Application of the control-volume method for the solution of problems in gas and fluid mechanics on unstructured grids

Authors

  • K.N. Volkov

Keywords:

неструктурированная сетка
уравнения Навье-Стокса
метод контрольного объема
течение около профиля
газовая динамика

Abstract

The control-volume method for solving problems in gas and fluid mechanics on unstructured grids is developed. The peculiarities of discretization for inviscid and viscous fluxes and for time derivatives in the Navier-Stokes equations are discussed. The potentiality of the approach under consideration is demonstrated by an example of solving some gas dynamic problems (flow around profiles).

New computational technologies

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Published

2005-02-14

Issue

Vol. 6 (2005): Issue 1.

Section

Section 1. Numerical methods and applications

Author Biography

K.N. Volkov

D.F. Ustinov Baltic State Technical University «Voenmekh»

References

  1. Barth T.J. Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations // VKI Lecture Series of Von Karman Institute for Fluid Dyanmics. N 1994-04, Belgium, 1994.
  2. Jameson A., Mavripils D. Finite volume solution of the two-dimensional Euler equations on a regular triangular mesh // AIAA Paper. 1985. N 85-0435.
  3. Morgan K., Perire J., Peiro J., Hassan O. The computation of three dimensional flows using unstructured grids // Computational Methods in Applied Mechanics Engineering. 1991. 87. 335-352.
  4. Hirsch C. Numerical computation of internal and external flows. New York: John Wiley & Sons, 1990.
  5. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes // Journal of Computational Physics. 1981. 43. 357-372.
  6. Luo H., Baum J.D., Lohner R. Edge-based finite element scheme for the Euler equations // AIAA Journal. 1994. 32. N 6. 1183-1190.
  7. Crumpton P.I., Moinier P., Giles M.B. An unstructured algorithm for high Reynolds number flows on highly stretched grids // Proceedings of the 10th International Conference on Numerical Methods for Laminar and Turbulent Flows, 21,-,25 July 1997, University of Wales. United Kingdom, Swansea, 1997.
  8. Jameson A. Transonic aerofoil calculations using the Euler equations // Proceedings of the IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, March 1981, Reading, United Kingdom / Edited by P.L. Roe. Academic Press, 1982. 289-308.
  9. Crumpton P.I. A cell vertex method for 3D Navier-Stokes solutions // Technical Report of the Oxford University Computing Laboratory. 1993. N NA-93/09.
  10. Moinier P., Giles M.B. Stability analysis of preconditioned approximations of the Euler equations on unstructured meshes // Journal of Computational Physics. 2002. 178. 498-519.
  11. Moinier P., Giles M.B. Compressible Navier-Stokes equations for low Mach number applications // Proceedings of the ECCOMAS Computational Fluid Dynamics Conference, 4,-,7 September 2001. United Kingdom, Swansea, 2001.
  12. Crumpton P.I., Giles M.B. Implicit time accurate solutions on unstructured dynamic grids // AIAA Paper. 1995. N 95-1671.
  13. Hackbusch W. Multi-grid convergence theory // Lecture Notes in Mathematics. N 960. Berlin: Springer-Verlag, 1982. 177-219.
  14. Brandt A. Multi-level adaptive solutions to boundary value problems // Mathematics of Computation. 1977. 31. 46-50.
  15. Abarbanel S., Gottlieb D. Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives // Journal of Computational Physics. 1981. 41. 1-33.
  16. Turkel E. Preconditioning-squared methods for multidimensional aerodynamics // AIAA Paper. 1997. N 97-2025.
  17. Pierce N.A., Giles M.B. Preconditioning compressible flow calculations on stretched meshes // AIAA Paper. 1996. N 96-0889.
  18. Spalart P.R., Allmaras S.R. A one equation turbulence model for aerodynamic flows // AIAA Paper. 1992. N 92-0439.
  19. Cook P.H., McDonald M.A., Firmin G.N. Aerofil RAE 2822 - pressure distribution and boundary layer and wake measurements // Experimental Data Base for Computer Program Assessment. Report of the Fluid Dynamics Panel Working Group (AGARD-AR). 1979. N 138. 36-64.