Abstracts - KTH Mechanics

18
Actual performance of improved WENO schemes on a
selection of test cases
I. Fedioun ∗ , L. Gougeon ∗ , I. Gokalp ∗
Due to its simplicity, Monotone Integrated Large Eddy Simulation (MILES) has
become astandardwayofLES. This form of LES is intended to capture the correct
flow energy up to some scale in the inertial range and then dissipate this energy at
a non linear rate depending on the numerical dissipation of the scheme. Very long
time simulations should then use highly accurate schemes in conjunction with a fine
enough grid to ensure that the results are not affected by the numerics 1 . From our
experience on Kelvin-Helmholtz instabilities 2 , WENO schemes are good candidates
for MILES but, in their initial form 3 , they still suffer from a relatively poor resolution
of contact discontinuities (with smearing for larger time) and may not always preserve
monotonicity. Recent works 4 5 allowed to fix these two key points, leading to a nearly
optimal numerical scheme. We analyse the actual performance of this kind of modified
WENO schemes and present an extension to multi-fluid simulations. This analysis is
performed on several test cases sorted by order of complexity :(i) asymptotic analysis
of the effective modified wave number, (ii) mono and multi-fluid shock tube problem,
(iii) IWPCTM8’s test cases 6 #2(Rayleigh-Taylor) and #3 (Kelvin-Helmholtz) in 2D,
(iv) 2DH2/air reacting jet with detailed chemistry and variable transport coefficients
(Figure 1).
∗ Laboratoire de Combustion et Systemes Reactifs, C.N.R.S., 1 C avenue de la Recherche Scientifique,
45071 Orleans cedex 2, FRANCE
1 Fedioun et al., Journal of Computational Physics 174, 1 (2001).
2 Lardjane, These de l’Universite d’Orleans (2002).
3 Shu, ICASE Report, 97-65 (1997).
4 Balsara et al., Journal of Computational Physics, 160, 405 (2000).
5 Xu et al., Journal of Computational Physics 205, 458 (2005).
6 IWPCTM8’s test problems; http://www.llnl.gov/iwpctm/html/test.htm
Figure 1: MILES of a subsonic H2/air reacting jet: instantaneous contours of H2O
mass fraction.