A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions

Gentile, Nicholas A.; Hayes, John C.

doi:10.1080/23324309.2018.1497992

Title: A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions

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Abstract

We obtain here a solution to a zone-centered discretization of the one dimensional time-dependent diffusion equation with arbitrary initial conditions and source, constant absorption and scattering opacity, and constant zone size and time step. The solution is obtained using the discrete Green’s functions of the discretized equation. The solution of the discretized equation is useful in the testing of computer codes, because the code can be expected to agree with the solution to the discrete equation, to within small errors caused by roundoff. This is in contrast to solutions of the differential equation, with which the code results only approximately agree. Finally, the usefulness of the solution for tests of an inertial confinement fusion code is demonstrated.

Authors:

Gentile, Nicholas A. ^[1]; Hayes, John C. ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Publication Date:: Sun Nov 11 00:00:00 EST 2018

Research Org.:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1489467

Report Number(s):: LLNL-JRNL-753609
Journal ID: ISSN 2332-4309; 940135

Grant/Contract Number:: AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Computational and Theoretical Transport

Additional Journal Information:: Journal Volume: 47; Journal Issue: 4-6; Journal ID: ISSN 2332-4309

Publisher:: Taylor and Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; diffusion equation; deterministic method; radiation transport

Citation Formats


                    Gentile, Nicholas A., and Hayes, John C. A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions.  United States: N. p., 2018. 
Web.  doi:10.1080/23324309.2018.1497992.

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                    Gentile, Nicholas A., & Hayes, John C. A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions.  United States.  https://doi.org/10.1080/23324309.2018.1497992

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                    Gentile, Nicholas A., and Hayes, John C. Sun .  
"A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions".  United States.  https://doi.org/10.1080/23324309.2018.1497992.  https://www.osti.gov/servlets/purl/1489467.

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@article{osti_1489467,

  title        = {A Test Problem for Codes Solving the Discretized Diffusion Equation in Cartesian Geometry Derived Via Discrete Green’s Functions},

  author       = {Gentile, Nicholas A. and Hayes, John C.},

  abstractNote = {We obtain here a solution to a zone-centered discretization of the one dimensional time-dependent diffusion equation with arbitrary initial conditions and source, constant absorption and scattering opacity, and constant zone size and time step. The solution is obtained using the discrete Green’s functions of the discretized equation. The solution of the discretized equation is useful in the testing of computer codes, because the code can be expected to agree with the solution to the discrete equation, to within small errors caused by roundoff. This is in contrast to solutions of the differential equation, with which the code results only approximately agree. Finally, the usefulness of the solution for tests of an inertial confinement fusion code is demonstrated.},

  doi          = {10.1080/23324309.2018.1497992},

  journal      = {Journal of Computational and Theoretical Transport},

  number       = 4-6,

  volume       = 47,

  place        = {United States},

  year         = {Sun Nov 11 00:00:00 EST 2018},

  month        = {Sun Nov 11 00:00:00 EST 2018}

}

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