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Volumn 228, Issue 8, 2009, Pages 2834-2846

A splitting method for incompressible flows with variable density based on a pressure Poisson equation

Author keywords

Fractional time stepping; Navier Stokes; Projection method; Variable density flows

Indexed keywords

NAVIER STOKES EQUATIONS; POISSON EQUATION;

EID: 61349154150     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.036     Document Type: Article
Times cited : (167)

References (32)
  • 1
    • 0008688174 scopus 로고    scopus 로고
    • A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations
    • Almgren A.S., Bell J.B., Colella P., Howell L.H., and Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142 1 (1998) 1-46
    • (1998) J. Comput. Phys. , vol.142 , Issue.1 , pp. 1-46
    • Almgren, A.S.1    Bell, J.B.2    Colella, P.3    Howell, L.H.4    Welcome, M.L.5
  • 2
    • 0001373981 scopus 로고
    • A second-order projection method for variable-density flows
    • Bell J.B., and Marcus D.L. A second-order projection method for variable-density flows. J. Comput. Phys. 101 (1992) 334-348
    • (1992) J. Comput. Phys. , vol.101 , pp. 334-348
    • Bell, J.B.1    Marcus, D.L.2
  • 4
    • 0000135764 scopus 로고    scopus 로고
    • Accurate projection methods for the incompressible Navier-Stokes equations
    • Brown D.L., Cortez R., and Minion M.L. Accurate projection methods for the incompressible Navier-Stokes equations. J. Comput. Phys. 168 2 (2001) 464-499
    • (2001) J. Comput. Phys. , vol.168 , Issue.2 , pp. 464-499
    • Brown, D.L.1    Cortez, R.2    Minion, M.L.3
  • 5
    • 84968510911 scopus 로고
    • Numerical solution of the Navier-Stokes equations
    • Chorin A.J. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 745-762
    • (1968) Math. Comput. , vol.22 , pp. 745-762
    • Chorin, A.J.1
  • 6
    • 0001235787 scopus 로고
    • Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures
    • Douglas Jr. J., and Russell T.F. Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Numer. Anal. 19 (1982) 871-885
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 871-885
    • Douglas Jr., J.1    Russell, T.F.2
  • 8
    • 0035660044 scopus 로고    scopus 로고
    • Approximation of variable density incompressible flows by means of finite elements and finite volumes
    • Fraigneau Y., Guermond J.-L., and Quartapelle L. Approximation of variable density incompressible flows by means of finite elements and finite volumes. Commun. Numer. Methods Eng. 17 (2001) 893-902
    • (2001) Commun. Numer. Methods Eng. , vol.17 , pp. 893-902
    • Fraigneau, Y.1    Guermond, J.-L.2    Quartapelle, L.3
  • 10
    • 0030503315 scopus 로고    scopus 로고
    • Some practical implementations of projection methods for Navier-Stokes equations
    • Guermond J.-L. Some practical implementations of projection methods for Navier-Stokes equations. M2AN Math. Model. Numer. Anal. 30 5 (1996) 637-667
    • (1996) M2AN Math. Model. Numer. Anal. , vol.30 , Issue.5 , pp. 637-667
    • Guermond, J.-L.1
  • 11
    • 0038934567 scopus 로고    scopus 로고
    • Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale
    • Also in C.R. Acad. Sci. Paris, Série I, 325:1329-1332, 1997
    • Guermond J.-L. Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier-Stokes par une technique de projection incrémentale. M2AN Math. Model. Numer. Anal. 33 1 (1999) 169-189 Also in C.R. Acad. Sci. Paris, Série I, 325:1329-1332, 1997
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.1 , pp. 169-189
    • Guermond, J.-L.1
  • 12
    • 33745954324 scopus 로고    scopus 로고
    • Subgrid stabilized projection method for 2d unsteady flows at high Reynolds number
    • Guermond J.-L., Marra A., and Quartapelle L. Subgrid stabilized projection method for 2d unsteady flows at high Reynolds number. Comput. Methods Appl. Mech. Eng. 195 (2006)
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.195
    • Guermond, J.-L.1    Marra, A.2    Quartapelle, L.3
  • 13
    • 33746140897 scopus 로고    scopus 로고
    • An overview of projection methods for incompressible flows
    • Guermond J.L., Minev P., and Shen J. An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 44-47 (2006) 6011-6045
    • (2006) Comput. Methods Appl. Mech. Eng. , vol.195 , Issue.44-47 , pp. 6011-6045
    • Guermond, J.L.1    Minev, P.2    Shen, J.3
  • 14
    • 49449112583 scopus 로고    scopus 로고
    • Entropy-based nonlinear viscosity for fourier approximations of conservation laws
    • Guermond J.-L., and Pasquetti R. Entropy-based nonlinear viscosity for fourier approximations of conservation laws. C.R. Math. Acad. Sci. Paris 346 (2008) 913-918
    • (2008) C.R. Math. Acad. Sci. Paris , vol.346 , pp. 913-918
    • Guermond, J.-L.1    Pasquetti, R.2
  • 16
    • 0002374668 scopus 로고    scopus 로고
    • Calculation of incompressible viscous flows by an unconditionally stable projection FEM
    • Guermond J.-L., and Quartapelle L. Calculation of incompressible viscous flows by an unconditionally stable projection FEM. J. Comput. Phys. 132 1 (1997) 12-33
    • (1997) J. Comput. Phys. , vol.132 , Issue.1 , pp. 12-33
    • Guermond, J.-L.1    Quartapelle, L.2
  • 17
    • 0032358205 scopus 로고    scopus 로고
    • On the approximation of the unsteady Navier-Stokes equations by finite element projection methods
    • Guermond J.-L., and Quartapelle L. On the approximation of the unsteady Navier-Stokes equations by finite element projection methods. Numer. Math. 80 5 (1998) 207-238
    • (1998) Numer. Math. , vol.80 , Issue.5 , pp. 207-238
    • Guermond, J.-L.1    Quartapelle, L.2
  • 18
    • 0007566219 scopus 로고    scopus 로고
    • A projection FEM for variable density incompressible flows
    • Guermond J.-L., and Quartapelle L. A projection FEM for variable density incompressible flows. J. Comput. Phys. 165 1 (2000) 167-188
    • (2000) J. Comput. Phys. , vol.165 , Issue.1 , pp. 167-188
    • Guermond, J.-L.1    Quartapelle, L.2
  • 19
    • 5644272882 scopus 로고    scopus 로고
    • On the error estimates for the rotational pressure-correction projection methods
    • electronic
    • Guermond J.-L., and Shen J. On the error estimates for the rotational pressure-correction projection methods. Math. Comput. 73 248 (2004) 1719-1737 electronic
    • (2004) Math. Comput. , vol.73 , Issue.248 , pp. 1719-1737
    • Guermond, J.-L.1    Shen, J.2
  • 20
    • 45149144830 scopus 로고
    • A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/Least-Squares method for advection-diffusive equations
    • Hughes T.J.R., Franca L.P., and Hulbert G.M. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/Least-Squares method for advection-diffusive equations. Comput. Methods Appl. Mech. Eng. 73 (1989) 173-189
    • (1989) Comput. Methods Appl. Mech. Eng. , vol.73 , pp. 173-189
    • Hughes, T.J.R.1    Franca, L.P.2    Hulbert, G.M.3
  • 22
    • 85190073810 scopus 로고    scopus 로고
    • P.-L. Lions, Mathematical topics in fluid mechanics, 1. Incompressible models, Oxford Lecture Series in Mathematics and its Applications, 3. The Clarendon Press, Oxford University Press, New York, 1996.
    • P.-L. Lions, Mathematical topics in fluid mechanics, vol. 1. Incompressible models, Oxford Lecture Series in Mathematics and its Applications, vol. 3. The Clarendon Press, Oxford University Press, New York, 1996.
  • 23
    • 46949108143 scopus 로고    scopus 로고
    • Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity
    • electronic
    • Liu C., and Walkington N.J. Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. SIAM J. Numer. Anal. 45 3 (2007) 1287-1304 electronic
    • (2007) SIAM J. Numer. Anal. , vol.45 , Issue.3 , pp. 1287-1304
    • Liu, C.1    Walkington, N.J.2
  • 24
    • 33846182594 scopus 로고    scopus 로고
    • Gauge-Uzawa methods for incompressible flows with variable density
    • Pyo J.-H., and Shen J. Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221 1 (2007) 181-197
    • (2007) J. Comput. Phys. , vol.221 , Issue.1 , pp. 181-197
    • Pyo, J.-H.1    Shen, J.2
  • 25
    • 0000686243 scopus 로고
    • On Chorin's projection method for the incompressible Navier-Stokes equations
    • The Navier-Stokes Equations II-Theory and Numerical Methods Oberwolfach, Springer, Berlin, Germany
    • R. Rannacher, On Chorin's projection method for the incompressible Navier-Stokes equations, in: The Navier-Stokes Equations II-Theory and Numerical Methods (Oberwolfach, 1991), Lecture Notes in Math., vol. 1530, Springer, Berlin, Germany, 1992, pp. 167-183.
    • (1991) Lecture Notes in Math , vol.1530 , pp. 167-183
    • Rannacher, R.1
  • 26
    • 0026819596 scopus 로고
    • On error estimates of projection methods for the Navier-Stokes equations: first-order schemes
    • Shen J. On error estimates of projection methods for the Navier-Stokes equations: first-order schemes. SIAM J. Numer. Anal. 29 (1992) 57-77
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 57-77
    • Shen, J.1
  • 27
    • 0002043336 scopus 로고    scopus 로고
    • Efficient Chebyshev-Legendre Galerkin methods for elliptic problems
    • A.V. Ilin, R.L. Scott Eds, Math
    • J. Shen, Efficient Chebyshev-Legendre Galerkin methods for elliptic problems, in: A.V. Ilin, R.L. Scott (Eds.), Proceedings of ICOSAHOM'95, Houston J. Math., 1996, pp. 233-240.
    • (1996) Proceedings of ICOSAHOM'95, Houston J , pp. 233-240
    • Shen, J.1
  • 28
    • 0041765520 scopus 로고
    • Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires II
    • Temam R. Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires II. Arch. Rat. Mech. Anal. 33 (1969) 377-385
    • (1969) Arch. Rat. Mech. Anal. , vol.33 , pp. 377-385
    • Temam, R.1
  • 29
    • 0000082056 scopus 로고
    • Une méthode d'approximation de la solution des équations de Navier-Stokes
    • Temam R. Une méthode d'approximation de la solution des équations de Navier-Stokes. Bull. Soc. Math. France 96 (1968) 115-152
    • (1968) Bull. Soc. Math. France , vol.96 , pp. 115-152
    • Temam, R.1
  • 30
    • 0029674537 scopus 로고    scopus 로고
    • An approximate projection scheme for incompressible flow using spectral elements
    • Timmermans L.J.P., Minev P.D., and van de Vosse F.N. An approximate projection scheme for incompressible flow using spectral elements. Int. J. Numer. Methods Fluids 22 (1996) 673-688
    • (1996) Int. J. Numer. Methods Fluids , vol.22 , pp. 673-688
    • Timmermans, L.J.P.1    Minev, P.D.2    van de Vosse, F.N.3
  • 31
    • 0000635210 scopus 로고
    • Numerical simulation of Rayleigh-Taylor instability
    • Tryggvason G. Numerical simulation of Rayleigh-Taylor instability. J. Comput. Phys. 75 (1988) 253-282
    • (1988) J. Comput. Phys. , vol.75 , pp. 253-282
    • Tryggvason, G.1
  • 32
    • 27744571569 scopus 로고    scopus 로고
    • Convergence of the discontinuous Galerkin method for discontinuous solutions
    • Walkington N.J. Convergence of the discontinuous Galerkin method for discontinuous solutions. SIAM J. Numer. Anal. 42 5 (2004) 1801-1817
    • (2004) SIAM J. Numer. Anal. , vol.42 , Issue.5 , pp. 1801-1817
    • Walkington, N.J.1


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