Study of Entropy Properties of a Linearized Version of Godunov’s Method
The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics poi...
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| Veröffentlicht in: | Computational mathematics and mathematical physics 2020-04, Vol.60 (4), p.628-640 |
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| container_title | Computational mathematics and mathematical physics |
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| creator | Godunov, S. K. Denisenko, V. V. Klyuchinskii, D. V. Fortova, S. V. Shepelev, V. V. |
| description | The ideas of formulating a weak solution for a hyperbolic system of one-dimensional gas dynamics equations are presented. An important aspect is the examination of the scheme for the fulfillment of the nondecreasing entropy law, which must hold for weak solutions and is obligatory from a physics point of view. The concept of a weak solution is defined in a finite-difference formulation with the help of the simplest linearized version of the classical Godunov scheme. It is experimentally shown that this version guarantees an entropy nondecrease. As a result, the growth of entropy on shock waves can be simulated without using any correction terms or additional conditions. |
| doi_str_mv | 10.1134/S0965542520040089 |
| format | Article |
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| subjects | Computational Mathematics and Numerical Analysis Entropy Finite difference method Gas dynamics Hyperbolic systems Linearization Mathematics Mathematics and Statistics Shock waves |
| title | Study of Entropy Properties of a Linearized Version of Godunov’s Method |
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