Thermodynamic interpolation

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A method for constructing bicubic interpolation polynomials for the pressure P and internal energy E that are thermodynamically consistent at the mesh ponts and continuous across mesh boundaries is presented. The slope boundary conditions for the pressure and energy are derived from finite differences of the data and from Maxwell�s consistency relation. Monotonicity of the sound speed and the specific heat is obtained by a bilinear interpolation of the slopes of the tabulated data. Monotonicity of the functions near steep gradients may be achieved by mesh refinement or by using a non-consistent bilinear to the data. Mesh refinement is very ... continued below

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Maiden, D E October 1, 1998.

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A method for constructing bicubic interpolation polynomials for the pressure P and internal energy E that are thermodynamically consistent at the mesh ponts and continuous across mesh boundaries is presented. The slope boundary conditions for the pressure and energy are derived from finite differences of the data and from Maxwell�s consistency relation. Monotonicity of the sound speed and the specific heat is obtained by a bilinear interpolation of the slopes of the tabulated data. Monotonicity of the functions near steep gradients may be achieved by mesh refinement or by using a non-consistent bilinear to the data. Mesh refinement is very efficient for uniform-linear or uniform-logarithmic spaced data because a direct table lookup can be used. The direct method was compared to binary search and was 37 percent faster for logarithmic-spaced data and 106 percent faster for linear-spaced data. This improvement in speed is very important in the radiation-transport opacity-lookup part of the calculation. Interpolation in P-E space, with mesh refinement, can be made simple, robust, and conserve energy. In the final analysis the interpolation of the free energy and entropy (Maiden and Cook) remains a competitor.

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128 Kilobytes

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  • 1998 Nuclear Explosives Development Conference, Las Vegas, NV, October 25-30,1998

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  • Other: DE00007449
  • Report No.: UCRL-JC-132744
  • Grant Number: W-7405-Eng-48
  • Office of Scientific & Technical Information Report Number: 7449
  • Archival Resource Key: ark:/67531/metadc707296

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  • October 1, 1998

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  • Sept. 12, 2015, 6:31 a.m.

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  • May 6, 2016, 11:08 p.m.

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Maiden, D E. Thermodynamic interpolation, article, October 1, 1998; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc707296/: accessed July 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.