An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non...An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.展开更多
The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent...The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent. In this paper, the transport of conservative,adsorbing and degradable solutes through a 1 m heterogeneous soil column under steady flow condition was simulated by ADE and MIM, and sensitivity analysis was conducted. Results show that MIM tends to prolong the breakthrough process and decrease peak concentration for all three solutes, and tailing and skewness are more pronounced with increasing dispersivity. Breakthrough curves of the adsorbing solute simulated by MIM are less sensitive to the retardation factor compared with the results simulated by ADE. The breakthrough curves of degradable solute obtained by MIM and ADE nearly overlap with a high degradation rate coefficient, indicating that MIM and ADE perform similarly for simulating degradable solute transport when biochemical degradation prevails over the mass exchange between mobile and immobile zones. The results suggest that the physical significance of dispersivity should be carefully considered when MIM is applied to simulate the degradable solute transport and/or ADE is applied to simulate the adsorbing solute transport in highly dispersive soils.展开更多
Based on the recent development in shallow flow modelling, this paperpresents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrixsystem of conservation laws that comprise the shallow water and ...Based on the recent development in shallow flow modelling, this paperpresents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrixsystem of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserveexactly the solution of lake at rest so that no special numerical technique is necessaryin order to construct a well-balanced scheme. The HLLC approximate Riemann solveris used to evaluate the interface fluxes. Second-order accuracy is achieved using theMUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the resultsare in excellent agreement with analytical solutions or other published numerical predictions.展开更多
文摘An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.
基金funded by Projects of the National Natural Science Foundation of China (51379207, 51321001)
文摘The traditional advection-dispersion equation(ADE) and the mobile-immobile model(MIM) are widely used to describe solute transport in heterogeneous porous media. However, the fitness of the two models is casedependent. In this paper, the transport of conservative,adsorbing and degradable solutes through a 1 m heterogeneous soil column under steady flow condition was simulated by ADE and MIM, and sensitivity analysis was conducted. Results show that MIM tends to prolong the breakthrough process and decrease peak concentration for all three solutes, and tailing and skewness are more pronounced with increasing dispersivity. Breakthrough curves of the adsorbing solute simulated by MIM are less sensitive to the retardation factor compared with the results simulated by ADE. The breakthrough curves of degradable solute obtained by MIM and ADE nearly overlap with a high degradation rate coefficient, indicating that MIM and ADE perform similarly for simulating degradable solute transport when biochemical degradation prevails over the mass exchange between mobile and immobile zones. The results suggest that the physical significance of dispersivity should be carefully considered when MIM is applied to simulate the degradable solute transport and/or ADE is applied to simulate the adsorbing solute transport in highly dispersive soils.
基金This work is supported by the UK Engineering and Physical Sciences Research Council(EPSRC)through grant:EP/F030177/1.
文摘Based on the recent development in shallow flow modelling, this paperpresents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrixsystem of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserveexactly the solution of lake at rest so that no special numerical technique is necessaryin order to construct a well-balanced scheme. The HLLC approximate Riemann solveris used to evaluate the interface fluxes. Second-order accuracy is achieved using theMUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the resultsare in excellent agreement with analytical solutions or other published numerical predictions.
