Higher-order jump conditions for conservation laws
The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynam...
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| Veröffentlicht in: | Theoretical and computational fluid dynamics 2018-08, Vol.32 (4), p.399-409 |
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| creator | Oksuzoglu, Hakan |
| description | The hyperbolic conservation laws admit discontinuous solutions where the solution variables can have finite jumps in space and time. The jump conditions for conservation laws are expressed in terms of the speed of the discontinuity and the state variables on both sides. An example from the Gas Dynamics is the Rankine–Hugoniot conditions for the shock speed. Here, we provide an expression for the acceleration of the discontinuity in terms of the state variables and their spatial derivatives on both sides. We derive a jump condition for the shock acceleration. Using this general expression, we show how to obtain explicit shock acceleration formulas for nonlinear hyperbolic conservation laws. We start with the Burgers’ equation and check the derived formula with an analytical solution. We next derive formulas for the Shallow Water Equations and the Euler Equations of Gas Dynamics. We will verify our formulas for the Euler Equations using an exact solution for the spherically symmetric blast wave problem. In addition, we discuss the potential use of these formulas for the implementation of shock fitting methods. |
| doi_str_mv | 10.1007/s00162-018-0458-0 |
| format | Article |
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| subjects | Acceleration Analysis Classical and Continuum Physics Computational Science and Engineering Conservation Conservation laws Conservation laws (Physics) Discontinuity Dynamics Engineering Engineering Fluid Dynamics Euler-Lagrange equation Eulers equations Gas dynamics Gasdynamics Mathematical analysis Mathematical models Original Article Shallow water Shallow water equations |
| title | Higher-order jump conditions for conservation laws |
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