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Appl. Sci. 2016, 6(11), 354; doi:10.3390/app6110354

Analysis of the Numerical Diffusion in Anisotropic Mediums: Benchmarks for Magnetic Field Aligned Meshes in Space Propulsion Simulations

1
Aerospace Engineering Group, Universidad Carlos III de Madrid (UC3M), Av. de la Universidad, 30, 28911 Leganés, Madrid, Spain
2
Universidad Carlos III de Madrid (UC3M), Av. de la Universidad, 30, 28911 Leganés, Madrid, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Francisco José Galindo Rosales
Received: 6 October 2016 / Revised: 30 October 2016 / Accepted: 7 November 2016 / Published: 15 November 2016
(This article belongs to the Special Issue Applications of Complex Fluids)
View Full-Text   |   Download PDF [3341 KB, uploaded 15 November 2016]   |  

Abstract

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. View Full-Text
Keywords: flow anisotropy; numerical diffusion; meshing; gradient reconstruction; magnetic field aligned mesh flow anisotropy; numerical diffusion; meshing; gradient reconstruction; magnetic field aligned mesh
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Pérez-Grande, D.; Gonzalez-Martinez, O.; Fajardo, P.; Ahedo, E. Analysis of the Numerical Diffusion in Anisotropic Mediums: Benchmarks for Magnetic Field Aligned Meshes in Space Propulsion Simulations. Appl. Sci. 2016, 6, 354.

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