scholarly journals A Leap-Frog Finite Difference Method for Strongly Coupled System from Sweat Transport in Porous Textile Media

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Qian Zhang ◽  
Chao Huang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Moisture Transfer ◽  
Coupled System ◽  
Optimal Error Estimates ◽  
Strongly Coupled ◽  
Physical Mechanisms ◽  
Uniqueness Of The Solution ◽  
Heat And Moisture

In this paper, we present an uncoupled leap-frog finite difference method for the system of equations arising from sweat transport through porous textile media. Based on physical mechanisms, the sweat transport can be viewed as the multicomponent flow that coupled the heat and moisture transfer, such that the system is nonlinear and strongly coupled. The leap-frog method is proposed to solve this system, with the second order accuracy in both spatial and temporal directions. We prove the existence and uniqueness of the solution to the system with optimal error estimates in the discrete L2 norm. Numerical simulations are presented and analyzed, respectively.

Characteristic fractional step finite difference method for nonlinear section coupled system

2014 ◽  
Vol 35 (10) ◽  
pp. 1311-1330 ◽  
Author(s):  
Yi-rang Yuan ◽  
Chang-feng Li ◽  
Tong-jun Sun ◽  
Yun-xin Liu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Coupled System ◽  
Fractional Step

scholarly journals On the Existence, Uniqueness and Application of the Finite Difference Method for Solving Robin Elliptic Boundary Value Problem

2019 ◽  
Vol 11 (1) ◽  
pp. 26
Author(s):  
Germain Nguimbi ◽  
Diogène Vianney Pongui Ngoma ◽  
Vital Delmas Mabonzo ◽  
Bienaime Bervi Bamvi Madzou ◽  
Melchior Josièrne Jupy Kokolo
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Simulations ◽  
Difference Method ◽  
Numerical Solutions ◽  
Classical Method ◽  
Elliptic Boundary ◽  
Boundary Condi Tions ◽  
Elliptic Boundary Value ◽  
Uniqueness Of The Solution

This paper refers to mathematical modelling and numerical analysis. The analysis to be presented through this paper deals with Robin’s problem which boundary equation is a linear combination of Dirichlet and Neumann-type boundary condi-tions. For this purpose we proved the existence and uniqueness of the solution. It is worth noting that the implementation of numerical simulations depends on the type of problem since it requires a search for explicit solution. Consequently, the motivation exists in this paper for choosing a classical method of variation of constants and employing a finite difference method to find the exact and numerical solutions, respectively so that numerical simulations were implemented in Scilab.

scholarly journals Mathematical modeling of the unsteady moisture condition of enclosures with application of the discrete-continuous approach

Vestnik MGSU ◽  
2020 ◽  
pp. 244-256
Author(s):  
Vladimir G. Gagarin ◽  
Kirill P. Zubarev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Moisture Transfer ◽  
Heat Insulation ◽  
Moisture Distribution ◽  
Analytical Expression ◽  
Continuous Approach ◽  
The Finite Difference Method ◽  
Moisture Potential

Introduction. The paper considers mathematical models developed by K.F. Fokin, A.V. Lykov, V.I. Lukyanov, V.N. Bogoslovskiy, and H.M. Künzel and shows the advantages of using the moisture potential as compared with separate consideration of the transfer potentials. An analytical expression for the moisture potential F developed by V.G. Gagarin and V.V. Kozlov is given. Materials and methods. The article formulated a differential moisture transfer equation with time-constant coefficients and and described boundary conditions. An analytical expression determining the moisture potential using the discrete-continuous approach was obtained. Results. The article compares some calculation methods on the theory of moisture potential F for the single-layer aerated concrete enclosure, the two-layer brick wall, as well as two composite facade heat-insulation systems with external plaster layers with heat-insulation of mineral wool and foamed polystyrene. The solution of the unsteady equation of moisture transfer by the finite difference method using an explicit difference scheme and by the discrete-continuous method, the solution of the stationary equation of moisture transfer are considered. Conclusions. The moisture distribution obtained using the discrete-continuous approach, both quantitatively and qualitatively, coincides with the moisture distribution by the finite difference method. However, this distribution is obtained by the final formula without using the numerical method, which simplifies the calculation. The scientific novelty of the research consists in the development of a mathematical model based on the moisture potential F as well as in solving the equation of the unsteady moisture transfer through the discrete-continuous approach. The possibility of obtaining moisture distribution over the thickness of the enclosure according to the obtained formula is the practical relevance of the research.

Optimal Error Estimates of Compact Finite Difference Discretizations for the Schrödinger-Poisson System

2013 ◽  
Vol 13 (5) ◽  
pp. 1357-1388 ◽  
Author(s):  
Yong Zhang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Error Estimates ◽  
Difference Method ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method

AbstractWe study compact finite difference methods for the Schrodinger-Poisson equation in a bounded domain and establish their optimal error estimates under proper regularity assumptions on wave function and external potential V(x). The Crank-Nicolson compact finite difference method and the semi-implicit compact finite difference method are both of order Ҩ(h4 + τ2) in discrete l2,H1 and l∞ norms with mesh size h and time step t. For the errors ofcompact finite difference approximation to the second derivative andPoisson potential are nonlocal, thus besides the standard energy method and mathematical induction method, the key technique in analysisis to estimate the nonlocal approximation errors in discrete l∞ and H1 norm by discrete maximum principle of elliptic equation and properties of some related matrix. Also some useful inequalities are established in this paper. Finally, extensive numerical re-sults are reported to support our error estimates of the numerical methods.

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