Front capturing by level set method for the reactive Euler equations. (20th May 2021)

• Record Type: Journal Article
• Authors: Xiao, Min; Ni, Guoxi; Wang, Cheng; Yang, Tonghui
• Is Part Of: International journal for numerical methods in fluids. Volume 93:Number 8(2021)
• Page Start: 2723
• Page End: 2743
• Publication Date: 2021-05-20
• Subjects: conservative interface -- cut cell -- front capturing -- level set function -- reactive Euler equations -- ZND detonation model; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4995
• Languages: English
• ISSNs: 0271-2091

Abstract

Abstract: 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. Abstract : A sharp interface method utilizing the level set technique is presented for simulating the chemical reactive flows, and this method is applicable when combined with mixing reaction model. Based on the modified finite volume discretization and a Riemann solver, conservative numerical model is obtained. Resulting scheme can capture an accurate propagation speed of the shock discontinuity and remove the spurious numerical phenomenon.