In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & d...In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand, the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand, because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.展开更多
The classical 1-D vertical advection-diffusion model was improved in this work. The main advantages of the improved model over the previous one are: 1) The applicable condition of the 1-D model is made clear in the im...The classical 1-D vertical advection-diffusion model was improved in this work. The main advantages of the improved model over the previous one are: 1) The applicable condition of the 1-D model is made clear in the improved model, in that it is substantively applicable only to a vertical domain on which two end-member water masses are mixing. 2) The substitution of parameter f(z) in the equation of the classical 1-D model with end-member fraction f 1z makes the model more precisely and easily solved. 3) All the terms in the improved model equation have specific physical meanings, which makes the model easily understood. Practical application of the improved model to predict the vertical profiles of dissolved oxygen and micronutrients in abyssal ocean water of the North Pacific proved that the improvement of the 1-D advection-diffusion model is successful and practicable.展开更多
A Fulx Difference Splitting (FDS) scheme was used in a 2D depth-averaged flow-pollutant model. Within the framework of the Finite Volume Method (FVM) a 2D simulation was transferred into solving a series of local 1D p...A Fulx Difference Splitting (FDS) scheme was used in a 2D depth-averaged flow-pollutant model. Within the framework of the Finite Volume Method (FVM) a 2D simulation was transferred into solving a series of local 1D problems based on the rotational invariance property of the flux. The FDS scheme was employed to estimate the normal numerical flux of variables including water mass, momentum and pollutant concentration across the interface between cells. The scheme was checked with exact solutions and verified by observations in the Nantong reach of the Yangtze River. Calculated results well match both exact solutions and observations.展开更多
基金funded by NSFC 40076005 and Frontier Innovation Project L390221103 from the Chinese Academy of Sciencesthe financial support from the National Tenth Five-Year Key Project H57022113.
文摘In the light of the problem of oil pollution brought about by ships, in this paper we present the concept of backward tracing oil spills. In the course of backward calculation of the two-dimensional convection & diffusion equation, on the one hand, the advection term itself has the strong unilateral property, which means information in the upper reaches is transmitted downstream via the advection term; on the other hand, because of the opposite direction of calculation, it is essential for information to be conveyed upstream by means of the advection term. In addition, unlike that in the forward calculation, the diffusion term in the backward calculation is prone to accumulate errors, and thus renders the whole scheme unstable. Therefore, we adopt the central difference to deal with both the convectional term and the diffusion term. By examining two practical examples (1) under the unlimited boundary condition, and (2) under the limited boundary condition, it is proven that this method could achieve fundamentally satisfactory results not only in the open ocean but also in the closed or semi-closed bay.
文摘The classical 1-D vertical advection-diffusion model was improved in this work. The main advantages of the improved model over the previous one are: 1) The applicable condition of the 1-D model is made clear in the improved model, in that it is substantively applicable only to a vertical domain on which two end-member water masses are mixing. 2) The substitution of parameter f(z) in the equation of the classical 1-D model with end-member fraction f 1z makes the model more precisely and easily solved. 3) All the terms in the improved model equation have specific physical meanings, which makes the model easily understood. Practical application of the improved model to predict the vertical profiles of dissolved oxygen and micronutrients in abyssal ocean water of the North Pacific proved that the improvement of the 1-D advection-diffusion model is successful and practicable.
文摘A Fulx Difference Splitting (FDS) scheme was used in a 2D depth-averaged flow-pollutant model. Within the framework of the Finite Volume Method (FVM) a 2D simulation was transferred into solving a series of local 1D problems based on the rotational invariance property of the flux. The FDS scheme was employed to estimate the normal numerical flux of variables including water mass, momentum and pollutant concentration across the interface between cells. The scheme was checked with exact solutions and verified by observations in the Nantong reach of the Yangtze River. Calculated results well match both exact solutions and observations.
