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WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions

By Panagiotis Tsoutsanis, Vladimir A. Titarev and Dimitris Drikakis

Abstract

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases and the compressible Euler equations on various types of grids. Schemes of up to fifth order of spatial accuracy are considered

Topics: WENO, Unstructured, Tetrahedral, Hexahedral, Prismatic, Pyramidal, Mixed-element, Three space dimensions, Very high order, Euler
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.jcp.2010.11.023.
OAI identifier: oai:dspace.lib.cranfield.ac.uk:1826/4773
Provided by: Cranfield CERES
Journal:

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Citations

  1. (1959). A ¯nite di®erence method for the computation of discontinuous solutions of the equations of °uid dynamics.
  2. (2002). A technique for treating negative weights in WENO schemes. doi
  3. (2004). ADER schemes for the solution of conservation laws on adaptive triangulations. In: Iske, A., Randen, doi
  4. (2007). Arbitrary high order non-oscillatory ¯-nite volume schemes on unstructured meshes for linear hyperbolic systems. doi
  5. (2007). Arbitrary high-order Discontinuous Galerkin schemes for the magnetohydrodynamic equations. doi
  6. (2009). Assessment of large-eddy simulation of internal separated °ow. doi
  7. (2006). Derivative Riemann solvers for systems of conservation laws and ADER methods. doi
  8. (1996). E±cient implementation of weighted ENO schemes. doi
  9. (2004). Finite-volume WENO schemes for threedimensional conservation laws. doi
  10. (1990). Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. In: doi
  11. (2002). Mathematical Aspects of Numerical Solution of Hyperbolic Systems. doi
  12. (2000). Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. doi
  13. (1998). Multilevel k-way partitioning scheme for irregular graphs. doi
  14. (2007). On the implicit large eddy simulations of homogeneous decaying turbulence. doi
  15. (2007). Quadrature-free non-oscillatory ¯nite volume schemes on unstructured meshes for nonlinear hyperbolic systems. doi
  16. (2009). Riemann solvers and numerical methods for °uid dynamics, 3rd Edition. doi
  17. (2002). Space-time discontinuous Galerkin ¯nite element method with dynamic grid motion for inviscid compressible °ows: I. General formulation. doi
  18. (1964). Summary Report on Aerodynamic Characteristics of Standard Models HB-1 and HB-2. In:
  19. (2009). Third order WENO scheme on three dimensional tetrahedral meshes.
  20. (2001). Towards very high order Godunov schemes. In: doi
  21. Uniformly high-order schemes on arbitrary unstructured meshes for advection-di®usion equations. Computers and Fluids, doi
  22. (1998). Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. doi
  23. (1994). Weighted essentially non-oscillatory schemes. doi

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