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Article information
2015 , Volume 20, ¹ 5, p.65-84
Kovenya V.M., Babintsev P.V.
Splitting Algorithms in finite volume method
We propose a class of the finite volume predictor-corrector algorithms for the numerical solution of the Euler and Navier - Stokes equations presented in the integral form in the case of a compressible heat-conducting gas. In the predictor step we have introduced a special form of splitting of the governing equations. In the approximation of the Euler equations, the vector flows across the borders of a cell is split into two vectors: the first vector contains only the convective terms, and the second one contains the terms with pressure and internal energy, which is an analogue of splitting into physical processes in the differential form. This kind of splitting is equivalent to representation of the original equations in the form of two systems that approximate the original Euler equation. Upon the introduction of this splitting, we are able to reduce the solution of equations in fractional steps to effective scalar sweeps. Approximation of the Navier - Stokes was introduced by analogy with the splitting of the Euler equations: flux vector is the sum of two vectors, the first of which includes convective and dissipative terms of the equations, and the second term includes pressure in the same way as it was done for the splitting of the Euler equations. In the corrector step we deal with the complete system of equations in the conservative form using the explicit scheme. The algorithm is tested on the two problems with the exact solution: the Riemann problem and the flow in a channel with variable cross-section. For the flow of gas in the convergent channel with regular and irregular reflection effects we have numerically confirmed the existence of the set of dual solutions, depending on the initial data.
[full text]
Keywords: Euler and Navier-Stokes equations, splitting method, finite-volume method, regular and Mach reflection of waves
Author(s):
Kovenya Viktor Mikhailovich
Dr. , Professor
Position: General Scientist
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, academician M.A. Lavrentiev avenue, 6
Phone Office: (383) 330 61 68
E-mail: kovenya@ict.nsc.ru
Babintsev Pavel Vasiljevich
Office: Novosibirsk State University
Address: Russia, Novosibirsk, Novosibirsk, academician M.A. Lavrentiev avenue, 6
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Bibliography link:
Kovenya V.M., Babintsev P.V. Splitting Algorithms in finite volume method // Computational technologies. 2015. V. 20. ¹ 5. P. 65-84
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