Numerical simulation of moving boundary problem by modified Keller box method with boundary immobilisation technique

IF 1.9 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Pramana Pub Date : 2023-02-04 DOI:10.1007/s12043-022-02506-9

V P Rabeeb Ali, Ashish Awasthi

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引用次数: 0

Abstract

A modified Keller box (MKB) method is applied to the moving boundary problem (MBP) based on the boundary immobilisation technique. MBP is the modelling of the melting or solidification process. The mathematical importance of this problem is that the boundary of the domain is also unknown. The moving front position depends on time; hence this problem is inherently non-linear. Simulation time is used to evaluate the computational complexity of the schemes. The proposed scheme is compared to the existing schemes in the literature regarding the accuracy and simulation time. In both space and time, the proposed scheme has a second-order accuracy. For the known boundary, the constant boundary condition is taken and the proposed numerical algorithm is validated with the corresponding similarity solution. The MKB method provides good agreement with the similarity solution and also confirms that the computational rate of convergence of our scheme is two. This paper gives an idea of the MKB scheme for an MBP. This mathematical framework can be extended to 2D and 3D MBPs.

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基于边界固定技术的改进Keller盒法移动边界问题的数值模拟

基于边界固定技术，将改进的Keller box (MKB)方法应用于移动边界问题。MBP是熔化或凝固过程的模型。这个问题在数学上的重要性在于域的边界也是未知的。移动前沿位置取决于时间;因此这个问题本质上是非线性的。用仿真时间来评价方案的计算复杂度。并在精度和仿真时间方面与文献中已有的方案进行了比较。在空间和时间上，该方案都具有二阶精度。对于已知边界，采用恒定边界条件，用相似解对所提出的数值算法进行了验证。MKB方法与相似解具有较好的一致性，并证实了该方案的计算收敛速度为2。本文给出了一种MBP的MKB方案。该数学框架可以扩展到2D和3D MBPs。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Pramana 物理-物理：综合

CiteScore

3.60

自引率

7.10%

发文量

206

审稿时长

3 months

期刊介绍： Pramana - Journal of Physics is a monthly research journal in English published by the Indian Academy of Sciences in collaboration with Indian National Science Academy and Indian Physics Association. The journal publishes refereed papers covering current research in Physics, both original contributions - research papers, brief reports or rapid communications - and invited reviews. Pramana also publishes special issues devoted to advances in specific areas of Physics and proceedings of select high quality conferences.