Commun. Comput. Phys., 14 (2013), pp. 425-442.


A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows

Xueying Zhang 1*, Haiyan Tian 2, Leihsin Kuo 2, Wen Chen 3

1 College of Science, Hohai University, Nanjing, Jiangsu 210098, P.R. China.
2 Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406, USA.
3 Department of Engineering Mechanics, Hohai University, Nanjing, Jiangsu 210098, P.R. China.

Received 14 December 2011; Accepted (in revised version) 26 September 2012
Available online 4 January 2013
doi:10.4208/cicp.141211.260912a

Abstract

In this paper, we study a class of contact smoothed particle hydrodynamics (SPH) by introducing Riemann solvers and using high-order limiters. In particular, a promising concept of WENO interpolation as limiter is presented in the reconstruction process. The physical values relating interactional particles used as the initial values of the Riemann problem can be reconstructed by the Taylor series expansion. The contact solvers of the Riemann problem at contact points are incorporated in SPH approximations. In order to keep the fluid density at the wall rows to be consistent with that of the inner fluid wall boundaries, several lines of dummy particles are placed outside of the solid walls, which are assigned according to the initial configuration. At last, the method is applied to compressible flows with sharp discontinuities such as the collision of two strong shocks and the interaction of two blast waves and so on. The numerical results indicate that the method is capable of handling sharp discontinuity and efficiently reducing unphysical oscillations.

AMS subject classifications: 76N15, 35L03

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Key words: Meshless method, SPH method, the Riemann solution, high-order limiter, Taylor series.

*Corresponding author.
Email: zhangxy.math@gmail.com (X. Zhang), haiyan.tian@usm.edu (H. Tian), Leihsin.kuo@eagles.usm.edu (L. Kuo), chenwen@hhu.edu.cn (W. Chen)
 

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