Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have b...Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.展开更多
WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between thir...WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]展开更多
The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airway...The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.展开更多
Based on the previous works of the second author, a kind of finite difference scheme with third-crder accuracy for the homogeneous diffusion equation on non -uniform grid is presented. The proposed scheme is unconditi...Based on the previous works of the second author, a kind of finite difference scheme with third-crder accuracy for the homogeneous diffusion equation on non -uniform grid is presented. The proposed scheme is unconditionally stable.展开更多
文摘Numerical diffusion and oscillatory behavior characteristics are averted applying numerical solutions of advection-diffusion equation are themselves immensely sophisticated. In this paper, two numerical methods have been used to solve the advection diffusion equation. We use an explicit finite difference scheme for the advection diffusion equation and semi-discretization on the spatial variable for advection-diffusion equation yields a system of ordinary differential equations solved by Euler’s method. Numerical assessment has been executed with specified initial and boundary conditions, for which the exact solution is known. We compare the solutions of the advection diffusion equation as well as error analysis for both schemes.
基金ProjectsupportedbytheMajorStateBasicResearchDevelopmentProgram (No .G19990 436 )andthe"Trans CenturyTrainingProgramFoundationfo
文摘WT5”BZ]A high-order-accurate difference scheme with unconditional stability is developed for the diffusion equation on nonuniform grids. The theoretical analysis shows that the accuracy of this scheme is between third order and fourth order, and fourth-order accuracy is achieved in the case of the same grid steps being used within the computational domain. Two numerical examples are given to demonst ate the advantages of the proposed scheme. Compared with the conventional difference scheme, more accurate numerical solution can be obtained by using the proposed scheme even with relatively larger grid sizes. It is also pointed out that the appropriate structure of the nonuniform grid can not only make the proposed scheme more practical, but lead to a solution superior to that for a uniform grid structure. [WT5”HZ]
文摘The lung is an important organ that takes part in the gas exchange process. In the study of gas transport and exchange in the human respiratory system, the complicated process of advection and diffusion (AD) in airways of human lungs is considered. The basis of a lumped parameter model or a transport equation is modeled during the inspiration process, when oxygen enters into the human lung channel. The quantitative measurements of oxygen are detached and the model equation is solved numerically by explicit finite difference schemes. Numerical simulations were made for natural breathing conditions or normal breathing conditions. The respiratory flow results for the resting conditions are found strongly dependent on the AD effect with some contribution of the unsteadiness effect. The contour of the flow rate region is labeled and AD effects are compared with the variation of small intervals of time for a constant velocity when breathing is interrupted for a negligible moment.
文摘Based on the previous works of the second author, a kind of finite difference scheme with third-crder accuracy for the homogeneous diffusion equation on non -uniform grid is presented. The proposed scheme is unconditionally stable.
