In this paper,the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model...In this paper,the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model.Both two-dimensional and axisymmetric configurations are used for modeling cylindrical and spherical expansions,respectively.The chemical parameters are chosen for a stable gaseous explosive mixture in which the cellular detonation structure is highly regular.Adaptive mesh refinement(AMR)is used to resolve the detonation wave structure and its evolution during the transmission.The numerical results show that the critical channel width and critical diameter over the detonation cell size are about 1371 and 2571,respectively.These numerical findings are comparable with the experimental observation and confirm again that the critical channel width and critical diameter differ essentially by a factor close to 2,equal to the geometrical scaling based on front curvature theory.Unlike unstable mixtures where instabilities manifested in the detonation front structure play a significant role during the transmission,the present numerical results and the observed geometrical scaling provide again evidence that the failure of detonation diffraction in stable mixtures with a regular detonation cellular pattern is dominantly caused by the global curvature due to the wave divergence resulting in the global decoupling of the reaction zone with the expanding shock front.展开更多
We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral...We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 （Ω）-context along with local discrete Helmholtz-type decompositions of the edge element space.展开更多
基金This work is supported by the Natural Sciences and Engineering Research Council of Canada(NSERC)(No.341889)National Natural Science Foundation of China(Nos.11390363,11325209).
文摘In this paper,the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model.Both two-dimensional and axisymmetric configurations are used for modeling cylindrical and spherical expansions,respectively.The chemical parameters are chosen for a stable gaseous explosive mixture in which the cellular detonation structure is highly regular.Adaptive mesh refinement(AMR)is used to resolve the detonation wave structure and its evolution during the transmission.The numerical results show that the critical channel width and critical diameter over the detonation cell size are about 1371 and 2571,respectively.These numerical findings are comparable with the experimental observation and confirm again that the critical channel width and critical diameter differ essentially by a factor close to 2,equal to the geometrical scaling based on front curvature theory.Unlike unstable mixtures where instabilities manifested in the detonation front structure play a significant role during the transmission,the present numerical results and the observed geometrical scaling provide again evidence that the failure of detonation diffraction in stable mixtures with a regular detonation cellular pattern is dominantly caused by the global curvature due to the wave divergence resulting in the global decoupling of the reaction zone with the expanding shock front.
基金supported in part by China NSF under the grant 60873177by the National Basic Research Project under the grant 2005CB321702
文摘We consider H（curl, Ω）-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a H^1 （Ω）-context along with local discrete Helmholtz-type decompositions of the edge element space.
