Abstract
An automatic algorithm of time step control for solving the boundary value problems for nonstationary parabolic equations is presented. The solution is obtained using complete stable implicit schemes, and the time step is evaluated using of the explicit scheme solution. The time step evaluation formulas are derived using the estimation of the approximation error at next time step. Calculation results obtained for several neutron diffusion problems demonstrate reliability of the proposed algorithm for time step control.
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Avvakumov, A.V., Strizhov, V.F., Vabishchevich, P.N., Vasilev, A.O.: Algorithms for numerical simulation of non-stationary neutron diffusion problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. LNCS, pp. 212–219. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57099-0_21
Acknowledgements
This work are supported A.V. Avvakumov and V.F. Strizhov by the Russian Foundation for Basic Research #16-08-01215, P.N. Vabishchevich by the grant of the Russian Federation Government #14.Y26.31.0013 and A.O. Vasilev by the Russian Foundation for Basic Research #18-31-00315.
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Avvakumov, A.V., Strizhov, V.F., Vabishchevich, P.N., Vasilev, A.O. (2019). Automatic Time Step Selection for Numerical Solution of Neutron Diffusion Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_14
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DOI: https://doi.org/10.1007/978-3-030-11539-5_14
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