In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly suppo...In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly supported spline wavelets. Then we get the inheritive fast adaptive spline interpolation scheme and the prop- erties of singularity detecting with waveltets. As a result, the adaptive spline wavelets orthogonal collocation methods for initial boundary value problems are obtained.展开更多
A major shortcoming of polynomial approximation in the medelling of distillation columns isthe difficulty encountered while choosing the number and location of collocation points,which are usually doneby rule of the t...A major shortcoming of polynomial approximation in the medelling of distillation columns isthe difficulty encountered while choosing the number and location of collocation points,which are usually doneby rule of the thumb,inevitably giving rise to high dimensionality and longer computation time for the resultingmodel.In order to take full advantage of polynomial approximation in the modelling of complicatedmulticomponent distillation columns,modifications must be made to the model reduction procedure originallyproposed by Cho.This is achieved by putting in special polynomials to each of the variable profiles.Furthermore,the number and location of the collocation points can be determined by the optimization of anappropriate objective function.This would bring about less dimensionality and less computation time for theresulting reduced--order model as compared with Cho’s procedure while its accuracy is still kept excellent.Theeffectiveness of such modifications is illustrated by two simulation examples.展开更多
Mathematical models of the mamalian urine concentrating mechanism consist of a large system of coupled, nonlinear and stiff equations. An efficient numerical orthogonal collocation method was employed to solve the ste...Mathematical models of the mamalian urine concentrating mechanism consist of a large system of coupled, nonlinear and stiff equations. An efficient numerical orthogonal collocation method was employed to solve the steady-state formulation of urine concentrating mechanism. This method was used to solve the stiff and high order equations of electrolyte transport in a central core, single nephron model of the renal outer medulla. The presented results were in good agreement with implicit finite difference method’s results, but this new method was faster and more stable. Due to the greater stability and larger convergence domain of collocation method over Newton’s method, a parametric study on concentrated urine was investigated. The results showed that this model was sensitive to non-ideal countercurrent exchange between medulla interstitium and vasa recta. Although distal tubule lies in the cortex interstitium, it affects on the inflow to the collecting duct. This study showed that the effect of changing membrane transport properties of distal tubule wall on properties of outflow from the outer medulla collecting duct was considerable.展开更多
This study involves the applications of different numerical techniques in a more general way to the design of a simulator for an enhanced oil recovery process with surfactant assisted water flooding. The data from a h...This study involves the applications of different numerical techniques in a more general way to the design of a simulator for an enhanced oil recovery process with surfactant assisted water flooding. The data from a hypothetical oil well and a Nigerian oil well were used for the validation of the simulator. The process is represented by a system of nonlinear partial differential equations: the continuity equation for the transport of the components and Darcy’s equation for the phase flow. The orthogonal collocation, finite difference and coherence theory techniques were used in solving the equations that characterized the multidimensional, multiphase and multicomponent flow problem. Matlab computer programs were used for the numerical solution of the model equ- ations. The predicted simulator, obtained from the resulting numerical exercise confers uncondi- tional stability and more insight into the physical reservoir description. The results of the ortho- gonal collocation solution were compared with those of finite difference and coherence solutions. The results indicate that the concentration of surfactants for orthogonal collocation show more features than the predictions of the coherence solution and the finite difference, offering more opportunities for further understanding of the physical nature of the complex problem. We have found out that the partition of the three components between the two-phases determines other physical property data and hence the oil recovery. The oil recovery for the Nigerian oil reservoir is higher than the recovery predicted for the hypothetical crude. The displacement mechanism for the multicomponent and multiphase system is stable in the Nigerian oil reservoir due to the mod- erate value of the oil/water viscosity instead of the hypothetical reservoir with high value of oil/water ratio.展开更多
文摘In this paper, we construct the general odd degree semi-orthogonal multi-knots spline wavelets space with point value vanishing properties under energy inner product, and present two kinds of low order compactly supported spline wavelets. Then we get the inheritive fast adaptive spline interpolation scheme and the prop- erties of singularity detecting with waveltets. As a result, the adaptive spline wavelets orthogonal collocation methods for initial boundary value problems are obtained.
基金This work was supported by the National Laboratory of Industrial Control Technique of China
文摘A major shortcoming of polynomial approximation in the medelling of distillation columns isthe difficulty encountered while choosing the number and location of collocation points,which are usually doneby rule of the thumb,inevitably giving rise to high dimensionality and longer computation time for the resultingmodel.In order to take full advantage of polynomial approximation in the modelling of complicatedmulticomponent distillation columns,modifications must be made to the model reduction procedure originallyproposed by Cho.This is achieved by putting in special polynomials to each of the variable profiles.Furthermore,the number and location of the collocation points can be determined by the optimization of anappropriate objective function.This would bring about less dimensionality and less computation time for theresulting reduced--order model as compared with Cho’s procedure while its accuracy is still kept excellent.Theeffectiveness of such modifications is illustrated by two simulation examples.
文摘Mathematical models of the mamalian urine concentrating mechanism consist of a large system of coupled, nonlinear and stiff equations. An efficient numerical orthogonal collocation method was employed to solve the steady-state formulation of urine concentrating mechanism. This method was used to solve the stiff and high order equations of electrolyte transport in a central core, single nephron model of the renal outer medulla. The presented results were in good agreement with implicit finite difference method’s results, but this new method was faster and more stable. Due to the greater stability and larger convergence domain of collocation method over Newton’s method, a parametric study on concentrated urine was investigated. The results showed that this model was sensitive to non-ideal countercurrent exchange between medulla interstitium and vasa recta. Although distal tubule lies in the cortex interstitium, it affects on the inflow to the collecting duct. This study showed that the effect of changing membrane transport properties of distal tubule wall on properties of outflow from the outer medulla collecting duct was considerable.
文摘This study involves the applications of different numerical techniques in a more general way to the design of a simulator for an enhanced oil recovery process with surfactant assisted water flooding. The data from a hypothetical oil well and a Nigerian oil well were used for the validation of the simulator. The process is represented by a system of nonlinear partial differential equations: the continuity equation for the transport of the components and Darcy’s equation for the phase flow. The orthogonal collocation, finite difference and coherence theory techniques were used in solving the equations that characterized the multidimensional, multiphase and multicomponent flow problem. Matlab computer programs were used for the numerical solution of the model equ- ations. The predicted simulator, obtained from the resulting numerical exercise confers uncondi- tional stability and more insight into the physical reservoir description. The results of the ortho- gonal collocation solution were compared with those of finite difference and coherence solutions. The results indicate that the concentration of surfactants for orthogonal collocation show more features than the predictions of the coherence solution and the finite difference, offering more opportunities for further understanding of the physical nature of the complex problem. We have found out that the partition of the three components between the two-phases determines other physical property data and hence the oil recovery. The oil recovery for the Nigerian oil reservoir is higher than the recovery predicted for the hypothetical crude. The displacement mechanism for the multicomponent and multiphase system is stable in the Nigerian oil reservoir due to the mod- erate value of the oil/water viscosity instead of the hypothetical reservoir with high value of oil/water ratio.
