Investigations into the applicability of adaptive finite element methods to two‐dimensional infinite Prandtl number thermal and thermochemical convection
Investigations into the applicability of adaptive finite element methods to two‐dimensional infinite Prandtl number thermal and thermochemical convection
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自适应有限元方法对二维无限普朗特数热和热化学对流的适用性研究
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
P. Nithiarasu
中科院分区：
文献类型：
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作者：
D. R. Davies;J. Davies;O. Hassan;K. Morgan;P. Nithiarasu
提出了一种自适应有限元程序，用于提高地球动力学中对流主导问题的解的质量。该方法在高解梯度区域周围自动调整网格，提高了相关流特征的分辨率。该方法需要一个自动网格生成器、一个有限元流求解器和一个误差估计器的耦合。在本研究中，该程序与著名的地球动力学有限元代码ConMan一起实现。采用非结构化四边形网格生成器，通过网格再生实现网格自适应。这种再生利用基于插值的局部误差估计器提供的信息，从现有网格的计算解中获得。该技术通过使用成熟的基准解决方案解决热和热化学问题来验证。在纯热环境下，结果表明该方法非常成功，提高了求解精度，同时提高了计算效率。热化学模拟也可以得出同样的结论。然而，结果也表明，即使在自适应网格策略允许的更高空间分辨率下，用于模拟成分场的基于网格的方法也无法与该领域目前使用的其他方法（示踪粒子和标记链）竞争。
An adaptive finite element procedure is presented for improving the quality of solutions to convection‐dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well‐known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation‐based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well‐established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid‐based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.