A general objective shock wave detection from a geometric singular perturbation approach
| Autor: | Le Wang, Zhuopu Wang, Jiazhong Zhang, Yan Liu |
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| Rok vydání: | 2019 |
| Předmět: |
Physics
Shock wave Numerical Analysis Singular perturbation Applied Mathematics Mathematical analysis Motion (geometry) 01 natural sciences 010305 fluids & plasmas Shock (mechanics) Euler equations Slow motion symbols.namesake Flow (mathematics) Modeling and Simulation Ordinary differential equation 0103 physical sciences symbols 010306 general physics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 66:1-19 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2018.05.015 |
| Popis: | For the general unsteady multi-dimensional flow, the non-linear non-equilibrium nature of shock waves is investigated from the geometric singular perturbation theory. With the introduction of a pressure non-equilibrium term, the modified Euler equation can be reduced to systems of ordinary differential equations(ODEs) along carefully constructed curves. Along each curve, a slow-fast system is derived from the governing ODEs, and the geometric singular perturbation theory is then applied. The motion of the slow-fast system is decomposed to two parts, the quasi-equilibrium slow motion where the non-equilibrium effect is negligible and the fast motion where the non-equilibrium effect plays a dominating role. It is then shown that a shock wave can be recognized as the fast motion of a slow-fast system in an objective manner, and this shock detection method can serve as a rational foundation for practical shock detection problem. |
| Databáze: | OpenAIRE |
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