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Conservative sliding algorithms for hydrodynamics

Liu Quan Yu Ming Lin Zhong Wang Rui-Li

Conservative sliding algorithms for hydrodynamics

Liu Quan, Yu Ming, Lin Zhong, Wang Rui-Li
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  • The Lagrangian hydrodynamics algorithm using staggered mesh is one of the most important algorithms for engineering design and science computing. Some questions need to use the conservative scheme. Shashkov gave the idea how to get conservation with a material. He defined the conservative scheme to be a compatible algorithm. When we perform a numerical simulation with two or more materials, we should use sliding line or contact-impact algorithm. In this case, the Wilkins algorithm is used mostly. But this algorithm is not conservative. This paper presents a conservative method for sliding line based on the compatible Lagrangian hydrodynamics algorithm and Wilkins sliding algorithm. The conservation of total energy can be got by the local modification through the idea of contact force and contact work. This method can ensure the symmetric property and conservative property, and improve the numerical accuracy. In this paper, we give the detail in how to design the conservative sliding algorithm and how to impose the slave's edge artificial viscosity. We also gave some numerical simulations to prove that our scheme is right and useful.
      Corresponding author: Yu Ming, yu_ming@iapcm.ac.cn.
    • Funds: Project supported by National Natural Science Foundation of China (Grant Nos. 11372051, 11172050, 11272064), and NASF (Grant No. 11076015).
    [1]

    Yu M, Sun Y T, Liu Q 2015 Acta Phys. Sin. 64 114702(in Chinese) [于明, 孙宇涛, 刘全 2015 物理学报 64 114702]

    [2]

    Caramana E J, Burton D E, Shashkov M J, Whalen P P 1998 Journal of Computational Physics 146 227

    [3]

    Caramana E J, Shashkov M J 1998 Journal of Computational Physics 142 521

    [4]

    Caramana E J, Whalen P P 1998 Journal of Computational Physics 141 174

    [5]

    Caramana E J, Shashkov M J, Whalen P P 1998 Journal of Computational Physics 144 70

    [6]

    Bauer A L, Burton D E, Caramana E J 2006 Journal of Computational Physics 218 572

    [7]

    Wilkins M 1969 UCRL-7322, LLNL

    [8]

    Whirley R G, Engelmann B E 1993 UCRL-MA-110630

    [9]

    Hallquist J O, Goudreau G L, Benson D J 2009 Journal of Computational Physics 228 3911

    [10]

    Caramana E J 2009 Journal of Computational Physics 228 3911]

    [11]

    Wang R L, Liu Q, Lin Z 2012 Journal of Computational Physics 29 667(in Chinese) [王瑞利, 刘全, 林忠 2012 计算物理 29 667]

    [12]

    Liu Q, Lin Z, Wang R L 2012 Computational Mecanics 29 609(in Chinese) [刘全, 林忠, 王瑞利 2012 计算力学 29 609]

  • [1]

    Yu M, Sun Y T, Liu Q 2015 Acta Phys. Sin. 64 114702(in Chinese) [于明, 孙宇涛, 刘全 2015 物理学报 64 114702]

    [2]

    Caramana E J, Burton D E, Shashkov M J, Whalen P P 1998 Journal of Computational Physics 146 227

    [3]

    Caramana E J, Shashkov M J 1998 Journal of Computational Physics 142 521

    [4]

    Caramana E J, Whalen P P 1998 Journal of Computational Physics 141 174

    [5]

    Caramana E J, Shashkov M J, Whalen P P 1998 Journal of Computational Physics 144 70

    [6]

    Bauer A L, Burton D E, Caramana E J 2006 Journal of Computational Physics 218 572

    [7]

    Wilkins M 1969 UCRL-7322, LLNL

    [8]

    Whirley R G, Engelmann B E 1993 UCRL-MA-110630

    [9]

    Hallquist J O, Goudreau G L, Benson D J 2009 Journal of Computational Physics 228 3911

    [10]

    Caramana E J 2009 Journal of Computational Physics 228 3911]

    [11]

    Wang R L, Liu Q, Lin Z 2012 Journal of Computational Physics 29 667(in Chinese) [王瑞利, 刘全, 林忠 2012 计算物理 29 667]

    [12]

    Liu Q, Lin Z, Wang R L 2012 Computational Mecanics 29 609(in Chinese) [刘全, 林忠, 王瑞利 2012 计算力学 29 609]

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  • Received Date:  28 March 2015
  • Accepted Date:  07 May 2015
  • Published Online:  05 October 2015

Conservative sliding algorithms for hydrodynamics

    Corresponding author: Yu Ming, yu_ming@iapcm.ac.cn.
  • 1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
Fund Project:  Project supported by National Natural Science Foundation of China (Grant Nos. 11372051, 11172050, 11272064), and NASF (Grant No. 11076015).

Abstract: The Lagrangian hydrodynamics algorithm using staggered mesh is one of the most important algorithms for engineering design and science computing. Some questions need to use the conservative scheme. Shashkov gave the idea how to get conservation with a material. He defined the conservative scheme to be a compatible algorithm. When we perform a numerical simulation with two or more materials, we should use sliding line or contact-impact algorithm. In this case, the Wilkins algorithm is used mostly. But this algorithm is not conservative. This paper presents a conservative method for sliding line based on the compatible Lagrangian hydrodynamics algorithm and Wilkins sliding algorithm. The conservation of total energy can be got by the local modification through the idea of contact force and contact work. This method can ensure the symmetric property and conservative property, and improve the numerical accuracy. In this paper, we give the detail in how to design the conservative sliding algorithm and how to impose the slave's edge artificial viscosity. We also gave some numerical simulations to prove that our scheme is right and useful.

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