Contribution à l'étude théorique et numérique de certains systèmes de mécanique des fluides
Thèses d'Orsay, no. 745 (2008) , 118 p. 
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Adamy, Karine. Contribution à l'étude théorique et numérique de certains systèmes de mécanique des fluides. Thèses d'Orsay, no. 745 (2008), 118 p. https://www.numdam.org/item/BJHTUP11_2008__0745__A1_0/

[1] C. J. Amick, Regularity and uniqueness of solutions to the boussinesq system of equations, J. Diff. Eq., 54, 1984. | MR | Zbl | DOI

[2] E. Audusse, M. O. Bristeau, Transport of pollutant in shallow water, a two time steps kinetic method, M2 AN Math. Model. Num. Anal., 37, no. 2, 2003. | MR | Zbl | Numdam

[3] J. Bona, M. Chen, J. C. Saut, Boussinesq Equations and Other Systems for Small-amplitude Long Waves in Nonlinear Dispersive Media I : Derivation and Linear Theory, J. Nonlinear Sci. 12, no. 4, 2002. | MR | Zbl | DOI

[4] J. Bona, M. Chen, J. C. Saut, Boussinesq Equations and Other Systems for Small-amplitude Long Waves in Nonlinear Dispersive Media II : The nonlinear theory, Nonlinearity 17,, 2004. | MR | Zbl | DOI

[5] J. V. Boussinesq, Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal, C. R. Acad. Sci. Paris 73, 1871. | JFM

[6] C. Calgaro, J. Laminie, R. Temam, Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization Appl. Numer. Math. 23 (4), 1997. | MR | Zbl | DOI

[7] J. P. Chehab, Incremental unknowns method and compact schemes RAIRO Model. Math. Anal. Num. 32 (1), 1998. | MR | Zbl | Numdam

[8] M. Chen, R. Temam, Incremental unknowns for solving partial differential equations Numer. Math. 59, 1991. | MR | Zbl | DOI

[9] M. Chen, R. Temam, Incremental unknowns in finite differences : condition number of the matrix SIAM J. Matrix Anal. Appl. 14 (2), 1993. | MR | Zbl | DOI

[10] A. Debussche, J. Laminie, E. Zahrouni, A dynamical multi-level scheme for the Burgers equation : wavelet and hierarchical finite element J. Sci. Comput. 25 (3), 2005. | MR | Zbl | DOI

[11] T. Dubois, F. Jauberteau, R. Temam, Dynamic multilevel methods and the numerical simulation of turbulence Cambridge University Press, Cambridge, 1999. | MR | Zbl

[12] T. Dubois, F. Jauberteau, R. Temam, Incremental unknowns, multilevel methods and the numerical simulation of turbulence Comput. Methods Appl. Mech. Engrg. 159 (1-2), 1998. | MR | Zbl

[13] T. Dubois, F. Jauberteau, R. Temam, J. Tribbia, Multilevel schemes for the shallow water equations J. Comput. Phys. 207, 2005. | MR | Zbl | DOI

[14] S. Faure, J. Laminie, R. Temam, Finite volume discretization and multilevel methods in flow problems, J. Sci. Comput., 25 (1-2), 2005. | MR | Zbl | DOI

[15] S. Faure, Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur, Thèse de Doctorat.

[16] A. S. Fokas, B. Pelloni, Boundary Value Problems for Boussinesq Type Systems, Math. Phys., Anal. Geom. 8, 2005. | MR | Zbl | DOI

[17] A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160, 2000. | MR | Zbl

[18] A. Kurganov, G. Petrova, A third-order semi-discrete genuinely multidimensionnal central scheme for hyperbolic conservation laws and related problems Numer. Math. 88, 2001. | MR | Zbl | DOI

[19] A. Kurganov, S. Noelle, G. Petrova, Semidiscrete central upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23, no3, 2001. | MR | Zbl | DOI

[20] A. Kurganov, D. Levy, Central-upwind schemes for the Saint-Venant system, M2AN, Vol.36, no 3, 2002. | MR | Zbl | Numdam | DOI

[21] D. Lannes, Modélisation des ondes de surface et justification mathématique, Ecole d'été Théorie mathématique des ondes non linéaires dispersives, 2005.

[22] A. Mcdonald. A step toward transparent boundary conditions for meteorological models. Monthly Weather Review, 130 :140-151, 2001. | DOI

[23] A. Mcdonald. Transparent boundary conditions for the shallow-water equations : testing in a nested environment. Monthly Weather Review, 131 :698-705, 2002. | DOI

[24] A. J. C. De Saint Venant, Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Acad. Sci. Paris, 73, 1871. | JFM

[25] M. E. Schonbek, Existence of solutions for the Boussinesq system of equations, J. Differential Equations, 42, 1981, no. 3, 325-352. | MR | Zbl | DOI

[26] D. Serre, Systèmes hyperboliques de lois de conservation, I et II, Diderot, Paris, 1996. | MR | Zbl

[27] J. J. Stoker, Water waves, the mathematical theory with applications, Wiley, 1985. | Zbl | MR

[28] R. Temam, Inertial manifolds and multigrid methods SIAM J. Math. Anal., 21 (1), 1990. | MR | Zbl | DOI

[29] R. Temam, Multilevel methods for the simulation of turbulence. A simple model J. Comput. Phys., 127 (2), 1996. | MR | Zbl | DOI

[30] G. B. Whitham, Linear and non linear waves, Wiley and Sons Inc., New York, 1999. | MR | Zbl

[1] C. J. Amick, Regularity and uniqueness of solutions to the boussinesq system of equations, J. Diff. Eq., 54, 1984. | MR | Zbl | DOI

[2] T. B. Benjamin, Lectures on nonlinear wave motion, Lectures in Applied Mathematics, Vol. 15, Amer. Math. Soc., Providence, R.I., 1974. | MR

[3] J. Bona, R. Smith, A model for the two-way propagation of water waves in a channel, Math. Proc.Cambridge Philos., Soc. 79, 1976. | MR | Zbl | DOI

[4] J. Bona, V. Dougalis, An initial and boundary-value problem for a model equation for propagation of long waves, J. Math. Anal Appl., 75, 1980. | MR | Zbl | DOI

[5] J. Bona, M. Chen, J. C. Saut, Boussinesq Equations and Other Systems for Small-amplitude Long Waves in Nonlinear Dispersive Media I : Derivation and Linear Theory, J. Nonlinear Sci. 12, no. 4, 2002. | MR | Zbl | DOI

[6] J. Bona, M. Chen, J. C. Saut, Boussinesq Equations and Other Systems for Small-amplitude Long Waves in Nonlinear Dispersive Media II : The nonlinear theory, Non-linearity 17, 2004.

[7] J. R. Cannon, The One-dimensional Heat Equation, Encyclopedia of Mathematics and its Applications, 23, 1984. | MR | Zbl

[8] N. Dunford, J. Schwartz, Linear Operators. Part 1. Pure and Applied Mathematics, Vol. VII, Interscience Publishers, New York

[9] A. S. Fokas, B. Pelloni, Boundary Value Problems for Boussinesq Type Systems, Math. Phys., Anal. Geom. 8, 2005. | MR | Zbl | DOI

[10] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, N.J., 1964. | MR | Zbl

[11] P. D. Lax, Shock Waves and Entropy Contributions to Non-Linear Functionnal Analysis, Academic Press, New York, 1971. | MR | Zbl

[12] M. M. Rao, Z. D. Ren, Theory of Orlicz Spaces, Monographs and Textbooks in Pure and Applied Mathematics, 146, Marcel Dekker Inc., New York, 1991. | MR | Zbl

[13] W. Rudin, Functionnal Analysis, McGraw-Hill, New York, 1973. | MR | Zbl

[14] M. E. Schonbek, Existence of solutions for the Boussinesq system of equations, J. Differential Equations, 42, 1981, no. 3, 325-352. | MR | Zbl | DOI

[15] G. B. Whitham, Linear and Nonlinear Waves, Pure and Applied Mathematics, Wiley-Interscience, New-York-London-Sydney 1974. | MR | Zbl

[1] H. Brezis. Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North Holland Publishing Company, 1973 | MR | Zbl

[2] N. Burcq, P. Gérard. Contrôle optimal des équations aux dérivées partielles, Ecole Polytechnique, Palaiseau, France. 2003

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

[4] J. L. Lions, E. Magenes Problèmes aux limites non homogènes et applications, Dunod, 1968 | Zbl

[5] A. Mcdonald. A step toward transparent boundary conditions for meteorological models. Monthly Weather Review, 130 : 140-151, 2001. | DOI

[6] A. Mcdonald. Transparent boundary conditions for the shallow-water equations : testing in a nested environment. Monthly Weather Review, 131 : 698-705, 2002. | DOI

[7] A. Pazy. Semigroups of operators in Banach spaces. In Equadiff 82 (Würzburg, 1982), volume 1017 of Lecture Notes in Math., pages 508-524. Springer, Berlin, 1983. | MR | Zbl

[8] J. Pedlosky. Geophysical Fluid Dynamics, Springer, second edition, 1987. | Zbl

[9] W. Rudin. Functionnal Analysis, International series in Pure and Applied Mathematics, McGraw-Hill Inc., New York, second ed., 1991. | MR | Zbl

[10] R. Temam. Navier-Stokes equations. AMS Chelsea Publishing, Providence, RI, 2001. Theory and numerical analysis, Reedition of the 1984 edition. | MR | Zbl

[11] K. Yosida. Functionnal Analysis, Springer-Verlag, reprint of the sisth edition, 1995 | MR

[1] E. Audusse, F. Bouchut, M-O. Bristeau, R. Klein, B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows SIAM J. Sci. Comput. 25, 2004. | MR | Zbl | DOI

[2] E. Audusse, M-O. Bristeau, R. Klein, B. Perthame, Kinetic schemes for Saint-Venant equations sith source terms on unstructured grids INRIA Report RR-3989, 2000.

[3] C. Calgaro, J. Laminie, R. Temam, Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization Appl. Numer. Math. 23 (4), 1997. | MR | Zbl | DOI

[4] J. P. Chehab, Incremental unknowns method and compact schemes RAIRO Model. Math. Anal. Num. 32 (1), 1998. | MR | Zbl | Numdam

[5] M. Chen, R. Temam, Incremental unknowns for solving partial differential equations Numer. Math. 59, 1991. | MR | Zbl | DOI

[6] M. Chen, R. Temam, Incremental unknowns in finite differences : condition number of the matrix SIAM J. Matrix Anal. Appl. 14 (2), 1993. | MR | Zbl | DOI

[7] A. Debussche, J. Laminie, E. Zahrouni, A dynamical multi-level scheme for the Burgers equation : wavelet and hierarchical finite element J. Sci. Comput. 25 (3), 2005. | MR | Zbl | DOI

[8] T. Dubois, F. Jauberteau, R. Temam, Dynamic multilevel methods and the numerical simulation of turbulence Cambridge University Press, Cambridge, 1999. | MR | Zbl

[9] T. Dubois, F. Jauberteau, R. Temam, Incremental unknowns, multilevel methods and the numerical simulation of turbulence Comput. Methods Appl. Mech. Engrg. 159 (1-2), 1998. | MR | Zbl

[10] T. Dubois, F. Jauberteau, R. Temam, J. Tribbia, Multilevel schemes for the shallow water equations J. Comput. Phys. 207, 2005. | MR | Zbl | DOI

[11] R. Eymard, T. Gallouet, R. Herbin, Finite volume methods in Handbook of numerical analysis VII, p. 713-1020, North Holland, Amsterdam, 2000. | MR | Zbl

[12] S. Faure, J. Laminie, R. Temam, Finite volume discretization and multilevel methods in flow problems, J. Sci. Comput., 25 (1-2), 2005. | MR | Zbl | DOI

[13] S. Faure, Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur, Thèse de Doctorat.

[14] T. Gallouët, J.M. Hérard, N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography Comput. Fluids 32 (4), 2003. | MR | Zbl | DOI

[15] A. Kurganov, E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys. 160, 2000. | MR | Zbl

[16] A. Kurganov, G. Petrova, A third-order semi-discrete genuinely multidimensionnal central scheme for hyperbolic conservation laws and related problems Numer. Math. 88, 2001. | MR | Zbl | DOI

[17] A. Kurganov, S. Noelle, G. Petrova, Semidiscrete central upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J. Sci. Comput. 23, no3, 2001. | MR | Zbl | DOI

[18] A. Kurganov, D. Levy, Central-upwind schemes for the Saint-Venant system, M2AN, Vol. 36, no 3, 2002. | MR | Zbl | Numdam | DOI

[19] R. Temam, Inertial manifolds and multigrid methods SIAM J. Math. Anal., 21 (1), 1990. | MR | Zbl | DOI

[20] R. Temam, Multilevel methods for the simulation of turbulence. A simple model J. Comput. Phys., 127 (2), 1996. | MR | Zbl | DOI