and Applications (Springer-Verlag, New York Heidelberg Berlin, 1985). | MR

[17] D.B. Spalding, Int. J. for Num. Meth. in Eng. 4, 551 (1972).

[B1] Ch.H. Bruneau : A non conforming finite element method for solving a least-square formulation of Tricomi's problem, Comp. Meth. Appl. Mech. Eng. 39, 1983. | Zbl

[BCLG1] Ch.H. Bruneau, J.J. Chattot, J. Laminie, J. Guiu-Roux : Finite element least square methods for problem of mixed type, 4th Int. Symp. Fin. El. Meth. Flow, Tokyo 1982, Finite Element Flow Analysis, 1982. | Zbl

[BCLG2] Ch.H. Bruneau, J.J. Chattot, J. Laminie, J. Guiu-Roux : Finite element least square method for solving full steady Euler equations in a plane nozzle, 8th ICNMFD, Aachen 1982, Lecture Notes in Physics 170, 1983.

[BCLT1] Ch.H. Bruneau, J.J. Chattot, J. Laminie, R. Temam : Numerical solutions of the Euler equations with separation by a finite element method, 9th ICNMFD, Saclay 1984, Lecture Notes in Physics 218, 1985. | Zbl

[BCLT2] Ch.H. Bruneau, J.J. Chattot, J. Laminie, R. Temam : Computation of vortex flows past a flat plate at high angle of attack, 10th ICNMFD, Beijing 1986, Lecture Notes in Physics 264, 1987.

[BLC1] Ch.H. Bruneau, J. Laminie, J.J. Chattot : Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady Euler equations, Int. J. Num. Meth. Fluids 9, 1989. | MR | Zbl

[BLC2] Ch.H. Bruneau, J. Laminie, J.J. Chattot : Computation of hypersonic vortex flows with an Euler model, 11th ICNMFD, Williamsburg 1988, Lecture Notes in Physics 323, 1989.

[B2] Ch.H. Bruneau : Computation of hypersonic flows round a blunt body in 2D with Euler model, soumis à Computers and Fluids. | Zbl

[BJ1] Ch.H. Bruneau, C. Jouron : Un nouveau schéma décentré pour le problème de la cavité entraînée, C. R. Acad. Sci. Paris 301, série I, 1988. | MR | Zbl

[BJ2] Ch.H. Bruneau, C. Jouron, An efficient scheme for solving steady incompressible Navier-Stokes equations, à paraître dans J. Comp. Phys. | Zbl