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United States Department of Agriculture

Agricultural Research Service

Research Project: IMPROVING COMPUTATIONAL MODELING IN SUPPORT OF BETTER EROSION AND SEDIMENT MOVEMENT CONTROL IN AGRICULTURAL WATERSHEDS

Location: Watershed Physical Processes Research Unit

Title: An improved nearly-orthogonal structured mesh generation system with smoothness control functions

Authors
item Zhang, Y. -
item Jia, Y. -
item Wang, Sam -

Submitted to: Journal of Computational Physics 2
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: April 1, 2012
Publication Date: May 1, 2012
Citation: Zhang, Y., Jia, Y., Wang, S.S. 2012. An improved nearly-orthogonal structured mesh generation system with smoothness control functions. Journal of Computational Physics 2. 231(16):5289-5305. Available: http://www.journals.elsevier.com/journal-of-computational-physics/

Interpretive Summary: An improved C-L generation equation with smoothness control functions is proposed in this study. The smoothness control functions were derived based on the ratio between the Jacobian of the transformation matrix (J) and the Jacobian of the metric tensor (J/ = hnhg), whose differences are ignored in the original C-L equation in order to enforce the orthogonal conditions. This improved C-L equation generation system is capable of significantly improving mesh smoothness almost without affecting mesh orthogonality. With more smoothness conditions enforced from the smoothness control functions, the current generation system can produce smooth meshes at little cost of mesh orthogonality in complex geometries, where the original C-L equation failed to generate acceptable meshes without serious mesh distortion or overlapping. In the smoothness control functions, an effective Jacobian ratio re is used to control the intensity of the smoothness conditions enforced in the domain. This parameter can be user-specified constant or automatically evaluated by the original definition of the Jacobian ratio , the weak smoothness conditions, the strong smoothness conditions, or the modified definition of the Jacobian ratio. The sensitivity analysis suggests that the range of (0.9,1) for constant re in the whole domain may produce quality meshes with a good balance between mesh othogonality and smoothness. Among the automatic evaluation methods, for practical applications in complex gemetries, Jacobian ratio re evaluated using the weak smoothness condition has demonstrated better overall performances both in mesh orthogonality and smoothness.

Technical Abstract: This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are capable of relaxing the local strong orthogonal conditions so that nearly orthogonal but smooth mesh can be achieved. Examples and applications are also investigated in this paper to demonstrate the effects of the proposed mesh generation system.

Last Modified: 10/21/2014
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