俯冲动力学数值模拟中的网格选择
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中国地质科学院地质研究所

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中国地质调查局项目(DD20221630)、国家自然科学基金项目(42374121)、科技部项目(2019QZKK0901, 2021FY100101)和基本科研业务费项目(J2316)联合资助。


Computational Grid Selection in numerical modeling of Subduction Dynamics
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Institute of Geology, Chinses Academy of Geological Sciences

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    摘要:

    包括俯冲动力学数值模型在内的地学中各种基于数学物理方程的数值模型必然涉及由离散节点组成的计算网格,它控制着数值计算精度进而控制着数值模型在解决实际地球科学问题中的可信度。近年来俯冲动力学数值模拟取得了长足进步,然而随意使用计算网格导致的数值计算精度仍然不清楚。本文针对经典科学问题,基于3套精度不同的计算网格构建了数值模型,通过比较不同精度计算网格导致的数值结果偏差,评估了低精度网格在实际研究过程中的可能影响。本文认为近十年来较常用的加密区精度为2km×2km的计算网格有可能得到包含明显数值误差的计算结果,进而影响数值模型在地学中的应用。因此,可能有必要重新审视近年来低精度网格的模型及其相应的地学结论。随着俯冲动力学数值模型越来越高的非线性特征,选择尽可能高精度的计算网格可能是必然选择。对于高非线性问题使用低精度网格的情况,需要确切证据证明网格可靠性。本文提出了一套新的适用于俯冲动力学的网格剖分形式:含悬挂点的局部加密结构化四边形网格。该网格可能在网格总数较少的情况下完成高精度数值计算,并且实现过程相对简单。

    Abstract:

    Various numerical models based on mathematical physics equations in geosciences, including numerical modeling of subduction dynamics, necessarily involve computational grids consisting of discrete nodes, which control the accuracy of numerical calculations and thus the credibility of numerical models in solving practical geoscientific problems. The numerical modeling of subduction dynamics has made great progress in recent years; however, the numerical accuracy due to the arbitrary use of computational grids is still unclear. In this paper, we construct numerical models based on three sets of computational grids with different accuracies for a classical scientific problem, and evaluate the possible impact of low-precision grids in practical research. It is argued that the computational grid with an accuracy of 2km×2km for the encrypted zone, which has been more commonly used in the last decade, is likely to obtain computational results containing significant numerical errors, which in turn affects the application of numerical modeling in subduction dynamics. Therefore, it may be necessary to revisit models with low precision grids and their corresponding geologic conclusions in recent years. As numerical models of subduction dynamics become more and more highly nonlinear, the choice of computational grids with the highest possible accuracy may be inevitable. For the case of using low-precision grids for highly nonlinear problems, definitive evidence of grid reliability is needed. We propose a new set of grid pattern suitable for subduction dynamics: locally encrypted structured quadrilateral grids containing hanging nodes. This grid may accomplish high-precision numerical calculations with a small total number of grids and is relatively simple to implement.

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  • 收稿日期:2023-11-14
  • 最后修改日期:2024-01-30
  • 录用日期:2024-02-04
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