An h-adaptive RKDG method with troubled-cell indicator for one-dimensional detonation wave simulations

Zhu, Hongqiang; Gao, Zhen

doi:10.1007/s10444-016-9454-3

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…The initial free stream and periodical boundary conditions are imposed in the x-and ydirections respectively -cf. [14,15,37]. The colored contours in Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In particular, for the detonation waves simulating here, the meshes should be refined near the discontinuities in order to catch their sharp transitions. Therefore, following the ideas of [37], we coarse the mesh over untroubled cells and refine it for troubled cells. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, mesh refinement is performed in a recursive way.…”

Section: Algorithmmentioning

confidence: 99%

“…Let us note that although there is an h-adaptive RKDG method for one-dimensional detonation waves [37], all realistic detonation phenomena are essentially three-dimensional. Nevertheless, many important detonation structures can be detected during two-dimensional simulations -e.g.…”

Section: Introductionmentioning

confidence: 99%

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An h-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations

Gao¹

2019

EAJAM

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An h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method with a positivity-preserving technique to simulate classical two-dimensional detonation waves is developed. The KXRCF troubled-cell indicator is used to detect the troubled cells with possible discontinuities or high gradients. At each time-level, an adaptive mesh is generated by refining troubled cells and coarsening others. In order to avoid the situations where detonation front moves too fast and there are not enough cells to describe detonation front before it leaves, a recursive multi-level mesh refinement technique is designed. The numerical results show that for smooth solutions, this h-adaptive method does not degrade the optimal convergence order of the nonadaptive method and outperforms it in terms of computational storage for shocked flows.

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“…The initial free stream and periodical boundary conditions are imposed in the x-and ydirections respectively -cf. [14,15,37]. The colored contours in Fig.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%