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Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

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Abstract

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed in the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows.

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Acknowledgments

This research was supported by the U.S. Army’s MAST CTA Center for Microsystem Mechanics with Mr. Chris Kroninger (ARL-VTD) as Technical Monitor.

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  1. Debojyoti Ghosh

    Present address: Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, 60439, USA

Authors and Affiliations

  1. Applied Mathematics and Statistics, and Scientific Computation, University of Maryland, College Park, MD, 20742, USA

    Debojyoti Ghosh

  2. Department of Aerospace Engineering, University of Maryland, College Park, MD, 20742, USA

    James D. Baeder

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  1. Debojyoti Ghosh
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  2. James D. Baeder
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Correspondence to Debojyoti Ghosh.

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Ghosh, D., Baeder, J.D. Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows. J Sci Comput 61, 61–89 (2014). https://doi.org/10.1007/s10915-014-9818-0

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  • DOI: https://doi.org/10.1007/s10915-014-9818-0

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