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An Evaluation of a Structured Overlapping Grid Implementation of FCT for High-Speed Flows

  • Chapter
Flux-Corrected Transport

Part of the book series: Scientific Computation ((SCIENTCOMP))

  • 2012 Accesses

Abstract

This study considers the development and assessment of a Flux-Corrected Transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered include smooth manufactured solutions, isolated shock and contact discontinuities, a modified Sod shock-tube problem, a two-shock Riemann problem, the Shu-Osher test problem, shock impingement on single cylinder, irregular Mach reflection of a strong shock striking an inclined plane, shock impingement on multiple fixed and movable cylinders, and an idealized Z-pinch implosion problem.

This work was partially supported by the DOE Office of Science, Advanced Scientific Computing Research-Applied Mathematics Program at Sandia National Laboratory under contract DE-AC04-94AL85000 and at Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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Authors and Affiliations

  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA, 94551, USA

    J. W. Banks

  2. Computational Sciences Research Institute, Sandia National Laboratories, Albuquerque, NM, 87185-1321, USA

    J. N. Shadid

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  1. J. W. Banks
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Correspondence to J. W. Banks .

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Editors and Affiliations

  1. , Chair of Applied Mathematics III, University of Erlangen-Nuremberg, Haberstr. 2, Erlangen, 91058, Germany

    Dmitri Kuzmin

  2. , School of Computational Sciences, George Mason University, 4400 University Drive MS 6A2, Fairfax, 22030, Virginia, USA

    Rainald Löhner

  3. Institute of Applied Mathematics, LS III, Dortmund University of Technology, Vogelpothsweg 87, Dortmund, 44227, Germany

    Stefan Turek

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Banks, J.W., Shadid, J.N. (2012). An Evaluation of a Structured Overlapping Grid Implementation of FCT for High-Speed Flows. In: Kuzmin, D., Löhner, R., Turek, S. (eds) Flux-Corrected Transport. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4038-9_11

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