Volume 1, Issue 4
A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids

Michael Yang & Z.J. Wang

Adv. Appl. Math. Mech., 1 (2009), pp. 451-480.

Published online: 2009-01

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  • Abstract

A parameter-free limiting technique is developed for high-order unstruc- tured-grid methods to capture discontinuities when solving hyperbolic conservation laws. The technique is based on a "troubled-cell" approach, in which cells requiring limiting are first marked, and then a limiter is applied to these marked cells. A parameter-free accuracy-preserving TVD marker based on the cell-averaged solutions and solution derivatives in a local stencil is compared to several other markers in the literature in identifying "troubled cells". This marker is shown to be reliable and efficient to consistently mark the discontinuities. Then a compact high-order hierarchical moment limiter is developed for arbitrary unstructured grids. The limiter preserves a degree p polynomial on an arbitrary mesh. As a result, the solution accuracy near smooth local extrema is preserved. Numerical results for the high-order spectral difference methods are provided to illustrate the accuracy, effectiveness, and robustness of the present limiting technique.

  • Keywords

Limiter shock-capturing high-order unstructured grids

  • AMS Subject Headings

65M70 76M20 76M22

  • Copyright

COPYRIGHT: © Global Science Press

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