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Boundary Closures for Sixth-Order Energy-Stable Weighted Essentially Non-Oscillatory Finite-Difference Schemes

  • Mark H. CarpenterEmail author
  • Travis C. Fisher
  • Nail K. Yamaleev
Part of the Fields Institute Communications book series (FIC, volume 66)

Abstract

A general strategy was presented in 2009 by Yamaleev and Carpenter (J. Comput. Phys. 228(11):4248–4272, 2009; J. Comput. Phys. 228(8):3025–3047, 2009), for constructing Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite-difference schemes on periodic domains. Fisher et al. (J. Comput. Phys. 230(10):3727–3752, 2011) provided boundary closures for the fourth-order ESWENO scheme that maintain, the WENO stencil biasing properties and satisfy the summation-by-parts (SBP) operator convention, thereby ensuring stability in an L 2 norm. Herein, the general capability of finite-domain schemes is extended by providing closures for the sixth-order case. Third-order and fifth-order boundary closures are developed that are stable in diagonal and block norms, respectively, and achieve fourth- and sixth-order global accuracy for hyperbolic systems. A novel set of nonuniform flux interpolation points is necessary near the boundaries to simultaneously achieve (1) accuracy, (2) the SBP convention, and (3) WENO stencil biasing mechanics. Complete implementation details for the diagonal-norm sixth-order operator are provided as well as examples that demonstrate shock capturing and multi-domain capabilities.

Keywords

WENO Scheme Boundary Closure Free Stream Mach Number Design Order Linear Advection Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Mark H. Carpenter
    • 1
    Email author
  • Travis C. Fisher
    • 1
  • Nail K. Yamaleev
    • 2
  1. 1.NASA Langley Research CenterHamptonUSA
  2. 2.Department of MathematicsNorth Carolina A&T State UniversityGreensboroUSA

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