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Splitting schemes for hyperbolic heat conduction equation

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Abstract

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat fluxes. In this paper we construct for the hyperbolic heat conduction equation the additive schemes of splitting with respect to directions. Unconditional stability of locally one-dimensional splitting schemes is established. New splitting schemes are proposed and studied for a system of equations written in terms of the temperature and heat fluxes.

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, 52, B. Tulskaya, 115191, Moscow, Russia

    Petr N. Vabishchevich

  2. North-Eastern Federal University, 58, Belinskogo, 677000, Yakutsk, Russia

    Petr N. Vabishchevich

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  1. Petr N. Vabishchevich
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Correspondence to Petr N. Vabishchevich.

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Communicated by Jan Hesthaven.

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Vabishchevich, P.N. Splitting schemes for hyperbolic heat conduction equation. Bit Numer Math 53, 755–778 (2013). https://doi.org/10.1007/s10543-013-0423-7

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  • DOI: https://doi.org/10.1007/s10543-013-0423-7

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