DOI: 10.17586/2226-1494-2016-16-1-174-180


P. V. Bulat, K. N. Volkov

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Article in Russian

For citation: Bulat P.V., Volkov K.N. WENO schemes for solution of unsteady one-dimensional gas dynamics test problems. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 1, pp. 174–180.


Creation of test solutions is an essential element in the general design contents for numerical methods aimed at integration of Euler equations. We consider numerical solution of Euler equations describing flows of inviscid compressible gas and allowing continuous and discontinuous solutions. Discretization of Euler equations is based on finite volume method and WENO finite difference schemes. The numerical solutions computed are compared with the exact solutions of Riemann problem. Monotonic correction of derivatives makes it possible to avoid new extremes and ensures monotonicity of the numerical solution near the discontinuity, but it leads to the smoothness of the existing minimums and maximums and to the loss of accuracy. Calculations with the use of WENO schemes allow obtaining accurate and monotonic solution with the presence of both weak and strong gas dynamical discontinuities.

Keywords: gas dynamics, finite difference scheme, shock wave, rarefaction wave, contact discontinuity, Riemann problem

Acknowledgements. The study has been carried out under financial support of the Ministry of Education and Science of the Russian Federation (agreement No.14.575.21.0057).


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