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RESEARCH PAPERS

# Assessment of Very High Order of Accuracy in Implicit LES models

[+] Author and Article Information
Andrew Mosedale

Fluid Mechanics & Computational Science Group, Aerospace Sciences Department, School of Engineering, Cranfield University, Cranfield MK43 0AL, United Kingdoma.d.mosedale@cranfield.ac.uk

Dimitris Drikakis

Fluid Mechanics & Computational Science Group, Aerospace Sciences Department, School of Engineering, Cranfield University, Cranfield MK43 0AL, United Kingdomd.drikakis@cranfield.ac.uk

J. Fluids Eng 129(12), 1497-1503 (Jul 27, 2007) (7 pages) doi:10.1115/1.2801374 History: Received February 15, 2007; Revised July 27, 2007

## Abstract

This paper looks at the use of high-resolution and very high-order methods for implicit large-eddy simulation (ILES), with the specific example of simulating the multicomponent two-dimensional single-mode Richtmyer–Meshkov instability for which experimental data is available. The two gases are air and SF6, making stringent demands on the models used in the code. The interface between the two gases is initialized with a simple sinusoidal perturbation over a wavelength of $59mm$, and a shock of strength Mach 1.3 is passed through this interface. The main comparison is between the second-order monotone upwind-centered scheme for conservation law methods of van Leer (1979, “Towards the Ultimate Conservative Difference Scheme  ,” J. Comput. Phys.32, pp. 101–136) and the current state-of-the-art weighted essentially nonoscillatory interpolation, which is presented to ninth order, concentrating on the effect on resolution of the instability on coarse grids. The higher-order methods as expected provide better resolved and more physical features than the second-order methods on the same grid resolution. While it is not possible to make a definitive statement, the simulations have indicated that the extra time required for the higher-order reconstruction is less than the time saved by being able to obtain the same or better accuracy at lower computational cost (fewer grid points). It should also be noted that all simulations give a good representation of the growth rate of the instability, comparing very favorably to the experimental results, and as such far better than the currently existing theoretical models. This serves to further indicate that the ILES approach is capable of providing accurately physical information despite the lack of any formal subgrid model.

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## Figures

Figure 1

Plot of volume fraction of SF6 showing the development of the instability over time, using fifth-order WENO on 80×240 grid, based on a sharp initial interface

Figure 2

Volume fraction plots of Richtmyer–Meshkov simulations with No. of cells per wavelength and reconstruction method (VL: second-order van Leer, W5: fifth-order WENO, W9: ninth-order WENO) for sharp initial interface and Atwood No. of 0.692

Figure 3

Growth of instability, as predicted by different methods (lines), compared to experimental measurements (circles relate to equivalent problem, and triangles to a weaker shock case), nondimensionalized

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