Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification

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Description

This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a ... continued below

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Blottner, F.G. & Lopez, A.R. October 1, 1998.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Laboratories, Albuquerque, NM, and Livermore, CA
    Place of Publication: Albuquerque, New Mexico

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Description

This investigation is concerned with the accuracy of numerical schemes for solving partial differential equations used in science and engineering simulation codes. Richardson extrapolation methods for steady and unsteady problems with structured meshes are presented as part of the verification procedure to determine code and calculation accuracy. The local truncation error de- termination of a numerical difference scheme is shown to be a significant component of the veri- fication procedure as it determines the consistency of the numerical scheme, the order of the numerical scheme, and the restrictions on the mesh variation with a non-uniform mesh. Genera- tion of a series of co-located, refined meshes with the appropriate variation of mesh cell size is in- vestigated and is another important component of the verification procedure. The importance of mesh refinement studies is shown to be more significant than just a procedure to determine solu- tion accuracy. It is suggested that mesh refinement techniques can be developed to determine con- sistency of numerical schemes and to determine if governing equations are well posed. The present investigation provides further insight into the conditions and procedures required to effec- tively use Richardson extrapolation with mesh refinement studies to achieve confidence that sim- ulation codes are producing accurate numerical solutions.

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  • Other: DE00001044
  • Report No.: SAND98-2222
  • Grant Number: AC04-94AL85000
  • DOI: 10.2172/1044 | External Link
  • Office of Scientific & Technical Information Report Number: 1044
  • Archival Resource Key: ark:/67531/metadc623447

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • October 1, 1998

Added to The UNT Digital Library

  • June 16, 2015, 7:43 a.m.

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  • Dec. 5, 2016, 2:01 p.m.

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Blottner, F.G. & Lopez, A.R. Determination of Solution Accuracy of Numerical Schemes as Part of Code and Calculation Verification, report, October 1, 1998; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc623447/: accessed November 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.