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Structure Functions for Numerical Shocks

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Numerical Fluid Dynamics

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

In this chapter, we will present an in-depth analysis of the structure of numerical shocks. Our analysis will feature the structure function, a simple technique to generate high-fidelity data for the structure of the numerical shock. We will describe two ODE models to analyze that data in terms of shock width, overshoot, and the dissipation that is explicit in the equations and implicit in the discretization. We will briefly summarize the methodology of shock capturing as employed in Lagrangian simulations and apply our ODE models to shocks generated by standard artificial viscosity formulations. We will review the recent application of finite scale theory to the structure of physical shocks, revealing the analogies between physical and numerical shocks, and exploiting them to design a new shock-capturing strategy. We will also consider shocks generated in nonoscillatory Eulerian simulations and compare their structure with comparable Lagrangian simulations.

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Acknowledgements

We gratefully acknowledge many illuminating discussions with Roy Baty, Don Burton, Tony Hirt, James Quirk, Scott Runnels, Misha Shashkov, and Diane E. Vaughan. This work was performed under the auspices of the U.S. Department of Energy’s NNSA by the Los Alamos National Laboratory, is managed by Triad National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract 89233218CNA000001.

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Authors and Affiliations

  1. Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    L. G. Margolin

  2. Applied Physics Division, Los Alamos National Laboratory, Los Alamos, NM, USA

    S. D. Ramsey

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  1. L. G. Margolin
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  2. S. D. Ramsey
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Correspondence to L. G. Margolin .

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Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

  3. ISAE-ENSMA, Institut Pprime, Futuroscope Chasseneuil Cedex, France

    Eric Goncalves Da Silva

  4. Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, USA

    Lucy T. Zhang

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Margolin, L.G., Ramsey, S.D. (2022). Structure Functions for Numerical Shocks. In: Zeidan, D., Merker, J., Da Silva, E.G., Zhang, L.T. (eds) Numerical Fluid Dynamics. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-9665-7_1

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