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Article information
2013 , Volume 18, ¹ 3, p.54-79
Khakimzyanov G.S., Shokina N.Y.
Adaptive grid method for one-dimensional shallow water equations
The questions of construction of difference schemes, which preserve monotonicity of a numerical solution, on uniform and adaptive grids are discussed using the examples for nonlinear scalar equation. Important properties of preservation of constant solution, stationary and moving shocks are shown. A new explanation of generation of nonphysical numerical solutions and the entropy fix are done using the method of differential approximation. An example of a TVD scheme, which increases a number of extremums, is given. A new approach to construction of any explicit two-layer divergence schemes on moving grids is suggested. The predictor-corrector scheme is used for numerical solution of one-dimensional non-stationary shallow water equations. Investigation of scheme properties has been done combined with its numerical testing
[full text]
Keywords: numerical modelling, finite-difference scheme, nonliner scalar equation, predictor-corrector, monotonicity preserving scheme, divergence scheme, entropy fix, adaptive grid, equidistribution method, nonlinear shallow water equations, numerical results
Author(s):
Khakimzyanov Gayaz Salimovich
Dr. , Professor
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave. 6
Phone Office: (383) 330 86 56
E-mail: khak@ict.nsc.ru
SPIN-code: 3144-0877Shokina Nina Yurievna
PhD.
Position: Research Scientist
Office: Medical Center University of Freiburg
Address: 79106, Germany, Freiburg, Killianstrasse, 5a
Phone Office: (49761) 270 73930
E-mail: nina.shokina@uniklinik-freiburg.de
SPIN-code: 8680-7439
Bibliography link:
Khakimzyanov G.S., Shokina N.Y. Adaptive grid method for one-dimensional shallow water equations // Computational technologies. 2013. V. 18. ¹ 3. P. 54-79
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