Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions

Scannapieco, Anthony J.

doi:10.1016/J.JCP.2014.10.040

Title: Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions

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Abstract

A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady statesmore »« less

Authors:: Scannapieco, Anthony J.

Publication Date:: Thu Jan 15 00:00:00 EST 2015

OSTI Identifier:: 22382175

Resource Type:: Journal Article

Journal Name:: Journal of Computational Physics

Additional Journal Information:: Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; DIFFUSION; DIFFUSION EQUATIONS; INTERFACES; STEADY-STATE CONDITIONS; THERMAL CONDUCTION; THREE-DIMENSIONAL CALCULATIONS; TIME DEPENDENCE; TRANSIENTS

Citation Formats


                    Dai, William W., E-mail: dai@lanl.gov, and Scannapieco, Anthony J. Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions.  United States: N. p., 2015. 
        Web.  doi:10.1016/J.JCP.2014.10.040.

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                    Dai, William W., E-mail: dai@lanl.gov, & Scannapieco, Anthony J. Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions.  United States.  https://doi.org/10.1016/J.JCP.2014.10.040

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                    Dai, William W., E-mail: dai@lanl.gov, and Scannapieco, Anthony J. 2015.  
        "Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions".  United States.  https://doi.org/10.1016/J.JCP.2014.10.040.

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@article{osti_22382175,

  title        = {Second-order accurate interface- and discontinuity-aware diffusion solvers in two and three dimensions},

  author       = {Dai, William W., E-mail: dai@lanl.gov and Scannapieco, Anthony J.},

  abstractNote = {A numerical scheme is developed for two- and three-dimensional time-dependent diffusion equations in numerical simulations involving mixed cells. The focus of the development is on the formulations for both transient and steady states, the property for large time steps, second-order accuracy in both space and time, the correct treatment of the discontinuity in material properties, and the handling of mixed cells. For a mixed cell, interfaces between materials are reconstructed within the cell so that each of resulting sub-cells contains only one material and the material properties of each sub-cell are known. Diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured. The discontinuity of material properties between different materials is correctly treated based on governing physics principles. The treatment is exact for arbitrarily strong discontinuity. The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes. The scheme is general in two and three dimensions. Since the scheme to be developed in this paper is intended for multi-physics code with adaptive mesh refinement (AMR), we present the scheme on mesh generated from AMR. The correctness and features of the scheme are demonstrated for transient problems and steady states in one-, two-, and three-dimensional simulations for heat conduction and radiation heat transfer. The test problems involve dramatically different materials.},

  doi          = {10.1016/J.JCP.2014.10.040},

  url          = {https://www.osti.gov/biblio/22382175},
  journal      = {Journal of Computational Physics},

  issn         = {0021-9991},

  number       = ,

  volume       = 281,

  place        = {United States},

  year         = {Thu Jan 15 00:00:00 EST 2015},

  month        = {Thu Jan 15 00:00:00 EST 2015}

}

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