A complete study of adsorption processes will be less complete if the structure and dynamics of its different elements and how they interact is not well captured. Therefore, the extensive study of adsorption thermodyn...A complete study of adsorption processes will be less complete if the structure and dynamics of its different elements and how they interact is not well captured. Therefore, the extensive study of adsorption thermodynamics in conjunction with adsorption kinetics is inevitable. Measurable thermodynamic </span><span style="font-family:Verdana;">properties such as temperature equilibrium constant and their non-measurable</span><span style="font-family:Verdana;"> counterparts such as Gibbs free energy change, enthalpy, entropy etc. are very important design variables usually deployed for the evaluation and prediction of the mechanism of adsorption processes.展开更多
Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface.Second order accuracy for the first derivative is obtained ...In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface.Second order accuracy for the first derivative is obtained as well.The method is based on the Ghost Fluid Method,making use of ghost points on which the value is defined by suitable interface conditions.The multi-domain formulation is adopted,where the problem is split in two sub-problems and interface conditions will be enforced to close the problem.Interface conditions are relaxed together with the internal equations(following the approach proposed in[10]in the case of smooth coefficients),leading to an iterative method on all the set of grid values(inside points and ghost points).A multigrid approach with a suitable definition of the restriction operator is provided.The restriction of the defect is performed separately for both sub-problems,providing a convergence factor close to the one measured in the case of smooth coefficient and independent on the magnitude of the jump in the coefficient.Numerical tests will confirm the second order accuracy.Although the method is proposed in one dimension,the extension in higher dimension is currently underway[12]and it will be carried out by combining the discretization of[10]with the multigrid approach of[11]for Elliptic problems with non-eliminated boundary conditions in arbitrary domain.展开更多
文摘A complete study of adsorption processes will be less complete if the structure and dynamics of its different elements and how they interact is not well captured. Therefore, the extensive study of adsorption thermodynamics in conjunction with adsorption kinetics is inevitable. Measurable thermodynamic </span><span style="font-family:Verdana;">properties such as temperature equilibrium constant and their non-measurable</span><span style="font-family:Verdana;"> counterparts such as Gibbs free energy change, enthalpy, entropy etc. are very important design variables usually deployed for the evaluation and prediction of the mechanism of adsorption processes.
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
文摘In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary interface.Second order accuracy for the first derivative is obtained as well.The method is based on the Ghost Fluid Method,making use of ghost points on which the value is defined by suitable interface conditions.The multi-domain formulation is adopted,where the problem is split in two sub-problems and interface conditions will be enforced to close the problem.Interface conditions are relaxed together with the internal equations(following the approach proposed in[10]in the case of smooth coefficients),leading to an iterative method on all the set of grid values(inside points and ghost points).A multigrid approach with a suitable definition of the restriction operator is provided.The restriction of the defect is performed separately for both sub-problems,providing a convergence factor close to the one measured in the case of smooth coefficient and independent on the magnitude of the jump in the coefficient.Numerical tests will confirm the second order accuracy.Although the method is proposed in one dimension,the extension in higher dimension is currently underway[12]and it will be carried out by combining the discretization of[10]with the multigrid approach of[11]for Elliptic problems with non-eliminated boundary conditions in arbitrary domain.
