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首页> 外文期刊>Applied Sciences >Analysis of the Numerical Diffusion in Anisotropic Mediums: Benchmarks for Magnetic Field Aligned Meshes in Space Propulsion Simulations
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Analysis of the Numerical Diffusion in Anisotropic Mediums: Benchmarks for Magnetic Field Aligned Meshes in Space Propulsion Simulations

机译：各向异性介质中数值扩散的分析：空间推进模拟中磁场对准网格的基准

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摘要

This manuscript explores numerical errors in highly anisotropic diffusion problems. First, the paper addresses the use of regular structured meshes in numerical solutions versus meshes aligned with the preferential directions of the problem. Numerical diffusion in structured meshes is quantified by solving the classical anisotropic diffusion problem; the analysis is exemplified with the application to a numerical model of conducting fluids under magnetic confinement, where rates of transport in directions parallel and perpendicular to a magnetic field are quite different. Numerical diffusion errors in this problem promote the use of magnetic field aligned meshes (MFAM). The generation of this type of meshes presents some challenges; several meshing strategies are implemented and analyzed in order to provide insight into achieving acceptable mesh regularity. Second, Gradient Reconstruction methods for magnetically aligned meshes are addressed and numerical errors are compared for the structured and magnetically aligned meshes. It is concluded that using the latter provides a more correct and straightforward approach to solving problems where anisotropicity is present, especially, if the anisotropicity level is high or difficult to quantify. The conclusions of the study may be extrapolated to the study of anisotropic flows different from conducting fluids.
机译：该手稿探讨了高度各向异性扩散问题中的数值误差。首先，本文讨论了在数值解中使用规则结构化网格，而不是与问题的优先方向对齐的网格。通过解决经典的各向异性扩散问题，可以量化结构化网格中的数值扩散。该分析以在磁约束下传导流体的数值模型中的应用为例，其中在平行和垂直于磁场的方向上的传输速率完全不同。此问题中的数值扩散误差促进了磁场对准网格（MFAM）的使用。这种类型的网格的产生提出了一些挑战。实施和分析了几种网格划分策略，以便深入了解实现可接受的网格划分规则。其次，解决了磁对准网格的梯度重建方法，并比较了结构化和磁对准网格的数值误差。结论是，使用后者为解决存在各向异性的问题提供了一种更正确和直接的方法，尤其是在各向异性水平很高或难以量化的情况下。该研究的结论可以推断为不同于传导流体的各向异性流动的研究。

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