International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Shaidurov V.   Щепановская Г.И.  

The Numerical Modeling of One-Dimensional Motion of Viscous Heat-Conductive Gas

Reporter: Щепановская Г.И.

     In this paper, an algorithm for the numerical solution of the equations of one-dimensional motion of viscous heat-conductive gas is proposed. The algorithm is based on the finite element method for modified equations which provide high-order accuracy of an approximate solution [1]. For the solution of the Navier-Stokes equations we mixed the trajectories method and the finite element method [2].
     The time derivative is approximated with the help of the backward difference time derivative along the trajectory of motion of a particle. To solve a system of linear algebraic equations with a tridiagonal matrix, we use the non-monotonic sweep method which is of high computational stability.
     Test calculations have been performed. The problem on propagation of heat impulse in gas is implemented. The tested computer model is used in the study of one-dimensional geodynamics processes [3]. The actual values of density and temperature in a ratio to the corresponding values at the Earth’s surface are taken as initial conditions.

The authors were supported by the project № 89 of the Siberian Branch of Russian Academy of Sciences with exterior scientific organizations.

[1] D. Anderson, J. Tannehill, R. Pletcher. Computational fluid mechanics and heat transfer, Hemisphere Publishing Corporation, New York, 1984.
[2] O. Pironneau. On the Transport-Diffusion Algorithm and Its Applications to the Navier-Stokes Equations, Numer. Math., 1982, 38, pp. 309-332.
[3] A. V. Vyatkin, V. V. Shaidurov, and G. I. Shchepanovskaya. Numerical Spherically-Symmetric Simulation of Deep-Seated Geodynamics, Journal of Applied and Industrial Mathematics, 2010, Vol. 4, No. 2, pp. 290–297.  

Abstracts file: Файл тезисов(Shchepanovskaya).doc

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