Stability conditions of explicit algorithms when using viscoelastic artificial boundaries

LIU Jingbo; BAO Xin; LI Shutao; WANG Fei

doi:10.11883/bzycj-2021-0196

Volume 42 Issue 3

Apr. 2022

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LIU Jingbo, BAO Xin, LI Shutao, WANG Fei. Stability conditions of explicit algorithms when using viscoelastic artificial boundaries[J]. Explosion And Shock Waves, 2022, 42(3): 034201. doi: 10.11883/bzycj-2021-0196

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LIU Jingbo, BAO Xin, LI Shutao, WANG Fei. Stability conditions of explicit algorithms when using viscoelastic artificial boundaries[J]. Explosion And Shock Waves, 2022, 42(3): 034201. doi: 10.11883/bzycj-2021-0196

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Stability conditions of explicit algorithms when using viscoelastic artificial boundaries

doi: 10.11883/bzycj-2021-0196

LIU Jingbo^1
,,
BAO Xin^{1
,
,},
LI Shutao^{1, 2},
WANG Fei^{1, 3}

1.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
2.
Institute of Defense Engineering, Academy of Military Science, Beijing 100036, China
3.
College of Defense Engineering, Army Engineering University of PLA, Nanjing 210007, Jiangsu, China

Received Date: 2021-05-17
Rev Recd Date: 2021-07-17

Available Online: 2022-03-02

Publish Date: 2022-04-07

Abstract

Abstract

Viscoelastic artificial boundary is a commonly used numerical simulation method to deal with the wave propagation problems in an infinite domain. When the explicit time-domain stepwise integration algorithm is adopted for such numerical analysis, the stability conditions of the artificial boundary area are more stringent than those of the internal domain due to the influence of the damping and stiffness of the viscoelastic artificial boundary. However, there is currently no clear and practical stability criterion for this problem, which affects the reasonable selection of the integral time step when using the viscoelastic artificial boundaries, and further restricts the application of viscoelastic artificial boundary in the explicit dynamic analysis. Aiming at the two-dimensional (2D) viscoelastic artificial boundary, two typical types of boundary subsystem that can represent the localized characteristics of the overall numerical model, namely the edge boundary subsystem and the corner boundary subsystem, were established and their motion equations as well as the transfer matrixes were obtained according to the stability analysis method based on the local subsystem. Then through the stability criteria based on the spectral radius of the transfer matrix, the analytical solutions of the stability conditions of different local subsystems were derived. Through the comparative analysis of the stability conditions of different calculation areas and their influencing factors, it is found that the stability of the overall model is controlled by the corner boundary subsystem. On that basis, a uniform stability criterion and a simplified practical calculation method of the stability condition for the overall model with 2D viscoelastic artificial boundary in explicit dynamic calculations were proposed. In practical applications, the dynamic calculation of the overall model can be successfully completed once the integral time step meets the proposed stability condition of the numerical system. This study provides theoretical guidance for the reasonable selection of the integral time step when applying 2D viscoelastic artificial boundaries in explicit dynamic calculations.
- explicit time domain integration,
- viscoelastic artificial boundary,
- numerical stability,
- local subsystem,
- transfer matrix

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References(30)

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