Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur
Thèses d'Orsay, no. 640 (2003) , 150 p.
@phdthesis{BJHTUP11_2003__0640__A1_0,
     author = {Faure, Sylvain},
     title = {M\'ethodes de volumes finis et multiniveaux pour les \'equations de {Navier-Stokes,} de {Burgers} et de la chaleur},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris IX UFR Scientifique d'Orsay},
     number = {640},
     year = {2003},
     language = {fr},
     url = {http://archive.numdam.org/item/BJHTUP11_2003__0640__A1_0/}
}
TY  - BOOK
AU  - Faure, Sylvain
TI  - Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur
T3  - Thèses d'Orsay
PY  - 2003
IS  - 640
PB  - Université de Paris IX UFR Scientifique d'Orsay
UR  - http://archive.numdam.org/item/BJHTUP11_2003__0640__A1_0/
LA  - fr
ID  - BJHTUP11_2003__0640__A1_0
ER  - 
%0 Book
%A Faure, Sylvain
%T Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur
%S Thèses d'Orsay
%D 2003
%N 640
%I Université de Paris IX UFR Scientifique d'Orsay
%U http://archive.numdam.org/item/BJHTUP11_2003__0640__A1_0/
%G fr
%F BJHTUP11_2003__0640__A1_0
Faure, Sylvain. Méthodes de volumes finis et multiniveaux pour les équations de Navier-Stokes, de Burgers et de la chaleur. Thèses d'Orsay, no. 640 (2003), 150 p. http://numdam.org/item/BJHTUP11_2003__0640__A1_0/

[BGH98] T. Buffard, T. Gallouet, and J.-M. Hérard. Un schéma simple pour les équations de Saint-Venant. C. R. Acad. Sci. Paris Sér. I Math., 326(3) : 385-390, 1998. | MR | Zbl

[BH96] S. Boivin and J.-M. Hérard. Un schéma de type volumes finis pour résoudre les équations de Navier-Stokes sur une triangulation. Rev. Européenne Elém. Finis, 5(4) : 461-490, 1996. | MR | Zbl

[BP03] M. Bernacki and S. Piperno. Schmas en volumes finis avec flux centrs pour la propagation des ondes en aroacoustique. Rapport de recherche de l'INRIA - Sophia Antipolis, RR-4699, 2003.

[Che98] J.-P. Chehab. Incremental unknowns method and compact schemes. RAIRO Modél. Math. Anal. Numér., 32(1) : 51-83, 1998. | MR | Zbl | Numdam | DOI

[Cho68] A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22 : 745-762, 1968. | MR | Zbl

[CLT97] C. Calgaro, J. Laminie, and R. Temam. Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization. Appl. Numer. Math., 23(4) : 403-442, 1997. | MR | Zbl

[DJT99] T. Dubois, F. Jauberteau, and R. Temam. Dynamic multilevel methods and the numerical simulation of turbulence. Cambridge University Press, Cambridge, 1999. | MR | Zbl

[GP01] J.-F. Gerbeau and B. Perthame. Derivation of viscous Saint-Venant system for laminar shallow water ; numerical validation. Discrete Contin. Dyn. Syst. Ser. B, 1(1) : 89-102, 2001. | MR | Zbl

[GS03] J. L. Guermond and J. Shen. A new class of truly consistent splitting schemes for incompressible flows. To appear in J. Comput. Phys., 2003. | MR | Zbl

[Hsu81] C. Hsu. A curvilinear-coordinate method for momentum, heat and mass transfer in domains of irregular geometry. Phd thesis, University of Minnesota, 1981.

[HW65] F. H. Harlow and J. E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids, 8(12), 1965. | MR | Zbl | DOI

[Lio69] J.-L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires. Original edition reprinted in 2002, Dunod, Paris, 1969. | MR | Zbl

[LZ03] J. Laminie and E. Zahrouni. A dynamical multilevel scheme for the burgers equation : wavelet and hierarchical finite element. To appear, 2003. | MR | Zbl

[Pat80] S. V. Patankar. Numerical heat transfer and fluid flow. Series in Computational Methods in Mechanics and Thermal Sciences. McGraw-Hill, New York, 1980. | Zbl

[PKP01] J. M. C. Pereira, M. H. Kobayashi, and J. C. F. Pereira. A fourth-order-accurate finite volume compact method for the incompressible Navier-Stokes solutions. J. Comput. Phys., 167(1) : 217-243, 2001. | MR | Zbl | DOI

[PKS88] M. Perić, R. Kessler, and G. Sheuerer. Comparison of finite-volume numerical methods with staggered and colocated grids. Comput. & Fluids, 16(4) : 389-403, 1988. | Zbl | DOI

[Pou96] F. Pouit. Stability study, error estimation, and condition number for semi-implicit schemes using incremental unknowns. Numer. Methods Partial Differential Equations, 12(6) : 743 766, 1996. | MR | Zbl | DOI

[Pra81] C. Prakash. A finite element method for predicting flow through ducts with arbitrary cross sections. Phd thesis, University of Minnesota, 1981.

[PRF02] S. Piperno, M. Remaki, and L. Fezoui. A nondiffusive finite volume scheme for the three-dimensional Maxwell's equations on unstructured meshes. SIAM J. Numer. Anal., 39(6) : 2089-2108 (electronic), 2002. | MR | Zbl | DOI

[Rhi81] C. Rhie. A numerical study of the flow past an isolated airfoil with separation. Phd thesis, University of Illinois, Urbana-Champaign, 1981.

[Tem69] R. Temam. Sur l'approximation de la solution des equations de navier-stokes par la méthode des pas fractionnaires, i et ii. Arch. Rational Mech. Anal., 32(2) : 135-153, 1969. | MR | Zbl | DOI

[Tem90] R. Temam. Inertial manifolds and multigrid methods. SIAM J. Math. Anal., 21(1) : 154-178, 1990. | MR | Zbl | DOI

[EEK94] M. Euler, N. Euler, and A. Köhler. On the construction of approximate solutions for a multidimensional nonlinear heat equation. J. Phys. A, 27(6) : 2083-2092, 1994. | MR | Zbl | DOI

[EGH00] R. Eymard, T. Gallouët, and R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, pages 713-1020. North-Holland, Amsterdam, 2000. | MR | Zbl

[Lio69] J.-L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires. Original edition reprinted in 2002, Dunod, Paris, 1969. | MR | Zbl

[Min62] George J. Minty. Monotone (nonlinear) operators in Hilbert space. Duke Math. J., 29 : 341-346, 1962. | MR | Zbl

[Min63] George J. Minty. on a "monotonicity" method for the solution of non-linear equations in Banach spaces. Proc. Nat. Acad. Sci. U.S.A., 50 : 1038-1041, 1963. | MR | Zbl | DOI

[Rép92] A. Répaci. Computing of the heat diffusion coefficient for the nonlinear heat equation by boundary value measurements. Appl. Math. Lett., 5(2) : 97-100, 1992. | MR | Zbl

[Rou90] T. Roubíček. Numerical solution of the nonlinear heat equation in heterogeneous media. Numer. Fund. Anal. Optim., 11(7-8) : 793-810, 1990. | MR | Zbl

[Tem01] R. Temam. Navier-Stokes Equations, Theory and Numerical Analysis, . 3rd revised edition, North-Holland, Amsterdam, reprinted in the AMS Chelsea series, AMS, Providence, 2001. | MR

[BH96a] S. Boivin and J.-M. Hérard. Un schéma de type volumes finis pour résoudre les équations de Navier-Stokes sur une triangulation. Rev. Européenne Élém. Finis, 5(4) : 461-490, 1996. | MR | Zbl | DOI

[BH96b] N. Botta and D. Hempel. A finite volume projection method for the numerical solution of the incompressible navier-stokes equations on triangular grids. In Proceedings of the First International Symposium on Finite Volumes for Complex Applications, Rouen, 15-18 July 1996.

[Cho68] A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22 : 745-762, 1968. | MR | Zbl

[EGH00] R. Eymard, T. Gallouët, and R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, pages 713 -1020. North-Holland, Amsterdam, 2000. | MR | Zbl

[FT03a] S. Faure and R. Temam. Collocated finite volume schemes for fluid flows. In prep., 2003.

[FT03b] S. Faure and R. Temam. Finite volume discretization and multilevel methods in flow problems. In prep., 2003. | Zbl

[Ler33] J. Leray. Etude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl., 12 : 1-82, 1933. | Zbl | Numdam | MR

[Ler34a] J. Leray. Essai sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math., 63 : 193-248, 1934. | MR | JFM

[Ler34b] J. Leray. Essai sur les mouvements plans d'un liquide visqueux que limitent des parois. J. Math. Pures Appl., 13 : 331-418, 1934. | JFM | Numdam

[LL94a] F. S. Lien and M. A. Leschziner. A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence- transport closure, part 1 : Computational implementation. Comput. Methods Appl. Mech. Engrg., 114 : 123-148, 1994. | MR

[LL94b] F. S. Lien and M. A. Leschziner. A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence- transport closure, part 2 : Application. Comput. Methods Appl. Mech. Engrg., 114 : 149-167, 1994. | MR

[MT98] M. Marion and R. Temam. Navier-Stokes equations : theory and approximation. In Handbook of numerical analysis, Vol. VI, pages 503-688. North-Holland, Amsterdam, 1998. | MR | Zbl

[RC83] C. M. Rhie and W. L. Chow. Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J., 21(11), 1983. | Zbl

[RT03] P. Rasch and S. J. Thomas. Computational and numerical methods in atmoshphere and ocean. In Lectures given at the Summer School on Applications of Advanced Mathematical and Computational Methods to Atmospheric and Oceanic Problems (MCAO2003), National Center for Atmospheric Research (NCAR), Boulder, Colorado, USA, In prep. July, 2003.

[Tem69] R. Temam. Sur l'approximation de la solution des equations de navier-stokes par la méthode des pas fractionnaires,i et ii. Arch. Rational Mech. Anal, 32(2) : 135-153, 1969. | MR | Zbl | DOI

[Tem01] R. Temam. Navier-Stokes Equations, Theory and Numerical Analysis. 3rd revised edition, North-Holland, Amsterdam, reprinted in the AMS Chelsea series, AMS, Providence, 2001. | MR

[VK86] J. Van Kan. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Statist. Comput., 7 : 870-891, 1986. | MR | Zbl | DOI

[Cho68] A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22 : 745-762, 1968. | MR | Zbl

[EGH00] R. Eymard, T. Gallouët, and R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, pages 713-1020. North-Holland, Amsterdam, 2000. | MR | Zbl

[FT03] S. Faure and R. Temam. Finite volume discretization and multilevel methods in flow problems. In prep., 2003. | Zbl

[GGS82] U. Ghia, K. N. Ghia, and C. T. Shin. High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method. J. Comput. Phys., 48 : 387-411, 1982. | Zbl | DOI

[GS03a] J. L. Guermond and J. Shen. A new class of truly consistent splitting schemes for incompressible flows. To appear in J. Comput. Phys., 2003. | MR | Zbl

[GS03b] J. L. Guermond and J. Shen. Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal., 41(1) : 112-134 (electronic), 2003. | MR | Zbl | DOI

[Hsu81] C. Hsu. A curvilinear-coordinate method for momentum, heat and mass transfer in domains of irregular geometry. Phd thesis, University of Minnesota, 1981.

[KM85] J. Kim and P. Moin. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys., 59(2) : 308-323, 1985. | MR | Zbl | DOI

[Lel92] S. K. Lele. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys., 103(1) : 16-42, 1992. | MR | Zbl | DOI

[MT98] M. Marion and R. Temam. Navier-Stokes equations : theory and approximation. In Handbook of numerical analysis, Vol. VI, pages 503-688. North-Holland, Amsterdam, 1998. | MR | Zbl

[Pat80] S. V. Patankar. Numerical heat transfer and fluid flow. Series in Computational Methods in Mechanics and Thermal Sciences. McGraw-Hill, New York, 1980. | Zbl

[PKS88] M. Perić, R. Kessler, and G. Sheuerer. Comparison of finite-volume numerical methods with staggered and colocated grids. Comput. & Fluids, 16(4) : 389-403, 1988. | Zbl | DOI

[Pra81] C. Prakash. A finite element method for predicting flow through ducts with arbitrary cross sections. Phd thesis, University of Minnesota, 1981.

[Rhi81] C. Rhie. A numerical study of the flow past an isolated airfoil with separation. Phd thesis, University of Illinois, Urbana-Champaign, 1981.

[She96] J. Shen. On error estimates of projection methods for navier-stokes equations : second-order schemes. Mathematica (Cluj), 65(215) : 1039-1065, 1996. | MR | Zbl

[Tem69] R. Temam. Sur l'approximation de la solution des equations de navier-stokes par la méthode des pas fractionnaires, i et ii. Arch. Rational Mech. Anal., 32(2) : 135-153, 1969. | MR | Zbl | DOI

[VK86] J. Van Kan. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Statist. Comput., 7 : 870-891, 1986. | MR | Zbl | DOI

[ZSK94] Y. Zang, R. L. Street, and J. R. Koseff. A non-staggered grid, fractional step method for time-dependent incompressible Navier-Stokes equations in curvilinear coordinates. J. Comput. Phys., 114(1) : 18-33, 1994. | MR | Zbl | DOI

[CDGT01] B. Costa, L. Dettori, D. Gottlieb, and R. Temam. Time marching multilevel techniques for evolutionary dissipative problems. SIAM J. Sci. Comput., 23(1) : 46-65 (electronic), 2001. | MR | Zbl | DOI

[CDL98] C. Calgaro, A. Debussche, and J. Laminie. On a multilevel approach for the two- dimensional Navier-Stokes equations with finite elements. Internat. J. Numer. Methods Fluids, 27(1-4, Special Issue) : 241-258, 1998. Finite elements in fluids. | MR | Zbl | DOI

[Che98] J.-P. Chehab. Incremental unknowns method and compact schemes. RAIRO Modél. Math. Anal. Numér., 32(1) : 51-83, 1998. | MR | Zbl | Numdam | DOI

[Cho68] A. J. Chorin. Numerical solution of the Navier-Stokes equations. Math. Comp., 22 : 745-762, 1968. | MR | Zbl

[CLT97] C. Calgaro, J. Laminie, and R. Temam. Dynamical multilevel schemes for the solution of evolution equations by hierarchical finite element discretization. Appl. Numer. Math., 23(4) : 403-442, 1997. | MR | Zbl

[CT91] M. Chen and R. Temam. The incremental unknown method. I, II. Appl. Math. Lett., 4(3) : 73-76, 77-80, 1991. | MR | Zbl

[DJT99] T. Dubois, F. Jauberteau, and R. Temam. Dynamic multilevel methods and the numerical simulation of turbulence. Cambridge University Press, Cambridge, 1999. | MR | Zbl

[EGH00] R. Eymard, T. Gallouët, and R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, pages 713-1020. North-Holland, Amsterdam, 2000. | MR | Zbl

[FT03] S. Faure and R. Temam. Collocated finite volume schemes for fluid flows. In prep., 2003.

[Gar00] S. Garcia. Incremental unknowns for solving the incompressible Navier-Stokes equations. Math. Comput. Simulation, 52(5-6) : 445-489, 2000. | MR | DOI

[Hou] Thomas Y. Hou, editor. Multiscale Modeling and Simulation.

[HW65] F. H. Harlow and J. E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids, 8(12), 1965. | MR | Zbl | DOI

[LL94a] F. S. Lien and M. A. Leschziner. A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, part 1 : Computational implementation. Comput. Methods Appl. Mech. Engrg., 114 : 123-148, 1994. | MR

[LL94b] F. S. Lien and M. A. Leschziner. A general non-orthogonal collocated finite volume algorithm for turbulent flow at all speeds incorporating second-moment turbulence-transport closure, part 2 : Application. Comput. Methods Appl. Mech. Engrg., 114 : 149-167, 1994. | MR

[LTW92a] J.-L. Lions, R. Temam, and S. H. Wang. New formulations of the primitive equations of atmosphere and applications. Nonlinearity, 5(2) : 237-288, 1992. | MR | Zbl | DOI

[LTW92b] J.-L. Lions, R. Temam, and S. H. Wang. On the equations of the large-scale ocean. Nonlinearity, 5(5) : 1007-1053, 1992. | MR | Zbl | DOI

[LZ03] J. Laminie and E. Zahrouni. A dynamical multilevel scheme for the burgers equation : wavelet and hierarchical finite element. To appear, 2003. | MR | Zbl

[PKS88] M. Perić, R. Kessler, and G. Sheuerer. Comparison of finite-volume numerical methods with staggered and colocated grids. Comput. & Fluids, 16(4) : 389-403, 1988. | Zbl | DOI

[Pou98] F. Pouit. Etude de schémas numériques multiniveaux utilisant les Inconnues Incrémentales, dans le cadre des différences finies : application à la mécanique des fluides. Thèse, Université Paris 11, 1998.

[RT03] P. Rasch and S. J. Thomas. Computational and numerical methods in atmoshphere and ocean. In Lectures given at the Summer School on Applications of Advanced Mathematical and Computational Methods to Atmospheric and Oceanic Problems (MCAO2003), National Center for Atmospheric Research (NCAR), Boulder, Colorado, USA, In prep. July, 2003.

[SBH] E. Stein, R. De Borst, and T. J.R. Hughes, editors. Encyclopedia of Computational Mechanics. J. Wiley and Sons, Ltd. | DOI

[SCV93] K. M. Smith, W. K. Cope, and S. P. Vanka. A multigrid procedure for three- dimensional flows on nonorthogonal collocated grids. Internat. J. Numer. Methods Fluids, 17(10) : 887-904, 1993. | MR | Zbl | DOI

[Tem69] R. Temam. Sur l'approximation de la solution des equations de navier-stokes par la méthode des pas fractionnaires, i et ii. Arch. Rational Mech. Anal., 32(2) : 135-153, 1969. | MR | Zbl | DOI

[Tem90] R. Temam. Inertial manifolds and multigrid methods. SIAM J. Math. Anal., 21(1) : 154-178, 1990. | MR | Zbl | DOI

[Tem93] Roger Temam. Méthodes multirésolutions en analyse numérique. In Boundary value problems for partial differential equations and applications, volume 29 of RMA Res. Notes Appl. Math., pages 253-276. Masson, Paris, 1993. | MR | Zbl

[Tem94] Roger Temam. Applications of inertial manifolds to scientific computing : a new insight in multilevel methods. In Trends and perspectives in applied mathematics, volume 100 of Appl. Math. Sci., pages 293-336. Springer, New York, 1994. | MR | Zbl | DOI

[Tem96] R. Temam. Multilevel methods for the simulation of turbulence. A simple model. J. Comput. Phys., 127(2) : 309-315, 1996. | MR | Zbl | DOI

[VK86] J. Van Kan. A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Statist. Comput., 7 : 870-891, 1986. | MR | Zbl | DOI