Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 1, Pages 62–75
This article is cited in 1 scientific paper (total in 1 paper)
A Shock Capturing Method
V. F. Kuropatenko
Russian Federal Nuclear Center — Zababakhin Institute of Applied Physics, Snezhinsk, Russian Federation
Strong discontinuities, or shocks in continua are a result of external dynamic loads. On the shock surface the conservation laws take the form of nonlinear algebraic equations for jumps across the shock. Entropy jumps across a strong discontinuity, and just this jump differs shocks from waves where the quantities vary continuously. In the heterogeneous difference schemes, the shock is treated as a layer of a finite thickness comparable with the cell size. This property of finite-difference schemes was called distraction. Since the state behind a shock is related to the state before it by the Hugoniot, in the distraction region there must act a mechanism that increases entropy. The physical viscosity and heat conductivity in continuum mechanics equations do not make it unnecessary to introduce a shock surface and hence cannot make the distraction length comparable with a few cells of the difference mesh. The paper considers a number of finite difference schemes where energy dissipation in the distraction region is defined by equations which are valid on the shock surface.
shock wave; differential method; distraction; energy dissipation; conservation laws.
PDF file (330 kB)
MSC: 76.L, 74.S
V. F. Kuropatenko, “A Shock Capturing Method”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:1 (2014), 62–75
Citation in format AMSBIB
\paper A Shock Capturing Method
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
A. V. Krasilnikov, V. F. Kuropatenko, “Propagation of a strong discontinuity in a binary mixture of gases”, J. Comp. Eng. Math., 5:3 (2018), 49–60
|Number of views:|