Commun. Comput. Phys., 9 (2011), pp. 627-648.


A Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids

Guanghui Hu 1*, Ruo Li 2, Tao Tang 3

1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA; and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.
2 CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China.
3 Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong.

Received 3 November 2009; Accepted (in revised version) 8 April 2010
Available online 17 September 2010
doi:10.4208/cicp.031109.080410s

Abstract

A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., 1(2008), pp. 92-112] proposed a finite volume solver to solve 2D steady Euler equations. Although the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the shock region, the overshoot or undershoot phenomenon can still be observed. Moreover, the numerical accuracy is degraded by using Venkatakrishnan limiter. To fix the problems, in this paper the WENO type reconstruction is employed to gain both the accurate approximations in smooth region and non-oscillatory sharp profiles near the shock discontinuity. The numerical experiments will demonstrate the efficiency and robustness of the proposed numerical strategy.

AMS subject classifications: 65N08, 65N22, 65N55, 76G25

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Key words: Steady Euler equations, finite volume method, WENO reconstruction, geometrical multigrid, Block LU-SGS.

*Corresponding author.
Email: ghhu@math.msu.edu (G. H. Hu), rli@math.pku.edu.cn (R. Li), ttang@math.hkbu.edu.hk (T. Tang)
 

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