The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and...The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a derivative reconstruction approach is proposed in the context of spectral volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. Two different reconstructions are used for advective and diffusive fluxes： the advective reconstruction makes use of the information contained in a spectral cell, and allows the formation of discontinuities at the spectral cells boundaries; the diffusive reconstruction makes use of the information contained in contiguous spectral cells, imposing the continuity of the reconstruction at the spectral cells boundaries. The method is demonstrated by a number of numerical experiments, including the solution of shallow-water equations, complemented with the advective-diffusive transport equation of a conservative substance, showing the promising abilities of the numerical scheme proposed.展开更多
Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting ...Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.展开更多
The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and co...The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and corresponding geodynamic processes. Vertical waveform data from six earthquakes with focal depths between 75 and 150 km and magnitudes Mb 5.0–6.0 since 2004 were collected from the short-period Hi-net array. Selected waveform data were processed for each event network pair using the Nth-root slant stack method to retrieve the SdP conversion phases from the possible 220 km(Lehmann) discontinuity. The conversion points related to the SdP phases show that there is a clear and flat velocity interface around 230 km, suggesting that there is a sinking of the Lehmann discontinuity beneath Tonga with no obvious undulation. The 230 km depth of the Lehmann discontinuity in this location could be explained by an hypothesis of transition in the deformation mechanism from dislocation creep to diffusion creep.展开更多
文摘The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a derivative reconstruction approach is proposed in the context of spectral volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. Two different reconstructions are used for advective and diffusive fluxes： the advective reconstruction makes use of the information contained in a spectral cell, and allows the formation of discontinuities at the spectral cells boundaries; the diffusive reconstruction makes use of the information contained in contiguous spectral cells, imposing the continuity of the reconstruction at the spectral cells boundaries. The method is demonstrated by a number of numerical experiments, including the solution of shallow-water equations, complemented with the advective-diffusive transport equation of a conservative substance, showing the promising abilities of the numerical scheme proposed.
基金This research is supported by the National Natural Science Foundation of China.
文摘Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.
基金sponsored by the National Natural Science Foundation of China (Grant No. 41074065)SinoProbe-Deep Exploration in China (Grant No. SinoProbe-07-04)
文摘The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and corresponding geodynamic processes. Vertical waveform data from six earthquakes with focal depths between 75 and 150 km and magnitudes Mb 5.0–6.0 since 2004 were collected from the short-period Hi-net array. Selected waveform data were processed for each event network pair using the Nth-root slant stack method to retrieve the SdP conversion phases from the possible 220 km(Lehmann) discontinuity. The conversion points related to the SdP phases show that there is a clear and flat velocity interface around 230 km, suggesting that there is a sinking of the Lehmann discontinuity beneath Tonga with no obvious undulation. The 230 km depth of the Lehmann discontinuity in this location could be explained by an hypothesis of transition in the deformation mechanism from dislocation creep to diffusion creep.
