Time Accurate Unstructured Grid Adaption in Two and Three Dimensions

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Title: Time Accurate Unstructured Grid Adaption in Two and Three Dimensions
Author: Carpenter, James Givens, V
Advisors: Dr. D. Scott McRae, Committee Chair
Dr. Jack R. Edwards, Committee Member
Dr. Hassan A. Hassan, Committee Member
Dr. C. T. Kelley, Committee Member
Abstract: The adaption algorithm of Benson et al is extended to three dimensional unstructured grids, building on the previous extension to two dimensional unstructured grids. R-refinement grid adaption is performed using a center of mass equation constructed from a weight function computed from solution gradients. Solution variables are updated using a coupled approach where the flux interface for each cell face is adjusted by the local grid velocity. Modifications to the integration scheme are incorporated to account for volume changes due to grid adaption through the introduction of an unsteady residual term which is resolved using sub-iterations at each timestep. The previous structured grid definition of grid velocity is shown to be inadequate for unstructured grid motion, and a new conservation based grid velocity equation is constructed from the local face displacement, which is designed to capture the volume change and preserve geometric conservation. Time accuracy is demonstrated for two and three dimensions using a shock tube simulation. Implementation for three dimensions is accomplished using a parallel, point implicit commercial flow solver. Incorporation of the gridspeed terms in the flux interface equations is presented along with the modifications to the implicit integration scheme required to account for the volume change as the grid is displaced. Extension to three dimensions required development of smoothing routines designed to preserve or recapture grid quality for arbitrary tetrahedral grids based on a geometric quality definition. A wing section under a prescribed sinusoidal motion is presented as a demonstration case to show the efficacy of the method. Computational results are compared to experimental data and solutions obtained using CFL3D.
Date: 2007-12-07
Degree: PhD
Discipline: Aerospace Engineering
URI: http://www.lib.ncsu.edu/resolver/1840.16/4115


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