A NONLINEAR FINITE-DIFFERENCE SCHEME WITH A LIMITER FOR RADIATION TRANSPORT SIMULATION
https://doi.org/10.26583/vestnik.2024.348
EDN: HZCNVX
Abstract
Numerical modeling of non-stationary radiation transfer process in the kinetic model is a very labor-intensive task. The complexity is caused by the large dimension of the problem and, additionally, for radiant energy transfer problems – by strong nonlinearity. For deterministic approaches based on discretization of the particle flight direction, it is necessary to solve a system of hyperbolic equations of large dimension. Accordingly, it is desirable that the schemes used for numerical modeling are economical both in terms of memory use and calculation time and show acceptable results for a wide range of Courant numbers. In the case of radiant transfer, the situation is aggravated by the strong nonlinearity of the problem being solved, which leads to a significant change in the properties of the medium at time steps. This imposes increased requirements for the monotonicity of the schemes with a change in optical thickness. According to Godunov's theorem, among two-layer linear schemes in time, there are no monotonic schemes of a higher approximation order. One of the directions of solving this problem is the development of NFC (Nonlinear Flux Correction) schemes of end-to-end counting, in which an increased order of accuracy on smooth solutions and monotonicity are achieved due to nonlinear correction of flows. The numerical solution is monotonized using a special algorithm in the vicinity of large gradients of the exact solution. The paper provides a brief overview and characteristics of the finite-difference scheme developed and successfully used for many years at RFNC-VNIITF to solve radiation transfer problems. The TVD (Total Variation Diminishing) methodology is used to monotonize the scheme.
About the Author
V. V. Zavyialov
FSUE «RFNC-VNIITF named after Academ. E.I. Zababakhin»
Russian Federation
Russian Federation
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Review
For citations:
Zavyialov V.V. A NONLINEAR FINITE-DIFFERENCE SCHEME WITH A LIMITER FOR RADIATION TRANSPORT SIMULATION. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2024;13(4):221-231. (In Russ.) https://doi.org/10.26583/vestnik.2024.348. EDN: HZCNVX
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