The construction of bicompact schemes of high order of approximation for unsteady transport equation numerical solving in 1D geometry by application of HOLO (High Order – Low Order) algorithm is considered. The fourth order of approximation in space and the third in time are achieved. Two variants for the boundary conditions for the LO part are considered: the classical one using fractional-linear functionals for the flux and radiation density ratio, and also by the radiation density value from the HO part of the system. The efficiency of the algorithm is demonstrated in comparison with the source iterations method. It is shown the second variant of the boundary conditions leads to the third order of convergence on smooth solutions, in contrast to the first method, which allows to obtain only the second order; however the efficiency of the HOLO algorithm can decrease.

transport equation, quasi-diffusion method, bicompact scheme, HOLO algorithms for transport equation solving, diagonally implicit Runge-Kutta method

Mathematical problems and theory of numerical methods

Aristova Elena Nikolaevna,  aristovaen@mail.ru,  orcid.org/0000-0003-1653-8166,  KIAM RAS

Karavaeva Nataliia Igorevna,  karavaeva@phystech.edu,  orcid.org/0000-0002-3300-3246,  KIAM RAS