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Keywords: Richtmyer-Meshkov instability, mixing, weighted essentially non-oscillatory shock-capturing method, hybrid method, cylindrical shells.

Summary

In this paper the mixing due to the Richtmyer-Meshkov instability in a stratified cylindrical shell is numerically studied by using a hybrid method combined with the weighted essentially non-oscillatory shock-capturing method and the tuned center difference scheme. In the regions away from shocks and material interfaces the tuned centre-difference scheme with low numerical dissipation and good wave-dispersion properties is adopted, while in the regions containing shocks and material interfaces the WENO scheme based on the characteristic decomposition is used. The hybrid scheme utilizes a discontinuity detection criterion to switch the two different schemes. In the tuned centre-difference scheme, the skew-symmetric form is employed to improve the numerical stability. A third-order strong-stability preserving Runge-Kutta scheme is adopted for the time integration. The fluxes of the viscous and diffusion transport terms are computed using explicit center-difference operator.

The implosion histories with various initial perturbations located at different interfaces have been simulated. It was found that motion of the flow exhibits three regimes during the evolution time, which are compression, rebound and mixing. The result of a typical case with random initial perturbation on the outer interface was given, including the density field, the volume fraction of the shell material, and the simulated density schlieren field.

To measure the mixing evolution history qualitatively and quantitatively, some statistical quantities together with the mixing zone width are defined based on the simulation data. Several problems such as the effect of the initial perturbation spectral distribution, actions of the viscous term, heat transport and molecular diffusion have been discussed. It was found that the mixing zone width exhibits significant sensitivity to the initial perturbation spectral distribution, especially during the first two stages. However, at the late-time mixing stage the growth rate of the mixing zone and the mixing fraction tend to be less dependent on the initial conditions. For the actions of the viscous term, heat transport and molecular diffusion, we found that the mixing evolution is not very sensitive to these factors except that these terms vary acutely.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 89 PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: M. Papadrakakis and B.H.V. Topping Paper 172 A Numerical Study of the Richtmyer-Meshkov Instability and Mixing in Stratified Cylindrical Shells L. Wang National Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China doi:10.4203/ccp.89.172 purchase the full-text of this paper Full Bibliographic Reference for this paper L. Wang, "A Numerical Study of the Richtmyer-Meshkov Instability and Mixing in Stratified Cylindrical Shells", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 172, 2008. doi:10.4203/ccp.89.172 Keywords: Richtmyer-Meshkov instability, mixing, weighted essentially non-oscillatory shock-capturing method, hybrid method, cylindrical shells. Summary In this paper the mixing due to the Richtmyer-Meshkov instability in a stratified cylindrical shell is numerically studied by using a hybrid method combined with the weighted essentially non-oscillatory shock-capturing method and the tuned center difference scheme. In the regions away from shocks and material interfaces the tuned centre-difference scheme with low numerical dissipation and good wave-dispersion properties is adopted, while in the regions containing shocks and material interfaces the WENO scheme based on the characteristic decomposition is used. The hybrid scheme utilizes a discontinuity detection criterion to switch the two different schemes. In the tuned centre-difference scheme, the skew-symmetric form is employed to improve the numerical stability. A third-order strong-stability preserving Runge-Kutta scheme is adopted for the time integration. The fluxes of the viscous and diffusion transport terms are computed using explicit center-difference operator. The implosion histories with various initial perturbations located at different interfaces have been simulated. It was found that motion of the flow exhibits three regimes during the evolution time, which are compression, rebound and mixing. The result of a typical case with random initial perturbation on the outer interface was given, including the density field, the volume fraction of the shell material, and the simulated density schlieren field. To measure the mixing evolution history qualitatively and quantitatively, some statistical quantities together with the mixing zone width are defined based on the simulation data. Several problems such as the effect of the initial perturbation spectral distribution, actions of the viscous term, heat transport and molecular diffusion have been discussed. It was found that the mixing zone width exhibits significant sensitivity to the initial perturbation spectral distribution, especially during the first two stages. However, at the late-time mixing stage the growth rate of the mixing zone and the mixing fraction tend to be less dependent on the initial conditions. For the actions of the viscous term, heat transport and molecular diffusion, we found that the mixing evolution is not very sensitive to these factors except that these terms vary acutely. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £95 +P&P)
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