High order finite volume schemes for numerical solution of 2D and 3D transonic flows

Jiří Fürst; Karel Kozel; Petr Furmánek

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 567-579
  • ISSN: 0023-5954

Abstract

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The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC). Two different test cases were chosen for the comparison - 1 ) two-dimensional transonic inviscid nonstationary flow over an oscillating NACA 0012 profile and 2) three-dimensional transonic inviscid stationary flow around the Onera M6 wing. Nonstationary effects were simulated with the use of Arbitrary Lagrangian–Eulerian Method (ALE). Experimental results for these regimes of flow are easily available and so the numerical results are compared both in-between and with experimental data. The obtained numerical results in all considered cases (2D and 3D) are in a good agreement with experimental data.

How to cite

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Fürst, Jiří, Kozel, Karel, and Furmánek, Petr. "High order finite volume schemes for numerical solution of 2D and 3D transonic flows." Kybernetika 45.4 (2009): 567-579. <http://eudml.org/doc/37717>.

@article{Fürst2009,
abstract = {The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC). Two different test cases were chosen for the comparison $-1$) two-dimensional transonic inviscid nonstationary flow over an oscillating NACA 0012 profile and 2) three-dimensional transonic inviscid stationary flow around the Onera M6 wing. Nonstationary effects were simulated with the use of Arbitrary Lagrangian–Eulerian Method (ALE). Experimental results for these regimes of flow are easily available and so the numerical results are compared both in-between and with experimental data. The obtained numerical results in all considered cases (2D and 3D) are in a good agreement with experimental data.},
author = {Fürst, Jiří, Kozel, Karel, Furmánek, Petr},
journal = {Kybernetika},
keywords = {ALE method; AUSMPW+; finite volume method; HLLC; nonstationary flow; transonic flow; TVD; finite volume method; ALE method; AUSMPW+; HLLC; nonstationary flow; transonic flow; TVD},
language = {eng},
number = {4},
pages = {567-579},
publisher = {Institute of Information Theory and Automation AS CR},
title = {High order finite volume schemes for numerical solution of 2D and 3D transonic flows},
url = {http://eudml.org/doc/37717},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Fürst, Jiří
AU - Kozel, Karel
AU - Furmánek, Petr
TI - High order finite volume schemes for numerical solution of 2D and 3D transonic flows
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 567
EP - 579
AB - The aim of this article is a qualitative analysis of two modern finite volume (FVM) schemes. First one is the so called Modified Causon’s scheme, which is based on the classical MacCormack FVM scheme in total variation diminishing (TVD) form, but is simplified in such a way that the demands on computational power are much smaller without loss of accuracy. Second one is implicit WLSQR (Weighted Least Square Reconstruction) scheme combined with various types of numerical fluxes (AUSMPW+ and HLLC). Two different test cases were chosen for the comparison $-1$) two-dimensional transonic inviscid nonstationary flow over an oscillating NACA 0012 profile and 2) three-dimensional transonic inviscid stationary flow around the Onera M6 wing. Nonstationary effects were simulated with the use of Arbitrary Lagrangian–Eulerian Method (ALE). Experimental results for these regimes of flow are easily available and so the numerical results are compared both in-between and with experimental data. The obtained numerical results in all considered cases (2D and 3D) are in a good agreement with experimental data.
LA - eng
KW - ALE method; AUSMPW+; finite volume method; HLLC; nonstationary flow; transonic flow; TVD; finite volume method; ALE method; AUSMPW+; HLLC; nonstationary flow; transonic flow; TVD
UR - http://eudml.org/doc/37717
ER -

References

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  10. Second and third order weighted ENO scheme on unstructured meshes, In: Proc. Finite Volumes for Complex Applications III (D. Herbin and D. Kröner, eds.), Hermes Penton Science, pp. 737–744. 
  11. Methods for the accurate computations of hypersonic flows, AUSMPW+ scheme. J. Comput. Physics 174 (2001), 38–80. MR1869671
  12. Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations, Comput. Methods Appl. Mech. Engrg. 134 (1996), 71–90. 
  13. Pressure Distributions on the ONERA-M6-Wing at Transonic Mach Numbers, Experimental Data Base for Computer Program Assessment. Report of the Fluid Dynamics Panel Working Group 04, AGARD AR 138, 1979. 
  14. A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods, Technical Memorandum 101088, NASA, Moffett Field, California 1989. 

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