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Cause and Cure - Deterioration in Accuracy of CFD Simulations With Use of High-Aspect-Ratio Triangular Tetrahedral Grids
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Author and Affiliation:
Chang, Sin-Chung(NASA Glenn Research Center, Cleveland, OH United States)
Chang, Chau-Lyan(NASA Langley Research Center, Hampton, VA United States)
Venkatachari, Balaji Shankar(National Inst. of Aerospace, Hampton, VA, United States)
Abstract: Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD re-searchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions and also cause numerical instability. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where triangular/tetrahedral elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identities the reason behind the difficulties in use of such high-aspect ratio triangular/tetrahedral elements is presented here. As will be shown, it turns out that the degree of accuracy deterioration of gradient computation involving a triangular element is hinged on the value of its shape factor Gamma def = sq sin Alpha1 + sq sin Alpha2 + sq sin Alpha3, where Alpha1; Alpha2 and Alpha3 are the internal angles of the element. In fact, it is shown that the degree of accuracy deterioration increases monotonically as the value of Gamma decreases monotonically from its maximal value 9/4 (attained by an equilateral triangle only) to a value much less than 1 (associated with a highly obtuse triangle). By taking advantage of the fact that a high-aspect ratio triangle is not necessarily highly obtuse, and in fact it can have a shape factor whose value is close to the maximal value 9/4, a potential solution to avoid accuracy deterioration of gradient computation associated with a high-aspect ratio triangular grid is given. Also a brief discussion on the extension of the current mathematical framework to the tetrahedral-grid case along with some of the practical results of this extension is also provided. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, the effectiveness of the gradient evaluation procedures within the CESE framework (that have their basis on the analysis presented here) to produce accurate and stable results on such high-aspect ratio meshes is also showcased.
Publication Date: Aug 14, 2017
Document ID:
20170007767
(Acquired Aug 18, 2017)
Subject Category: NUMERICAL ANALYSIS; FLUID MECHANICS AND THERMODYNAMICS
Report/Patent Number: NASA/TM-2017-219534, E-19390, GRC-E-DAA-TN44182
Document Type: Technical Report
Publication Information: (SEE 20170007699)
Contract/Grant/Task Num: WBS 109492.02.03.01.01.01
Financial Sponsor: NASA Glenn Research Center; Cleveland, OH United States
Description: 46p; In English
Distribution Limits: Unclassified; Publicly available; Unlimited
Rights: Copyright; Distribution as joint owner in the copyright
NASA Terms: SPACE-TIME CE/SE METHOD; COMPUTATIONAL FLUID DYNAMICS; HIGH ASPECT RATIO; DETERIORATION; TRIANGLES; TETRAHEDRONS; COMPUTERIZED SIMULATION; HIGH REYNOLDS NUMBER; BOUNDARY LAYERS; NAVIER-STOKES EQUATION; UNSTRUCTURED GRIDS (MATHEMATICS); COMPUTATIONAL GRIDS; WALLS; FLOW VELOCITY
Other Descriptors: CFD; CESE METHOD; MATHEMATICAL
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