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Article information
2014 , Volume 19, ¹ 4, p.42-60
Kovenya V.M.
Optimum of splitting algorithms for the numerical solutions of Euler and Navier - Stokes equations
Numerical solution of Euler and Navier-Stokes equations for compressed heat-conducting gas is considered. We present a class of the implicit differential schemes based on optimum splitting of the initial equations, which is common for the equations written in divergent and not divergent forms. The initial equations are represented in the form of special splitting on physical processes and the spatial directions which influence is minimum. The method is applied for economic differential schemes of predictor type. At the predictor stage, the differential equations are solved on fractional steps, using effective algorithms, for example, scalar sweeps. At the corrector stage, the conservatism of algorithm is restored. The obtained differential schemes approximate the equations with the second order on all variables. They are stable (certainly they are absolutely stable for two-dimensional problems for the appropriate choice of weight parameter and are conditionally steady for spatial problem) thus they are suitable for solution of stationary and non-stationary problems. Their realization is reduced to scalar sweeps unlike implicit differential schemes with directions splitting, which are realized by vector sweeps, where dimension is defined by the equations on space. The analysis of properties of the offered algorithms for the equations of various dimensions is carried out. Offered algorithms allow to choose various gasdynamic variables on fractional steps at the predictor stage that can lead to simplification of their realization and minimize number of arithmetic operations on grid points. Aknowlegements: This work was supported by RFBR grants 14-01-00191 and the integration project SB RAS ¹ 76 and 130. Received 22 January 2014.
[full text]
Keywords: Euler and Navier-Stokes equations, differential scheme, splitting and factorization methods
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
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Bibliography link:
Kovenya V.M. Optimum of splitting algorithms for the numerical solutions of Euler and Navier - Stokes equations // Computational technologies. 2014. V. 19. ¹ 4. P. 42-60
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