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A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability

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Abstract

The HLLC approximate Riemann solver improves upon the HLL Riemann solver by resolving contact discontinuities. This is a particularly desirable property for multi-material codes in which problems usually contain material interfaces. However, the HLLC solver is known to suffer from the carbuncle phenomenon, a numerical instability most apparent at grid-aligned shocks in multi-dimensional simulations. Many problems of interest, including high energy-density physics applications, require the accurate resolution of both material interfaces and hydrodynamic shocks. A variety of methods have been developed to cure this instability, with varying degrees of complexity. The objective of this work is to describe a simple approach to modify the HLLC Riemann solver and prevent the carbuncle instability. The method is then demonstrated for assorted two-dimensional test problems known to exhibit the shock instability. The performance of the new solver is compared with that of the standard HLL and HLLC Riemann solvers.

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Funding

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Department of Energy Computational Science Graduate Fellowship under Award Number DE-SC0021110. AB, SWJ, JCD, and PVFE were supported by the U.S. Department of Energy through the Los Alamos National Laboratory (LANL). LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy (Contract No. 89233218CNA000001). This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. This work has been assigned a document release number LA-UR-22-23378.

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Authors and Affiliations

  1. X Computational Physics (XCP) Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Alexandra Baumgart

  2. Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA

    Alexandra Baumgart

  3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Samuel W. Jones

  4. Computer, Computational, and Statistical Sciences (CCS) Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Philipp V. F. Edelmann & Joshua C. Dolence

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  1. Alexandra Baumgart
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  2. Samuel W. Jones
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  3. Philipp V. F. Edelmann
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  4. Joshua C. Dolence
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Correspondence to Alexandra Baumgart.

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Baumgart, A., Jones, S.W., Edelmann, P.V.F. et al. A Shock Stabilization of the HLLC Riemann Solver for the Carbuncle Instability. J Sci Comput 98, 33 (2024). https://doi.org/10.1007/s10915-023-02419-8

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  • DOI: https://doi.org/10.1007/s10915-023-02419-8

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