Volume 27, Issue 2
An Improved Pressure-Equilibrium Diffuse Interface Model for Solid-Fluid Interaction

Li Li, Qian Chen, Zhiwei He, Yousheng Zhang & Baolin Tian

Commun. Comput. Phys., 27 (2020), pp. 546-568.

Published online: 2019-12

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  • Abstract

For solid-fluid interaction, one of the phasic density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity, because the conservative variables in phasic density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves are introduced by the artificial treatment. In this paper, an improved pressure-equilibrium diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, the phasic density equations are replaced by the algebraic relation between phasic densities and inverse deformation gradient tensors. In consequence, the volume fractions and the phasic densities do not appear explicitly in the conservative equations any more. The degeneracy introduced by zero/unity volume fractions are prevented. A flux-splitting based finite difference algorithm suitable for this formulation is then presented. A series of one-dimensional and two-dimensional numerical tests demonstrate that the proposed model can present more accurate results near material interfaces.

  • Keywords

Solid-fluid interaction, diffuse interface model, phasic density equation, Mie-Grüneisen equation of state, Eulerian methods.

  • AMS Subject Headings

74F10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lilili606@163.com (Li Li)

chenqian900804@163.com (Qian Chen)

benny85@sina.com (Zhiwei He)

zhang_yousheng@iapcm.ac.cn (Yousheng Zhang)

tian_balin@iapcm.ac.cn (Baolin Tian)

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@Article{CiCP-27-546, author = {Li , Li and Chen , Qian and He , Zhiwei and Zhang , Yousheng and Tian , Baolin }, title = {An Improved Pressure-Equilibrium Diffuse Interface Model for Solid-Fluid Interaction}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {2}, pages = {546--568}, abstract = {

For solid-fluid interaction, one of the phasic density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity, because the conservative variables in phasic density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves are introduced by the artificial treatment. In this paper, an improved pressure-equilibrium diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, the phasic density equations are replaced by the algebraic relation between phasic densities and inverse deformation gradient tensors. In consequence, the volume fractions and the phasic densities do not appear explicitly in the conservative equations any more. The degeneracy introduced by zero/unity volume fractions are prevented. A flux-splitting based finite difference algorithm suitable for this formulation is then presented. A series of one-dimensional and two-dimensional numerical tests demonstrate that the proposed model can present more accurate results near material interfaces.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0261}, url = {http://global-sci.org/intro/article_detail/cicp/13458.html} }
TY - JOUR T1 - An Improved Pressure-Equilibrium Diffuse Interface Model for Solid-Fluid Interaction AU - Li , Li AU - Chen , Qian AU - He , Zhiwei AU - Zhang , Yousheng AU - Tian , Baolin JO - Communications in Computational Physics VL - 2 SP - 546 EP - 568 PY - 2019 DA - 2019/12 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0261 UR - https://global-sci.org/intro/article_detail/cicp/13458.html KW - Solid-fluid interaction, diffuse interface model, phasic density equation, Mie-Grüneisen equation of state, Eulerian methods. AB -

For solid-fluid interaction, one of the phasic density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity, because the conservative variables in phasic density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves are introduced by the artificial treatment. In this paper, an improved pressure-equilibrium diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, the phasic density equations are replaced by the algebraic relation between phasic densities and inverse deformation gradient tensors. In consequence, the volume fractions and the phasic densities do not appear explicitly in the conservative equations any more. The degeneracy introduced by zero/unity volume fractions are prevented. A flux-splitting based finite difference algorithm suitable for this formulation is then presented. A series of one-dimensional and two-dimensional numerical tests demonstrate that the proposed model can present more accurate results near material interfaces.

Li Li, Qian Chen, Zhiwei He, Yousheng Zhang & Baolin Tian. (2019). An Improved Pressure-Equilibrium Diffuse Interface Model for Solid-Fluid Interaction. Communications in Computational Physics. 27 (2). 546-568. doi:10.4208/cicp.OA-2018-0261
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