A characteristic ADI finite difference method for spatial-fractional convection-dominated diffusion equation

2018 ◽  
Vol 74 (5) ◽  
pp. 765-787 ◽  
Author(s):  
Zhifeng Weng ◽  
Longyuan Wu ◽  
Shuying Zhai
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Convection Dominated

Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Anup Singh ◽  
S. Das ◽  
S. H. Ong ◽  
H. Jafari
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Conservative System ◽  
Computational Time ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nonlinear Reaction ◽  
Sink Term

In the present article, the advection–diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method.

Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

1988 ◽  
Vol 110 (2) ◽  
pp. 276-282 ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Solution Method ◽  
Basis Functions ◽  
Heat Diffusion ◽  
Simple Geometry ◽  
The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

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