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Higher-Order Discontinuous Galerkin-MLP Methods on Triangular and Tetrahedral Grids

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Authors
Park, Jin Seok; Kim, Chongam
Issue Date
2011-06
Publisher
AIAA
Citation
20th AIAA Computational Fluid Dynamics Conference, 2011-3059, pp. 1-18
Keywords
공학
Abstract
This paper deals with the continuous e orts of extending the multi-dimensional limiting
process (MLP) for high speed compressible
ows (or hyperbolic conservation laws), which
has been quite successful in nite volume methods (FVM), into discontinuous Galerkin
(DG) methods. From the previous works, it was observed that the MLP shows several
superior characteristics, such as e cient controlling of multi-dimensional oscillations and
accurate capturing of both discontinuous and continuous multi-dimensional
ow features
within the nite volume framework. Especially, the fundamental mechanism of oscillation-
control in multiple dimensions has been established by combining the local maximum prin-
ciple and the multi-dimensional limiting (MLP) condition, which leads to the formulation
of the e cient and accurate MLP-u slope limiters.
The MLP limiting strategy is now extended into the higher-order DG framework to
develop the hierarchical DG-MLP formulation of arbitrary higher-order (but up to P3 in
present computations) on triangular and tetrahedral grids, which facilitates the capturing
of detailed
ow structures very accurately. By combining the conjecture on the behavior
of local extrema with the augmented MLP condition, the hierarchical DG-MLP method
(MLP-based trouble-cell markers and MLP limiters in RKDG formulation) are developed
up to Pn. Through extensive numerical analyses and computations on triangular and tetra-
hedral grids, it is demonstrated that the proposed DG-MLP approach yields outstanding
performances in resolving non-compressive as well as compressive
ow features.
Language
English
URI
http://hdl.handle.net/10371/82442
DOI
https://doi.org/10.2514/6.2011-3059
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College of Engineering/Engineering Practice School (공과대학/대학원)Dept. of Mechanical Aerospace Engineering (기계항공공학부)Others_기계항공공학부
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