Analysis and design of numerical schemes for gas dynamics 1: Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence

International Journal of Computational Fluid Dynamics

Volumn 4, Issue 3-4, 1995, Pages 171-218

  Jameson, A ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Artificial diffusion; Flux limited dissipation; Numerical compressible fluid dynamics; Upwind schemes

Indexed keywords

EID: 84954695021     PISSN: 10618562     EISSN: 10290257     Source Type: Journal    
DOI: 10.1080/10618569508904524     Document Type: Article

References (22)

1. Aiso, H. (1993) Admissibility of Difference Approximations for Scalar Conservation Laws. Hiroshima Math. Journal, 23, 15–61.
2. Anderson, B. K., Thomas, J. and Van Leer, B. (1985) A Comparison of Flux Vector Splittings for the Euler Equations. AIAA Paper 85–0122, Reno, NV, January.
3. Arminjon, P. and Dervieux, A. (1993) Construction of TVD-like Artifical Viscosities on 2-dimensional Arbitrary FEM grids. J. Comp. Phys., 106, 176–198. Published also as 1NRIA Report 1111, October 1989.
4. Balakrishnan, N. and Deshpande, S. M. (1991) New Upwind schemes with Wave-Particle Splitting for Inviscid Compressible Flows. Report 91 FM 12, Indian Institute of Science.
5. Barth, T. J. and Jespersen, D. C. The Design and Application of Upwind Schemes on Unstructured Meshes. AIAA paper 89–0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, January.
6. Boris, J. P. and Book, D. L., (1973) Flux Corrected Transport, 1 SHASTA, a Fluid Transport Algorithm That Works. J. Comp. Phys„ 11, 38–69.
7. Busch, R. J. Jr. Computational Fluid Dynamics in the Design of the Northrop/McDonnell Douglas YF-23 ATF Prototype. AIAA paper 91–1627, AIAA 21st Fluid Dynamics, Plasmadynamics and Lasers Conference, Honolulu, Hawaii 1991
8. Denton, J. D. (1983) An Improved Time Marching Method for Turbomachinery Flow Calculations. J. Engr.for Gas Turbines and Power, 105.
9. Einfeldt, B. (1988) On Godunov-Type Methods for Gas Dynamics. SIAM J, Num. Anal., 25, 294–318.
10. Godunov, S. K. (1960) A Difference Method for the Numerical Calculation of Discontinuous Solutions of Hydrodynamic Equations. Mat. Sbornik, 47,271–306,1959. Translated as JPRS 7225 by U.S. Dept, of Commerce
11. Harten, A. (1983) High Resolution Schemes for Hyperbolic Conservation Laws, J. Comp. Phys., 49, 357–393.
12. Harten, A., Lax, P. D. and Van Leer, B., (1983) On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws. SIAM Review, 25, 35–61.
13. Hirsch, Ch. and Lacor, C. (1989) Upwind Algorithms Based on a Diagonalisation for the Multidimensional Euler Equations. AIAA paper 89-1958-CP, AIAA 9th Computational Fluid Dynamics Conference, Buffalo, New York.
14. Hirsch,Ch. Lacor, C. and Deconinck, H. Convection Algorithms Based on a Diagonalisation Procedure for the Multidimensional Euler Equations. AIAA paper 87-1163-CP, AIAA 8th Computational Fluid Dynamics Conference, Honolulu, Hawaii, 1987.
15. Hughes, T.J.R., Franca, L. P. and Mallet, M. (1986) A new Finite Element Formulation for Computational Fluid Dynamics, I, Symmetric forms of the Compressible Euler and Na vier-Stokes Equations and the Second Law of Thermodynamics. Comp. Meth. Appl. Mech. and Eng., 59, 223–231.
16. Jameson, A. (1983) Solution of the Euler Equations for two Dimensional Transonic Flow by a Multigrid Method. Appl. Math. Comp., 13, 327–356.
17. Jameson, A. (1985) Non-Oscillatory Shock Capturing Scheme Using Flux Limited Dissipation. In B.E. Engquist, S. Osher, and R. C. J. Sommerville, editors, Lectures in Applied Mathematics, Vol. 22, Part 1, Large Scale Computations in Fluid Mechanics, pages 345–370. AMS.
18. Jameson, A, (1986) Multigrid Algorithms for Compressible Flow Calculations. In W. Hackbusch and U. Trottenberg, editors, Lecture Notes in Mathematics. Vol. 1228, pages 166–201. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985, Springer-Veriag.
19. Jameson, A. Successes and Challenges in Computational Aerodynamics. AIAA paper 87-1184-CP, AIAA 8th Computational Fluid Dynamics Conference, Honolulu, Hawaii, 1987.
20. Jameson, A. Airfoils Admitting Non-Unique Solutions of the Euler Equations, AIAA paper 91–1625, AIAA 22nd Fluid Dynamics, Plasmadynamics and Lasers Conference, Honolulu, Hawaii, June, 1991.
21. Jameson, A. Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Accuracy and Multigrid Convergence in Transonic and Hypersonic Flow. AIAA paper 93–3359, AIAA 11 th Computational Fluid Dynamics Conference, Orlando, Florida, July, 1993.
22. Jameson, A. (1993) Computational Algorithms for Aerodynamic Analysis and Design. Appl. Num. Math., 13, 383–422.