PSEUDO-COMPRESSIBILITY METHODS FOR THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

We present in this paper a up-to-date review on the error analysis of a class of pseudo-compressibility methods and their time discretizations for the unsteady incompressible Navier-Stokes equations.

[1]  P. Colella,et al.  A second-order projection method for the incompressible navier-stokes equations , 1989 .

[2]  J. Douglas,et al.  Stabilized mixed methods for the Stokes problem , 1988 .

[3]  R. Rannacher On chorin's projection method for the incompressible navier-stokes equations , 1992 .

[4]  R. Rannacher,et al.  Finite element approximation of the nonstationary Navier-Stokes problem. I : Regularity of solutions and second-order error estimates for spatial discretization , 1982 .

[5]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[6]  R. Temam Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (I) , 1969 .

[7]  L. R. Scott,et al.  Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials , 1985 .

[8]  A. Chorin Numerical solution of the Navier-Stokes equations , 1968 .

[9]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[10]  R. Temam,et al.  Navier-Stokes equations: theory and numerical analysis: R. Teman North-Holland, Amsterdam and New York. 1977. 454 pp. US $45.00 , 1978 .

[11]  Jian‐Guo Liu,et al.  Projection method I: convergence and numerical boundary layers , 1995 .

[12]  R. Temam Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (II) , 1969 .

[13]  F. Thomasset Finite element methods for Navier-Stokes equations , 1980 .

[14]  M. Bercovier Perturbation of mixed variational problems. Application to mixed finite element methods , 1978 .

[15]  Jie Shen,et al.  On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes , 1996, Math. Comput..

[16]  C. Bernardi,et al.  Approximations spectrales de problèmes aux limites elliptiques , 2003 .

[17]  P. Moin,et al.  Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations , 1984 .

[18]  J. Tinsley Oden,et al.  Stability of some mixed finite element methods for Stokesian flows , 1984 .

[19]  Alexandre J. Chorin,et al.  On the Convergence of Discrete Approximations to the Navier-Stokes Equations , 1969 .