This article is cited in 7 scientific papers (total in 7 papers)
Newton's method as applied to the Riemann problem for media with general equations of state
N. Ya. Moiseev, T. A. Mukhamadieva
All-Russia Research Institute of Technical Physics, Russian Federal Nuclear Center, Box 245, Snezhinsk, 456770, Russia
An approach based on Newton's method is proposed for solving the Riemann problem for media with normal equations of state. The Riemann integrals are evaluated using a cubic approximation of an isentropic curve that is superior to the Simpson method in terms of accuracy, convergence rate, and efficiency. The potentials of the approach are demonstrated by solving problems for media obeying the Mie–Grüneisen equation of state. The algebraic equation of the isentropic curve and some exact solutions for configurations with rarefaction waves are explicitly given.
gasdynamic equation, Riemann problem, Newton's method, Mie–Grüneisen equation of state.
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Computational Mathematics and Mathematical Physics, 2008, 48:6, 1039–1047
N. Ya. Moiseev, T. A. Mukhamadieva, “Newton's method as applied to the Riemann problem for media with general equations of state”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 1102–1110; Comput. Math. Math. Phys., 48:6 (2008), 1039–1047
Citation in format AMSBIB
\by N.~Ya.~Moiseev, T.~A.~Mukhamadieva
\paper Newton's method as applied to the Riemann problem for media with general equations of state
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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G. P. Prokopov, “K voprosu o priblizhennykh realizatsiyakh metoda Godunova”, Preprinty IPM im. M. V. Keldysha, 2011, 004, 31 pp.
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