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Volume 33, Issue 4
A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

Chengjie Zhan, Zhenhua Chai, Baochang Shi, Ping Jiang, Shaoning Geng & Dongke Sun

DOI: 10.4208/cicp.OA-2022-0294

Commun. Comput. Phys., 33 (2023), pp. 1164-1188.

Published online: 2023-05

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  • Abstract

In this work, we proposed a diffuse-interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter, and the diffuse-interface based governing equations for the dendritic growth are presented. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are designed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, we performed some simulations of the dendritic growth to test the present diffuse-interface LB method, and found that the numerical results are in good agreements with some previous works.

  • Keywords

Dendritic growth, diffuse interface, lattice Boltzmann method, phase-field method.

  • AMS Subject Headings

74N05, 76D05, 80A20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-33-1164, author = {Zhan , ChengjieChai , ZhenhuaShi , BaochangJiang , PingGeng , Shaoning and Sun , Dongke}, title = {A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection}, journal = {Communications in Computational Physics}, year = {2023}, volume = {33}, number = {4}, pages = {1164--1188}, abstract = {

In this work, we proposed a diffuse-interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter, and the diffuse-interface based governing equations for the dendritic growth are presented. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are designed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, we performed some simulations of the dendritic growth to test the present diffuse-interface LB method, and found that the numerical results are in good agreements with some previous works.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0294}, url = {http://global-sci.org/intro/article_detail/cicp/21673.html} }
TY - JOUR T1 - A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection AU - Zhan , Chengjie AU - Chai , Zhenhua AU - Shi , Baochang AU - Jiang , Ping AU - Geng , Shaoning AU - Sun , Dongke JO - Communications in Computational Physics VL - 4 SP - 1164 EP - 1188 PY - 2023 DA - 2023/05 SN - 33 DO - http://doi.org/10.4208/cicp.OA-2022-0294 UR - https://global-sci.org/intro/article_detail/cicp/21673.html KW - Dendritic growth, diffuse interface, lattice Boltzmann method, phase-field method. AB -

In this work, we proposed a diffuse-interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter, and the diffuse-interface based governing equations for the dendritic growth are presented. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are designed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, we performed some simulations of the dendritic growth to test the present diffuse-interface LB method, and found that the numerical results are in good agreements with some previous works.

Zhan , ChengjieChai , ZhenhuaShi , BaochangJiang , PingGeng , Shaoning and Sun , Dongke. (2023). A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection. Communications in Computational Physics. 33 (4). 1164-1188. doi:10.4208/cicp.OA-2022-0294
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