The weighted reconstruction of reproducing kernel particle method for one-dimensional shock wave problems. (1st February 2018)

• Record Type: Journal Article
• Authors: Sun, C.T.; Guan, P.C.; Jiang, J.H.; Kwok, O.L.A.
• Is Part Of: Ocean engineering. Volume 149(2018)
• Page Start: 325
• Page End: 340
• Publication Date: 2018-02-01
• Subjects: Shock capturing -- Non-oscillating method -- Meshfree methods -- High-order approximation -- Reproducing kernel particle method; Ocean engineering -- Periodicals; Ocean engineering; Periodicals; 620.4162
• DOI: 10.1016/j.oceaneng.2017.12.017
• Languages: English
• ISSNs: 0029-8018

Abstract

Abstract: When high-order numerical approximation method is applied to model the propagation of shock wave or discontinuity, it usually creates unstable unreal numerical oscillations around the discontinuous regions. In this research, we propose a non-oscillation meshfree scheme based on reproducing kernel particle method (RKPM) which can maintain the accuracy and minimize the oscillation in the modeling of shock wave propagation. In the proposed method, the original influence domain of high-order RK approximation is divided into several subdomains. Then we apply low-order RK approximation within each subdomain. Instead of directly using the discrete particles to build the numerical approximation, we consider that the high-order approximation is constructed by the summation of those low-order approximations multiplied by a local weight function. By adjusting these local weights with the "smoothness indicator", we can determine the "effect" of the corresponding subdomain and the discrete particles inside this subdomain. Therefore, the subdomain containing discontinuity would not participate in the high-order approximation, and the numerical oscillation is automatically suppressed. The proposed method does not need artificial viscosity or numerical damping to stabilize the solution. Several benchmark problems with shock wave propagation are tested. The results show that the proposed method can maintain high-order accuracy without numerical oscillation. Highlights: An adaptable meshfree (meshless) method is developed for shock wave propagation. A non-oscillating meshfree algorithm is developed without artificial viscosity. The solution has high-order accuracy without numerical oscillation. The proposed method can solve strong discontinuous wave propagation.