한국전산유체공학회지 (Journal of computational fluids engineering)

한국전산유체공학회 (Korean Society of Computational Fluids Engineering)
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1-D 오일러 방정식에 관한 Modal 불연속 갤러킨 기법에서의 Limiter 성능 비교

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

  • Karchani, A. (Graduate School of Mechanical and Aerospace Engineering, Gyeongsang Nat'l Univ.) ;
  • Myong, R.S. (Graduate School of Mechanical and Aerospace Engineering, Gyeongsang Nat'l Univ.)
  • 투고 : 2016.03.03
  • 심사 : 2016.06.01
  • 발행 : 2016.06.30
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초록

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($p^1$, $p^2$, and $p^3$) 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.

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참고문헌

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피인용 문헌

  1. Computational simulations of near-continuum gas flow using Navier-Stokes-Fourier equations with slip and jump conditions based on the modal discontinuous Galerkin method vol.2, pp.1, 2016, https://doi.org/10.1186/s42774-020-00032-z