Free access
Issue
ESAIM: M2AN
Volume 42, Number 2, March-April 2008
Page(s) 303 - 331
DOI http://dx.doi.org/10.1051/m2an:2008005
Published online 27 March 2008
  1. P. Angot, V. Dolejší, M. Feistauer and J. Felcman, Analysis of a combined barycentric finite volume-nonconforming finite element method for nonlinear convection-diffusion problems. Appl. Math. 4 (1998) 263–310. [CrossRef]
  2. H. Bijl and P. Wesseling, A unified method for computing incompressible and compressible flows in boundary-fitted coordinates. J. Comp. Phys. 141 (1998) 153–173. [CrossRef]
  3. M.O. Bristeau, R. Glowinski, L. Dutto, J. Périaux and G. Rogé, Compressible viscous flow calculations using compatible finite element approximations. Internat. J. Numer. Methods Fluids 11 (1990) 719–749. [CrossRef] [MathSciNet]
  4. V. Casulli and D. Greenspan, Pressure method for the numerical solution of transient, compressible fluid flows. Internat. J. Numer. Methods Fluids 4 (1984) 1001–1012. [CrossRef]
  5. A.J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comp. 22 (1968) 745–762. [CrossRef] [MathSciNet]
  6. P.G. Ciarlet, Finite elements methods – Basic error estimates for elliptic problems, in Handbook of Numerical Analysis II, P. Ciarlet and J.-L. Lions Eds., North Holland (1991) 17–351.
  7. P. Colella and K. Pao, A projection method for low speed flows. J. Comp. Phys. 149 (1999) 245–269. [CrossRef]
  8. M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I. RAIRO Anal. Numér. 7 (1973) 33–75.
  9. K. Deimling, Nonlinear Functional Analysis. Springer, New-York (1980).
  10. I. Demirdžić, Ž. Lilek and M. Perić, A collocated finite volume method for predicting flows at all speeds. Internat. J. Numer. Methods Fluids 16 (1993) 1029–1050. [CrossRef]
  11. V. Dolejší, M. Feistauer, J. Felcman and A. Kliková, Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems. Appl. Math. 47 (2002) 301–340. [CrossRef] [MathSciNet]
  12. A. Ern and J.-L. Guermond, Theory and practice of finite elements, Applied Mathematical Sciences 159. Springer (2004).
  13. R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563–594. [CrossRef] [MathSciNet]
  14. R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, in Handbook of Numerical Analysis VII, P. Ciarlet and J.-L. Lions Eds., North Holland (2000) 713–1020.
  15. E. Feireisl, Dynamics of viscous compressible flows, Oxford Lecture Series in Mathematics and its Applications 6. Oxford University Press (2004).
  16. H. Feistauer, J. Felcman and I. Straškraba, Mathematical and computational methods for compressible flows, Oxford Science Publications. Clarendon Press (2003).
  17. M. Fortin, H. Manouzi and A. Soulaimani, On finite element approximation and stabilization methods for compressible viscous flows. Internat. J. Numer. Methods Fluids 17 (1993) 477–499. [CrossRef] [MathSciNet]
  18. J.-L. Guermond and L. Quartapelle, A projection FEM for variable density incompressible flows. J. Comp. Phys. 165 (2000) 167–188. [CrossRef] [MathSciNet]
  19. J.-L. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Engrg. 195 (2006) 6011–6045. [CrossRef] [MathSciNet]
  20. F.H. Harlow and A.A. Amsden, Numerical calculation of almost incompressible flow. J. Comp. Phys. 3 (1968) 80–93. [CrossRef]
  21. F.H. Harlow and A.A. Amsden, A numerical fluid dynamics calculation method for all flow speeds. J. Comp. Phys. 8 (1971) 197–213. [CrossRef]
  22. R.I. Issa, Solution of the implicitly discretised fluid flow equations by operator splitting. J. Comp. Phys. 62 (1985) 40–65. [CrossRef]
  23. R.I. Issa and M.H. Javareshkian, Pressure-based compressible calculation method utilizing total variation diminishing schemes. AIAA J. 36 (1998) 1652–1657. [CrossRef]
  24. R.I. Issa, A.D. Gosman and A.P. Watkins, The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme. J. Comp. Phys. 62 (1986) 66–82. [CrossRef]
  25. K.C. Karki and S.V. Patankar, Pressure based calculation procedure for viscous flows at all speeds in arbitrary configurations. AIAA J. 27 (1989) 1167–1174. [CrossRef]
  26. M.H. Kobayashi and J.C.F. Pereira, Characteristic-based pressure correction at all speeds. AIAA J. 34 (1996) 272–280. [CrossRef]
  27. B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows. J. Comp. Phys. 95 (1991) 59–84. [CrossRef] [MathSciNet]
  28. P.-L. Lions, Mathematical topics in fluid mechanics, Volume 2: Compressible models, Oxford Lecture Series in Mathematics and its Applications 10, Oxford University Press (1998).
  29. M. Marion and R. Temam, Navier-Stokes equations: Theory and approximation, in Handbook of Numerical Analysis VI, P. Ciarlet and J.-L. Lions Eds., North Holland (1998).
  30. F. Moukalled and M. Darwish, A high-resolution pressure-based algorithm for fluid flow at all speeds. J. Comp. Phys. 168 (2001) 101–133. [CrossRef]
  31. P. Nithiarasu, R. Codina and O.C. Zienkiewicz, The Characteristic-Based Split (CBS) scheme – a unified approach to fluid dynamics. Internat. J. Numer. Methods Engrg. 66 (2006) 1514–1546. [CrossRef] [MathSciNet]
  32. A. Novotný and I. Straškraba, Introduction to the mathematical theory of compressible flow, Oxford Lecture Series in Mathematics and its Applications 27. Oxford University Press (2004).
  33. G. Patnaik, R.H. Guirguis, J.P. Boris and E.S. Oran, A barely implicit correction for flux-corrected transport. J. Comp. Phys. 71 (1987) 1–20. [CrossRef]
  34. E.S. Politis and K.C. Giannakoglou, A pressure-based algorithm for high-speed turbomachinery flows. Internat. J. Numer. Methods Fluids 25 (1997) 63–80. [CrossRef]
  35. R. Rannacher and S. Turek, Simple nonconforming quadrilateral Stokes element. Numer. Methods Partial Differential Equations 8 (1992) 97–111. [CrossRef] [MathSciNet]
  36. R. Temam, 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.
  37. D.R. van der Heul, C. Vuik and P. Wesseling, Stability analysis of segregated solution methods for compressible flow. Appl. Numer. Math. 38 (2001) 257–274. [CrossRef] [MathSciNet]
  38. D.R. van der Heul, C. Vuik and P. Wesseling, A conservative pressure-correction method for flow at all speeds. Comput. Fluids 32 (2003) 1113–1132. [CrossRef] [MathSciNet]
  39. J.P. Van Dormaal, G.D. Raithby and B.H. McDonald, The segregated approach to predicting viscous compressible fluid flows. Trans. ASME 109 (1987) 268–277.
  40. D. Vidović, A. Segal and P. Wesseling, A superlinearly convergent Mach-uniform finite volume method for the Euler equations on staggered unstructured grids. J. Comput. Phys. 217 (2006) 277–294. [CrossRef] [MathSciNet]
  41. C. Wall, C.D. Pierce and P. Moin, A semi-implicit method for resolution of acoustic waves in low Mach number flows. J. Comp. Phys. 181 (2002) 545–563. [CrossRef]
  42. I. Wenneker, A. Segal and P. Wesseling, A Mach-uniform unstructured staggered grid method. Internat. J. Numer. Methods Fluids 40 (2002) 1209–1235. [CrossRef] [MathSciNet]
  43. P. Wesseling, Principles of computational fluid dynamics, Springer Series in Computational Mathematics 29. Springer (2001).
  44. O.C. Zienkiewicz and R. Codina, A general algorithm for compressible and incompressible flow – Part I. The split characteristic-based scheme. Internat. J. Numer. Methods Fluids 20 (1995) 869–885. [CrossRef] [MathSciNet]

Recommended for you