Skip to main content
SpringerLink
Log in

Evaluation of non-oscillatory schemes based on LED principle for supersonic flow computations

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The objective of the present paper is to evaluate the efficiency of several high resolution, non-oscillatory schemes based on the local extremum diminishing (LED) principle [1], [2] in the case of supersonic flow computation past obstacles in two dimensions. The Euler equations of gas dynamics have been solved in a cell-vertex finite volume framework in conjunction with the non-oscillatory dissipation schemes for simulation of supersonic flow fields. Satisfactory results have been obtained with the switched as well as the flux limited dissipation schemes, namely, SLIP and USLIP schemes using scalar diffusive flux. Four different types of flux splitting techniques have also been investigated along with the switched scheme. In particular, the wave-particle splitting proposed by Balakrishnan and Deshpande [3] for upwind schemes has been formulated and applied to the present symmetric or central scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ghosh, S., Niyogi, P.: A study of non-oscillatory schemes based on LED principle for inviscid flow computation past airfoils. Acta Mech. 139, 73–90 (2000).

    Google Scholar 

  • Jameson, A.: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows. In: 11th AIAA Computational Fluid Dynamics Conf., Orlando, FL, July 6–9, 1993, AIAA Paper 93–3359 (1993).

  • Balakrishnan, N., Deshpande, S. M.: New upwind method exploiting the wave-particle behavior of fluid flow. CFD Journal 3, 433–446 (1995).

    Google Scholar 

  • Rossow, C.: Comparison of cell centered and cell vertex finite volume schemes, In: Proc. 7th GAMM Conf. on Numerical Methods in Fluid Mechanics. Braunschweig: Vieweg 1988 (also appeared in: Notes on Num. Fluid Mech. 20, 327–334 (1988)).

  • Jameson, A., Schmidt, W., Turkel, E.: Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes. In: AIAA 14th Fluid and Plasma Dynamics Conf., Palo Alto, CA, June 23–25, 1981, AIAA Paper 81–1259 (1981).

  • Radespiel, R.: A cell-vertex multigrid method for the Navier-Stokes equations, NASA TM 101557 (1989).

  • Singh, J. P., Schwamborn, D.: Navier-Stokes solution for supersonic flow past airfoils. Paper presented at IMACS Int. Symp., Bangalore, India, 1992.

  • Hazra, S. B.: Computation of high-speed flow using non-oscillatory scheme, In: Hyperbolic Problems: Theory, Numerics, Applications. Proc. 7th Int. Conf. on Hyperbolic Problems, Zürich (Fey, M., Jeltsch, R., eds.), 1, pp. 465–474. Basel: Birkhäuser 1998.

  • Yee, H. C.: Construction of explicit and implicit symmetric TVD schemes and their applications. J. Comp. Phys. 68, 151–179 (1987).

    Google Scholar 

  • Ghosh, A. K., Deshpande, S. M.: A robust least squares kinetic upwind scheme for Euler equations. In: 14th Int. Conf. on Numerical Methods in Fluid Dynamics, Bangalore, India. Lecture Notes in Physics 453, New York: Springer 1994.

  • Deshpande, S. M., Kulkarni, P. S., Ghosh, A. K.: New developments in kinetic schemes. Comput. Math. Appl. 35 75–93 (1998).

    Google Scholar 

  • Kreiss, H. O.: Initial boundary value problems for hyperbolic systems. Comm. Pure App. Maths. 13, 277–298 (1970).

    Google Scholar 

  • Roe, P. L.: Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Phys. 43, 357–372 (1981).

    Google Scholar 

  • Chakrabartty, S. K.: A finite volume nodal point scheme for solving two-dimensional Navier-Stokes equations. Acta Mech. 84, 139–153 (1990).

    Google Scholar 

  • Jain, R. K.: Grid generation about an airfoil by an algebraic equation method. DFVLR-IB-129-83/40 (1983).

  • Mathur, J. S., Chakrabartty, S. K.: An approximate factorization scheme for elliptic grid generation with control functions. Num. Meth. Partial Differential Eqs. 10, 703–713 (1994).

    Google Scholar 

  • Pulliam, T. H., Barton, J. T.: Euler computations of AGARD working group 07 Airfoil Test Cases. In: AIAA 23rd Aerospace Sciences Meeting, Reno, Nev., 1985. AIAA Paper 85–0018 (1985).

  • Test cases for inviscid flow field methods. AGARD Advisory Report 211, Report of the Fluid Dynamics Panel Working Group 07, May 1985.

Download references

Author information

Authors and Affiliations

  1. Department of Basic Sciences and Humanities, College of Engineering and Management, Kolaghat, Purba Medinipur 721, 171, West Bengal, India

    S. Ghosh & P. Niyogi

Authors
  1. S. Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Niyogi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Ghosh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ghosh, S., Niyogi, P. Evaluation of non-oscillatory schemes based on LED principle for supersonic flow computations. Acta Mechanica 177, 29–41 (2005). https://doi.org/10.1007/s00707-005-0216-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-005-0216-4

Keywords

Search

Navigation