We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes.In the case of free surface incompressible flows,the FS-model is formally obtained,using formal ...We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes.In the case of free surface incompressible flows,the FS-model is formally obtained,using formal asymptotic analysis,which is an extension to more classical shallow water models.In the same way,when the pipe is full,we propose the P-model,which describes the evolution of a compressible inviscid flow,close to gas dynamics equations in a nozzle.In order to cope with the transition between a free surface state and a pressured(i.e.,compressible) state,we propose a mixed model,the PFS-model,taking into account changes of section and slope variation.展开更多
In view of the disastrous consequences of tailings dam break and its unique evolutionary process in complex areas,this paper constructs two-dimensional shallow water equations,rheological equations and mathematical mo...In view of the disastrous consequences of tailings dam break and its unique evolutionary process in complex areas,this paper constructs two-dimensional shallow water equations,rheological equations and mathematical models of tailings sand flows on the basis of Navier–Stokes equations(N–S equations).It performs total variation diminishing(TVD)discretization on these equations,develops forward simulation programs in MATLAB2016 and conducts numerical analyses on three kinds of dam breaks(ideal dam break,asymmetric dam break and dam break with obstacles in the downstream area).The results show that TVD discretization is effective in capturing shock waves.According to the analysis on consequences of Huangmailing Tailings Dam break,the author obtains the maximum distance of tailings sand flow,the flow rate of tailings and the time that tailings reach destinations in the downstream area,thereby providing scientific basis for disaster analyses on similar tailings dam breaks and supplying technical support for emergency rescues after disasters.展开更多
基金supported by the "Agence Nationale de la Recherche" referenced by ANR-08-BLAN-0301-01the second author was supported by the ERC Advanced Grant FP7-246775 NUMERIWAVES
文摘We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes.In the case of free surface incompressible flows,the FS-model is formally obtained,using formal asymptotic analysis,which is an extension to more classical shallow water models.In the same way,when the pipe is full,we propose the P-model,which describes the evolution of a compressible inviscid flow,close to gas dynamics equations in a nozzle.In order to cope with the transition between a free surface state and a pressured(i.e.,compressible) state,we propose a mixed model,the PFS-model,taking into account changes of section and slope variation.
文摘In view of the disastrous consequences of tailings dam break and its unique evolutionary process in complex areas,this paper constructs two-dimensional shallow water equations,rheological equations and mathematical models of tailings sand flows on the basis of Navier–Stokes equations(N–S equations).It performs total variation diminishing(TVD)discretization on these equations,develops forward simulation programs in MATLAB2016 and conducts numerical analyses on three kinds of dam breaks(ideal dam break,asymmetric dam break and dam break with obstacles in the downstream area).The results show that TVD discretization is effective in capturing shock waves.According to the analysis on consequences of Huangmailing Tailings Dam break,the author obtains the maximum distance of tailings sand flow,the flow rate of tailings and the time that tailings reach destinations in the downstream area,thereby providing scientific basis for disaster analyses on similar tailings dam breaks and supplying technical support for emergency rescues after disasters.
