How do numerical methods effect statistical details of richtmyer-meshkov instabilities.

Rider, W. J. ; Kamm, J. R. ; Zoldi, C.

Technical Information Center Oak Ridge Tennessee

关键词: Numerical analysis;    Hydrodynamics;    Instability;    Dimensions;    Fractals;   

RP-ID  :  DE2001782806

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

Over the past several years we have presented a less than glowing experimental comparison of hydrodynamic codes with the gas curtain experiment. Here, we discuss the manner in which the various details of the hydrodynamic integration techniques conspire to produce poor results. This also includes some progress in improving the results and agreement with experimental results. Our results are based upon the gas curtain, Richtmyer-Meshkov experiments conducted by Rightley et al. (Rightley et al. 1999) at Los Alamos. We also examine the results of a gas cylinder experiment conducted more recently by Prestridge and Zoldi which includes velocity data obtained via a PIV technique. Traditionally, the integral width of the mixing layer is used as a yardstick to measure the Richtmyer-Meshkov instability. This is also used when investigating the performance of numerical methods. Our focus has been on the details of the mixing below the integral scale. Because the flow is hydrodynamically unstable, we employ statistical measures in our comparisons. This is built upon a parallel effort by the experimentalists investigating the statistical nature of the mixing induced by shock waves. The principle tools we use to measure the spectral structure of the images of these flows are the fractal dimension and the continuous wavelet spectrum. The bottom line is that all the higher order methods used to simulate the gas curtain compare poorly with the experimental data when quantified with these spatial statistics. Moreover, the comparisons degrade under mesh refinement. This occurs despite the fact that the integral scale comparison is acceptable and consistent with the expectations from this class of methods. The most surprising result is that a first-order Godunov method does produce a good comparison relative to the assumed to be higher-order methods. We have examined a broad variety of methodologies associated with the high-order methods to illuminate this problematic result. In the next section we briefly describe the experiments. In Section the quantitative measures applied to the images are detailed; the results of these analyses are discussed in Section refsec:compare. The consideration of the relation between turbulence models and numerical methods was inspired by these results and is discussed.