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首页> 外文期刊>Computer physics communications >Spectral element spatial discretization error in solving highly anisotropic heat conduction equation
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Spectral element spatial discretization error in solving highly anisotropic heat conduction equation

机译：求解高各向异性热传导方程的谱元空间离散误差

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摘要

This paper describes a study of the effects of the overall spatial resolution, polynomial degree and computational grid directionality on the accuracy of numerical solutions of a highly anisotropic thermal diffusion equation using the spectral element spatial discretization method. The high-order spectral element macroscopic modeling code SEL/HiFi has been used to explore the parameter space. It is shown that for a given number of spatial degrees of freedom, increasing polynomial degree while reducing the number of elements results in exponential reduction of the numerical error. The alignment of the grid with the direction of anisotropy is shown to further improve the accuracy of the solution. These effects are qualitatively explained and numerically quantified in 2- and 3-dimensional calculations with straight and curved anisotropy.
机译：本文描述了使用光谱元素空间离散化方法研究整体空间分辨率，多项式度和计算网格方向性对高度各向异性热扩散方程数值解的精度的影响。高阶光谱元素宏观建模代码SEL / HiFi已用于探索参数空间。结果表明，对于给定数量的空间自由度，增加多项式度同时减少元素数会导致数值误差呈指数减小。显示了网格与各向异性方向的对齐，以进一步提高求解的准确性。定性地解释了这些影响，并在具有直线和曲线各向异性的二维和三维计算中对其进行了数值量化。

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