An Adaptive Order Godunov Type Central Scheme

  • Eitan Tadmor
  • Jared Tanner
Conference paper


Traditionally, high order Godunov-type central schemes employ local polynomial reconstructions. These reconstructions avoid transfer of information across discontinuities through nonlinear limiters which act as local edge detectors. Here we introduce an adaptive method which employ global edge detection to ensure that information is extracted in the direction of smoothness while maintaining computational stability. Additionally, the global edge detection substantially reduces the computational cost. The reconstruction incorporates the largest symmetric stencil possible without crossing discontinuities. Consequently, the spatial order of accuracy is proportional to the number of cells to the nearest discontinuity, reaching exponential order at the interior of regions of smoothness.


Rarefaction Wave Contact Discontinuity Central Scheme Total Variation Diminishing Piecewise Smooth Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Eitan Tadmor
    • 1
  • Jared Tanner
    • 2
  1. 1.Department of MathematicsInstitute for Physical Science & Technology and Center for Scientific Computation And Mathematical Modeling (CSCAMM), University of Maryland College Park
  2. 2.Department of MathematicsUniversity of California Davis

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