ISSN 2542–0380
Труды Института механики им. Р.Р. Мавлютова
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Proceedings of the Mavlyutov Institute of Mechanics


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Aganin A.A., Khismatullina N.A. Modifications of the Godunov method for computing disturbance propagation in an elastic body Proceedings of the Mavlyutov Institute of Mechanics. 2016. 11(1). 119–126.
2016. Vol. 11. Issue 1, Pp. 119–126
URL: http://proc.uimech.org/uim2016.1.018,en
DOI: 10.21662/uim2016.1.018
Modifications of the Godunov method for computing disturbance propagation in an elastic body
Aganin A.A.∗,∗∗, Khismatullina N.A.∗∗
Mavlyutov Institute of Mechanics, Ufa
∗∗Institute of Mechanics and Engineering, Kazan

Abstract

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

Keywords

linear waves in an elastic body,
Godunov method,
ENO-schemes,
UNO-schemes,
TVD-schemes