PERFORMANCE OF LIMITERS IN MODAL DISCONTINUOUS GALERKIN METHODS FOR 1-D EULER EQUATIONS

Title & Authors
PERFORMANCE OF LIMITERS IN MODAL DISCONTINUOUS GALERKIN METHODS FOR 1-D EULER EQUATIONS
Karchani, A.; Myong, R.S.;

Abstract
Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($\small{p^1}$, $\small{p^2}$, and $\small{p^3}$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.
Keywords
Discontinuous Galerkin(DG) method;hyperbolic system;1-D Euler equations;limiters;
Language
English
Cited by
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