INTEGRATING A BILINEAR INTERPOLATION FUNCTION ACROSS QUADRILATERAL CELL BOUNDARIES

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Computational models of particle dynamics often exchange solution data with discretized continuum-fields using interpolation functions. These particle methods require a series expansion of the interpolation function for two purposes: numerical analyses used to establish the models consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid. This report presents a new method of developing discrete-expansions for interpolation; they are similar to multi-variable expansions but, unlike a Taylor's series, discrete-expansions are valid throughout a discretized domain. Discrete-expansions are developed herein by parametrically integrating the interpolation function's total-differential between two particles located within separate, non-contiguous cells. Discrete-expansions are valid ... continued below

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192 Kilobytes pages

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BROCK, J. S. January 8, 2001.

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Description

Computational models of particle dynamics often exchange solution data with discretized continuum-fields using interpolation functions. These particle methods require a series expansion of the interpolation function for two purposes: numerical analyses used to establish the models consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid. This report presents a new method of developing discrete-expansions for interpolation; they are similar to multi-variable expansions but, unlike a Taylor's series, discrete-expansions are valid throughout a discretized domain. Discrete-expansions are developed herein by parametrically integrating the interpolation function's total-differential between two particles located within separate, non-contiguous cells. Discrete-expansions are valid for numerical analyses since they acknowledge the functional dependence of interpolation and account for mapping discontinuities across cell boundaries. The use of discrete-expansions for logical-coordinate evaluation provides an algorithmically robust and computationally efficient particle localization method. Verification of this new method is demonstrated herein on a simple test problem.

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192 Kilobytes pages

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  • Other Information: PBD: 8 Jan 2001

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  • Report No.: LA-UR-00-3329
  • Grant Number: W-7405-ENG-36
  • DOI: 10.2172/772922 | External Link
  • Office of Scientific & Technical Information Report Number: 772922
  • Archival Resource Key: ark:/67531/metadc716243

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  • January 8, 2001

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  • Sept. 29, 2015, 5:31 a.m.

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  • March 25, 2016, 11:57 a.m.

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BROCK, J. S. INTEGRATING A BILINEAR INTERPOLATION FUNCTION ACROSS QUADRILATERAL CELL BOUNDARIES, report, January 8, 2001; New Mexico. (digital.library.unt.edu/ark:/67531/metadc716243/: accessed December 13, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.