The spatial and temporal variability of nutrients and suspended solids were investigated for two years in a 1.8 km agricultural headwater stream, located by Chaohu Lake, southeastern China. The stream form was greatly...The spatial and temporal variability of nutrients and suspended solids were investigated for two years in a 1.8 km agricultural headwater stream, located by Chaohu Lake, southeastern China. The stream form was greatly modified by human activities into channelized, pond and estuary shapes. The stream could be divided into 4 channelized reaches(1.3 km), a pond reach(0.15 km) and 3 estuary reaches(0.36 km). It was found that nutrients and TSS concentrations in the stream showed temporal variability, and higher concentrations occurred in months with high precipitation and intensive agricultural activities. And, retention of total nitrogen(TN), nitrate(NO- 3-N), ammonium(NH+ 4-N) and total suspended solids(TSS) predominantly occurred in the pond reach and estuary reaches with larger width and low current velocity. Pollutants retained in these reaches accounted for more than 50% of those retained in whole stream. The retention mostly happened in the rain-runoff events and it was 7 to 27 times than that in base flow. The results showed that the channelized reach was the most important source for pollutants release under either runoff or base flow, and its release accounted for more than 90% of whole stream release. There was a high spatial variability of nutrients retention in different channelized reaches. The channelized reach directly discharging into the pond did always retain nutrients and TSS under base flow and runoff conditions, whereas the other channelized reaches performed differently in different hydrological conditions. The high spatial and temporal variability of nutrients and TSS in the stream indicated that anthropogenic disturbance of the agricultural headwater stream, such as channelization and excavation, would be expected to decrease the capacity of nutrients retention in the stream.展开更多
In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinea...In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It ...The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.展开更多
文摘The spatial and temporal variability of nutrients and suspended solids were investigated for two years in a 1.8 km agricultural headwater stream, located by Chaohu Lake, southeastern China. The stream form was greatly modified by human activities into channelized, pond and estuary shapes. The stream could be divided into 4 channelized reaches(1.3 km), a pond reach(0.15 km) and 3 estuary reaches(0.36 km). It was found that nutrients and TSS concentrations in the stream showed temporal variability, and higher concentrations occurred in months with high precipitation and intensive agricultural activities. And, retention of total nitrogen(TN), nitrate(NO- 3-N), ammonium(NH+ 4-N) and total suspended solids(TSS) predominantly occurred in the pond reach and estuary reaches with larger width and low current velocity. Pollutants retained in these reaches accounted for more than 50% of those retained in whole stream. The retention mostly happened in the rain-runoff events and it was 7 to 27 times than that in base flow. The results showed that the channelized reach was the most important source for pollutants release under either runoff or base flow, and its release accounted for more than 90% of whole stream release. There was a high spatial variability of nutrients retention in different channelized reaches. The channelized reach directly discharging into the pond did always retain nutrients and TSS under base flow and runoff conditions, whereas the other channelized reaches performed differently in different hydrological conditions. The high spatial and temporal variability of nutrients and TSS in the stream indicated that anthropogenic disturbance of the agricultural headwater stream, such as channelization and excavation, would be expected to decrease the capacity of nutrients retention in the stream.
基金supported by National Foundation of Natural Science under the Grant 11071216
文摘In this paper, we propose a two-grid algorithm for solving the stream function formulation of the stationary Navies-Stokes equations. The algorithm is constructed by reducing the original system to one small, nonlinear system on the coarse mesh space and two similar linear systems （with same stiffness matrix but different right-hand side） on the fine mesh space. The convergence analysis and error estimation of the algorithm are given for the case of conforming elements. Furthermore, the Mgorithm produces a numerical solution with the optimal asymptotic H^2-error. Finally, we give a numerical illustration to demonstrate the effectiveness of the two-grid algorithm for solving the Navier-Stokes equations.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
文摘The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is presented, which is easy to be performed. It is strictly proved that the numerical solution possesses the accuracy of second-order in time and higher order in space.
