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首页> 外文期刊>Applied Mathematical Modelling >A multiple-grid-time-step lattice Boltzmann method for transport phenomena with dissimilar time scales: Application in dendritic solidification
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A multiple-grid-time-step lattice Boltzmann method for transport phenomena with dissimilar time scales: Application in dendritic solidification

机译：时间尺度不同的传输现象的多重网格时步格子玻尔兹曼方法：在树枝状凝固中的应用

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摘要

In this paper, a multiple-grid-time-step model was developed for lattice Boltzmann (LB) simulations when combined transport equations need to be solved, so that the time step and grid size can be selected independently for each transport domain. The proposed multiple-grid-time-step technique was applied for modeling dendritic solidification of metallic alloys which involves a combination of transport phenomena occurring over different time and length scales. Momentum, solute and heat transfer equations with dissimilar diffusive properties were solved to model growth of a single dendrite. When dendrite growth is simulated under diffusive and convective transport, significant computational saving is achieved by applying the multiple-grid-time-step technique. When the heat transport equation is added, a high Lewis number requires the multiple-grid-time-step model in order to achieve a stable solution of the LB equations. In this case, it is shown that either a smaller time step or a larger grid size for the heat transfer domain compared to the solute transfer domain can stabilize the solution. The computing time is discussed for various cases. It is shown how the proposed model can significantly improve the computational efficiency when multiple transport equations with dissimilar properties need to be solved using the LB method.
机译：本文针对需要求解组合输运方程的格子玻尔兹曼（LB）仿真，开发了一个多网格时步模型，以便可以针对每个输运域分别选择时间步长和网格大小。所提出的多重网格时步技术被用于对金属合金的树枝状凝固进行建模，该过程涉及在不同时间和长度范围内发生的传输现象的组合。求解了具有不同扩散特性的动量，溶质和传热方程，以模拟单个枝晶的生长。当在扩散和对流输运下模拟枝晶生长时，通过应用多重网格时步技术可以显着节省计算量。当添加热传递方程时，高Lewis数需要多重网格时间步长模型，以便获得LB方程的稳定解。在这种情况下，表明与溶质传递域相比，对于传热域而言，较小的时间步长或较大的网格尺寸都可以使溶液稳定。讨论了各种情况下的计算时间。结果表明，当需要使用LB方法求解具有不同性质的多个输运方程时，所提出的模型如何显着提高计算效率。

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