Pseudospectral approximation compared with control volume formulation and finite differences- some test cases

• Autorzy: Tyliszczak A. , Bogusławski A.
• Języki publikacji: EN

Abstrakty

EN

The paper presents comparison of the pseudospectral method with low-order approximation for two test cases. The first test case is quasi one-dimensional supersonic flow through converging-diverging nozzle for which exact solution exists. The comparison of the error of pseudospectral approximation and upwind finite-differences using Steger-Warming flux splitting method shows high accuracy of the pseudospectral method even for few collocation points. The same conclusion is formulated for the second test case, namely incompressible flow in two-dimensional driven cavity solved by control volume formulation with modified QUICK upwinding scheme and SIMPLEC algorithm for pressure correction. As usually conclusions concerning accuracy of numerical methods are flow case dependent, but the two examples shown give some idea about the accuracy and resolution of spectral approximation versus standard CFD schemes.

Słowa kluczowe

EN

computational fluid dynamics CFD; CFD; spectral methods; pseudospectral method; supersonic flows; driven cavity

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2000
• Tom: Vol. 4, No 2
• Strony: 193--202
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Tyliszczak A.

• Institute of Thermal Machinery, Technical University of Czestochowa, Armii Krajowej 21, Czestochowa, Poland
• von Karman Institute for Fluid Dynamics, Aeronautics and Aeorespace Department, Chaussee de Waterloo 72, 1640 Rhode Saint Geriese, Belgium

autor

Bogusławski A.

• Institute of Thermal Machinery, Technical University of Częstochowa, Armii Krajowej 21, 42-200 Częstochowa, Poland

Bibliografia

• [1] Canuto C., Hussaini M. Y., Quarteroni A. and Zang T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin-Heidelberg, 1988
• [2] Fletcher C. A. J., Computational Technics for Fluid Dynamics. Volume II. Specific Techniques for Different Flow Categories, Springer-Verlag, Berlin-Heidelberg, 1991
• [3] Fox L. and Parker I. B., Chebyschevpolynomials in numerical analysis, Oxford Univ. Press, London 1968
• [4] Hirsch Ch., Numerical computation of internal and external flows, Volume II, John Wiley & Sons, Chichester 1990
• [5] Pollard A. and Siu W. L., The calculation of some laminar flow using various discretisation schemes, Comp. Meth. Appl. Mechanical Engineering., 35, 293, 1982
• [6] Rivlin T. J., The Chebyschev polynomials, John Wiley & Sons, New York 1974
• [7] Steger J. L. and Warming R. F., Flux vector splitting of the inviscid gasdynamic equations with application to finite difference methods, J. Comput. Phys., 40, 263, 1981