Compressible two-phase flows by central and upwind schemes

Smadar Karni; Eduard Kirr; Alexander Kurganov; Guergana Petrova

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2004)

  • Volume: 38, Issue: 3, page 477-493
  • ISSN: 0764-583X

Abstract

top
This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed.

How to cite

top

Karni, Smadar, et al. "Compressible two-phase flows by central and upwind schemes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.3 (2004): 477-493. <http://eudml.org/doc/245125>.

@article{Karni2004,
abstract = {This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed.},
author = {Karni, Smadar, Kirr, Eduard, Kurganov, Alexander, Petrova, Guergana},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Euler equations; two-phase flows; numerical methods; central schemes; upwind schemes; Godunov scheme; Roe scheme; pressure equilibrium},
language = {eng},
number = {3},
pages = {477-493},
publisher = {EDP-Sciences},
title = {Compressible two-phase flows by central and upwind schemes},
url = {http://eudml.org/doc/245125},
volume = {38},
year = {2004},
}

TY - JOUR
AU - Karni, Smadar
AU - Kirr, Eduard
AU - Kurganov, Alexander
AU - Petrova, Guergana
TI - Compressible two-phase flows by central and upwind schemes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 3
SP - 477
EP - 493
AB - This paper concerns numerical methods for two-phase flows. The governing equations are the compressible 2-velocity, 2-pressure flow model. Pressure and velocity relaxation are included as source terms. Results obtained by a Godunov-type central scheme and a Roe-type upwind scheme are presented. Issues of preservation of pressure equilibrium, and positivity of the partial densities are addressed.
LA - eng
KW - Euler equations; two-phase flows; numerical methods; central schemes; upwind schemes; Godunov scheme; Roe scheme; pressure equilibrium
UR - http://eudml.org/doc/245125
ER -

References

top
  1. [1] R. Abgrall and S. Karni, Computations of compressible multifluids. J. Comput. Phys. 169 (2001) 594–623. Zbl1033.76029
  2. [2] R. Abgrall and R. Saurel, Discrete equations for physical and numerical compressible multiphase flow mixtures. J. Comput. Phys. 186 (2003) 361–396. Zbl1072.76594
  3. [3] F. Coquel, K. El Amine, E. Godlewski, B. Perthame and P. Rascle, A numerical method using upwind schemes for the resolution of two-phase flows. J. Comput. Phys. 136 (1997) 272–288. Zbl0893.76052
  4. [4] D.A. Drew, Mathematical modelling of tow-phase flow. Ann. Rev. Fluid Mech. 15 (1983) 261–291. Zbl0569.76104
  5. [5] B. Einfeldt, C.-D. Munz, P.L. Roe and B. Sjogreen, On Godunov-type methods near low densities. J. Comput. Phys. 92 (1991) 273–295. Zbl0709.76102
  6. [6] A. Harten and S. Osher, Uniformly high-order accurate nonoscillatory schemes. I. SIAM J. Numer. Anal. 24 (1987) 279–309. Zbl0627.65102
  7. [7] S. Karni, Multi-component flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112 (1994) 31–43. Zbl0811.76044
  8. [8] A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. Zbl1137.65398
  9. [9] A. Kurganov, S. Noelle and G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23 (2001) 707–740. Zbl0998.65091
  10. [10] A. Kurganov and G. Petrova, Central schemes and contact discontinuities. ESAIM: M2AN 34 (2000) 1259–1275. Zbl0972.65055
  11. [11] B. van Leer, Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov’s method. J. Comput. Phys. 32 (1979) 101–136. Zbl0939.76063
  12. [12] H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. Zbl0697.65068
  13. [13] V.H. Ransom, Numerical benchmark tests, G.F. Hewitt, J.M. Delhay and N. Zuber Eds., Hemisphere, Washington, DC Multiphase Science and Technology 3 (1987). 
  14. [14] P.-A. Raviart and L. Sainsaulieu, Nonconservative hyperbolic systems and two-phase flows, International Conference on Differential Equations (Barcelona, 1991) World Sci. Publishing, River Edge, NJ 1, 2 (1993) 225–233. Zbl0938.35575
  15. [15] P.-A. Raviart and L. Sainsaulieu, A nonconservative hyperbolic system modeling spray dynamics. I. Solution of the Riemann problem. Math. Models Methods Appl. Sci. 5 (1995) 297–333. Zbl0837.76089
  16. [16] P.L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes. J. Comput. Phys. 43 (1981) 357–372. Zbl0474.65066
  17. [17] P.L. Roe, Fluctuations and signals - A framework for numerical evolution problems, in Numerical Methods for Fluid Dynamics, K.W. Morton and M.J. Baines Eds., Academic Press (1982) 219–257. Zbl0569.76072
  18. [18] P.L. Roe and J. Pike, Efficient construction and utilisation of approximate Riemann solutions, in Computing methods in applied sciences and engineering, VI (Versailles, 1983) North-Holland, Amsterdam (1984) 499–518. Zbl0558.76001
  19. [19] L. Sainsaulieu, Finite volume approximations of two-phase fluid flows based on an approximate Roe-type Riemann solver. J. Comput. Phys. 121 (1995) 1–28. Zbl0834.76070
  20. [20] R. Saurel and R. Abgrall, A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150 (1999) 425–467. Zbl0937.76053
  21. [21] H.B. Stewart and B. Wendroff, Two-phase flow: models and methods. J. Comput. Phys. 56 (1984) 363–409. Zbl0596.76103
  22. [22] I. Toumi and A. Kumbaro, An approximate linearized Riemann solver for a two-fluid model. J. Comput. Phys. 124 (1996) 286–300. Zbl0847.76056

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.