Abstract:
The construction of bicompact schemes for nonsteady quasi-diffusion equations used for acceleration of iterations over scattering and fission terms in a transport equation is considered. Differential-difference system of bicompact scheme equations is constructed by the method of lines on two points space stencil. The fourth order of approximation on space variable is achieved by calculating not only nodal values but integral averaged values of unknown function. This system is integrated over time by L-stable Runge–Kutta method of third order of approximation. Each stage of the method is equivalent to implicit Euler method which is realized by efficient method for boundary value problem. An iteration algorithm is proposed to save high order of approximation in presence of nonlinearity. It is shown that one additional iteration is sufficient for saving fourth order of convergence on space variable.
Keywords:
transport equation, quasi-diffusion method, HOLO algorithms for transport equation solving, diagonally implicit Runge–Kutta method.
Citation:
E. N. Aristova, N. I. Karavaeva, “Bicompact high order schemes for quasi-diffusion equations”, Keldysh Institute preprints, 2018, 045, 28 pp.
\Bibitem{AriKar18}
\by E.~N.~Aristova, N.~I.~Karavaeva
\paper Bicompact high order schemes for quasi-diffusion equations
\jour Keldysh Institute preprints
\yr 2018
\papernumber 045
\totalpages 28
\mathnet{http://mi.mathnet.ru/ipmp2407}
\crossref{https://doi.org/10.20948/prepr-2018-45}
\elib{https://elibrary.ru/item.asp?id=32676406}
Linking options:
https://www.mathnet.ru/eng/ipmp2407
https://www.mathnet.ru/eng/ipmp/y2018/p45
This publication is cited in the following 5 articles:
E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritma resheniya zadach perenosa izlucheniya v srede”, Preprinty IPM im. M. V. Keldysha, 2024, 064, 27 pp.
N. I. Karavaeva, “Bikompaktnye skhemy dlya resheniya odnogruppovoi sistemy uravnenii kvazidiffuzii sovmestno s uravneniem energii”, Preprinty IPM im. M. V. Keldysha, 2023, 025, 16 pp.
E. N. Aristova, N. I. Karavaeva, “The bicompact schemes for numerical solving of Reed problem using HOLO algorithms”, Math. Models Comput. Simul., 14:2 (2022), 187–202
E. N. Aristova, N. I. Karavaeva, “Realizatsiya bikompaktnoi skhemy dlya HOLO algoritmov resheniya uravneniya perenosa”, Preprinty IPM im. M. V. Keldysha, 2019, 021, 28 pp.
E. N. Aristova, N. I. Karavaeva, “The boundary conditions in the bicompact schemes for HOLO algorithms for solving the transport equation”, Math. Models Comput. Simul., 12:3 (2020), 271–281
Citation in format AMSBIB
Contact us: