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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 5, Pages 920–935
(Mi zvmmf9341)
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This article is cited in 6 scientific papers (total in 6 papers)
High-order accurate implicit running schemes
N. Ya. Moiseev All-Russia Research Institute of Technical Physics, Russian
Federal Nuclear Center, Box 245, Snezhinsk, 456770 Russia
Abstract:
An approach to the construction of high-order accurate implicit predictor–corrector schemes is proposed. The accuracy is improved by choosing a special time integration step for computing numerical fluxes through cell interfaces by using an unconditionally stable implicit scheme. For smooth solutions of advection equations with constant coefficients, the scheme is second-order accurate. Implicit difference schemes for multidimensional advection equations are constructed on the basis of Godunov's method with splitting over spatial variables as applied to the computation of “large” values at an intermediate layer. The numerical solutions obtained for advection equations and the radiative transfer equations in a vacuum are compared with their exact solutions. The comparison results confirm that the approach is efficient and that the accuracy of the implicit
predictor–corrector schemes is improved.
Key words:
multidimensional advection equations, implicit predictor–corrector schemes, Godunov's method.
Received: 14.05.2010
Citation:
N. Ya. Moiseev, “High-order accurate implicit running schemes”, Zh. Vychisl. Mat. Mat. Fiz., 51:5 (2011), 920–935; Comput. Math. Math. Phys., 51:5 (2011), 862–875
Linking options:
https://www.mathnet.ru/eng/zvmmf9341 https://www.mathnet.ru/eng/zvmmf/v51/i5/p920
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Abstract page: | 777 | Full-text PDF : | 465 | References: | 62 | First page: | 21 |
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