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Title: A one-dimensional meshfree particle formulation for simulating shock waves
Authors: Liu, M.B. 
Liu, G.R. 
Lam, K.Y.
Keywords: Corrective smoothed particle method
Meshfree method
Shock wave
Smoothed particle hydrodynamics
Taylor series expansion
Issue Date: Nov-2003
Citation: Liu, M.B., Liu, G.R., Lam, K.Y. (2003-11). A one-dimensional meshfree particle formulation for simulating shock waves. Shock Waves 13 (3) : 201-211. ScholarBank@NUS Repository.
Abstract: In this paper,a one-dimensional meshfree particle formulation is proposed for simulating shock waves,which are associated with discontinuous phenomena. This new formulation is based on Taylor series expansion in the piecewise continuous regions on both sides of a discontinuity. The new formulation inherits the meshfree Lagrangian and particle nature of SPH,and is a natural extension and improvement on the traditional SPH method and the recently proposed corrective smoothed particle method (CSPM). The formulation is consistent even in the discontinuous regions. The resultant kernel and particle approximations consist of a primary part similar to that in CSPM,and a corrective part derived from the discontinuity. A numerical study is carried out to examine the performance of the formulation. The results show that the new formulation not only remedies the boundary deficiency problem but also simulates the discontinuity well. The formulation is applied to simulate the shock tube problem and a 1-D TNT slab detonation. It is found that the proposed formulation captures the shock wave at comparatively lower particle resolution. These preliminary numerical tests suggest that the new meshfree particle formulation is attractive in simulating hydrodynamic problems with discontinuities such as shocks waves.
Source Title: Shock Waves
ISSN: 09381287
DOI: 10.1007/s00193-003-0207-0
Appears in Collections:Staff Publications

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