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Front capturing by level set method for the reactive Euler equations
Author(s) -
Xiao Min,
Ni Guoxi,
Wang Cheng,
Yang Tonghui
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4995
Subject(s) - euler equations , detonation , level set method , conservation of mass , mathematics , conservation law , euler's formula , shock (circulatory) , spurious relationship , finite volume method , discontinuity (linguistics) , mechanics , riemann problem , compressible flow , compressibility , computer science , mathematical analysis , physics , riemann hypothesis , organic chemistry , segmentation , artificial intelligence , medicine , chemistry , statistics , image segmentation , explosive material
In this article, we present a front capturing method for compressible reactive flows, where a shock tracking technique is applied with level set method. In stiff reaction problems, the difficulty arises when the time scale of the source term is significantly shorter than the time scale of the homogeneous conservation law. The spurious numerical phenomenon may occur due to the smeared out shock profiles. In order to overcome the difficulty, the detonation front is captured sharply by level set technique, and a modified finite volume scheme is developed at the computational cells cut by detonation front. The mass, momentum, and energy transitions are occurred on shock front for chemical reactive flows. In our method, the interface exchanges are calculated by considering a Riemann problem. Unlike the standard level set/ghost fluid method, our method can maintain the conservation on the shock discontinuity. One‐ and two‐dimensional numerical examples including stable and unstable detonation problems are illustrated to verify the good reliability and robustness of our method.