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TECHNICAL PAPERS

Single Grid Error Estimation Using Error Transport Equation

[+] Author and Article Information
Ismail Celik, Gusheng Hu

Department of Mechanical and Aerospace Engineering, West Virginia University, Morgantown, WV 26505-6106E-mail: Ismail.Celik@mail.wvu.edu

J. Fluids Eng 126(5), 778-790 (Dec 07, 2004) (13 pages) doi:10.1115/1.1792254 History: Received June 16, 2003; Revised March 02, 2004; Online December 07, 2004
Copyright © 2004 by ASME
Topics: Equations , Errors
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References

Figures

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Illustration of three-point stencil for implementation of boundary condition on a typical boundary, here denoted as the south boundary. (a) First grid node at the boundary, (b) first grid node outside the boundary.
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Typical computational cell arrangement used in finite volume discretization
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Influence circle with radius r in unstructured grid. Nodes filled with black color fall into the influence domain of the node 16.
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Exact versus calculated error for steady 1D convection diffusion equation, first order upwind scheme, 41 nodes, velocity varies to obtain different Peclet numbers, (a) Pe=10, PeΔ=0.25, (b) Pe=20, PeΔ=0.5, (c) Pe=100, PeΔ=2.5, (d) Pe=200, PeΔ=5.0
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Exact versus calculated error for steady 1D convection diffusion equation, central difference scheme, 41 nodes, velocity varies to obtain different Peclet numbers, (a) Pe=10, PeΔ=0.25, (b) Pe=20, PeΔ=0.5
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Exact versus calculated error for 2D Poisson equation, central difference scheme, 21* 21 grid; (a) exact error, (b) calculated error
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Exact versus calculated error for 2D Poisson equation along the line of y=0.5, central difference scheme, (a) 21* 21 grid, (b) 41* 41 grid
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Exact versus calculated error for 2D convection diffusion equation, 1st order upwind scheme, 41* 41 grid; (a) exact error, (b) calculated error
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Exact versus calculated error for 2D convection diffusion equation along the diagonal of the square domain, 1st order upwind scheme, x′ =distance from the origin along the diagonal line, (a) 41* 41 grid, (b) 81* 81 grid
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Exact versus calculated error for 2D convection diffusion equation, central difference scheme, 41* 41 grid; (a) exact error, (b) calculated error
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Exact versus calculated error for 2D convection diffusion equation, central difference scheme, (a) 41* 41 grid, (b) 81* 81 grid
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Exact versus calculated error for steady 1D Burger’s equation, first order upwind scheme, 41 nodes, inlet velocity varies to obtain different Reynolds numbers, (a) Re=10, ReΔ=0.25, (b) Re=200, ReΔ=5
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Exact versus calculated error for steady 1D Burger’s equation, central difference scheme, 41 nodes, inlet velocity varies to obtain different Peclet numbers, (a) Re=10, ReΔ=0.25, (b) Re=60, ReΔ=1.5

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