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KIAM Preprint  25, Moscow, 2023
Authors: Karavaeva N.I.
Bicompact schemes for the joint solution of a one-group system of quasi-diffusion equations with the energy equation
Abstract:
High-order bicompact schemes are proposed for one of the stages of the HOLO algorithm for solving the radiative transport equation and implemented. The system of quasi-diffusion equations is solved together with the energy equation. The schemes have a fourth-order approximation in space on a two-point stencil, integration over time is carried out using the diagonal-implicit RungeKutta method of the third order of approximation, each stage of the method can be represented as an implicit Euler method. It is proposed to organize an iterative process to find a solution, since the coefficients of the system are non-linear functions of temperature. The schemes are used for a number of analytical tests, the convergence in time and space with the declared orders is shown.
Keywords:
transport equation, quasi-diffusion method, HOLO algorithms for transport equation solving, diagonally implicit Runge-Kutta method
Publication language: russian,  pages: 16
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Karavaeva Nataliia Igorevna,  orcid.org/0000-0002-3300-3246KIAM RAS