A model for transient diffusion in bidisperse pore structures

A bidisperse model for transient diffusion and adsorption processes in porous materials is presented in this paper.The mathematical model is solved by numerical methods based on finite elements combined with the linear driving force approximation.A criterion based on the model to identify the diffusion controlling mechanism(macropore diffusion,micropore diffusion,or both)is proposed.The effects of different adsorption isotherms(linear,Freundlich,or Langmuir)on the concentration profiles and on curves of fractional uptake versus time are investigated.In addition,the influences of model parameters concerning the pore networks on the fractional uptake are studied as well.

New Insights on Convergence Properties of Peridynamic Models for Transient Diffusion and Elastodynamics

Recent analytical solutions for peridynamic(PD)models of transient diffusion and elastodynamics allow us to revisit convergence of 1D PD models to their classical counterparts.We find and explain the reasons for some interesting differences between the convergence behavior for transient diffusion and elastodynamics models.Except for very early times,PD models for transient diffusion converge monotonically to the classical one.In contrast,for elastodynamic problems this convergence is more complex,with some periodic/almost-periodic characteristics present.These special features are investigated for sine waves used as initial conditions.The analysis indicates that the convergence behavior of PD solutions to the classical one can be understood in terms of convergence properties for models using the Fourier series expansion terms of a particular initial condition.The results obtained show new connections between PD models and their corresponding classical versions.

Localized space-tim e method of fundamental solutions for three-dimensional transient diffusion problem

A localized space-time method of fundamental solutions(LSTMFS)is extended for solving three-dimensional transient diffusion problems in this paper.The interval segmentation in temporal direction is developed for the accurate simulation of long-time-dependent diffusion problems.In the LSTMFS,the whole space-time domain with nodes arranged i divided into a series of overlapping subdomains with a simple geometry.In each subdomain,the conventional method of fundamental solutions is utilized and the coefficients associated with the considered domain can be explicitly determined.By calculating a combined sparse matrix system,the value at any node inside the space-time domain can be obtained.Numerical experi-ments demonstrate that high accuracy and efficiency can be simultaneously achieved via the LSTMFS,even for the problems defined on a long-time and quite complex computational domain.