Journal
COMPUTER PHYSICS COMMUNICATIONS
Volume 181, Issue 5, Pages 837-841Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cpc.2009.12.018
Keywords
Anisotropy; High order; Spectral element; Finite element; Numerical error; Perpendicular diffusion
Funding
- DOE [DE-FC02-05ER54811]
- U.S. Department of Energy (DOE) [DE-FC02-05ER54811] Funding Source: U.S. Department of Energy (DOE)
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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. (C) 2009 Elsevier B.V. All rights reserved.
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