Bicompact schemes for the HOLO algorithm for solving the transport equation were applied to solve model problems of radiation transport in a medium (the first and the second Fleck problems). The main idea of HOLO algorithms is to accelerate the convergence of iterative processes due to the joint solving of high order (HO) and low order (LO) kinetic equations. The schemes are constructed by the method of lines on a minimal two-point stencil and have the fourth order of approximation in space. The Runge-Kutta method of the third order of approximation was used for integration over time. Verification and validation of the schemes were carried out. Solutions of the first and the second Fleck problems by the proposed method coincided well with solutions obtained by other methods. A modification of the second Fleck problem was proposed to investigate the dependence of the velocity of the thermal wave front on the absorption coefficient in the optically thick region.

transport equation, quasi-diffusion method, HOLO algorithms for transport equation solving, bicompact schemes, diagonally implicit Runge–Kutta method, Fleck problem

Mathematical problems and theory of numerical methods

Aristova Elena Nikolaevna,  ,  orcid.org/0000-0003-1653-8166,  KIAM RAS

Karavaeva Nataliia Igorevna,  ,  orcid.org/0000-0002-3300-3246,  KIAM RAS