An unconditionally stable algorithm for multiterm time fractional advection–diffusion equation with variable coefficients and convergence analysis

2020 ◽  
Author(s):  
Adivi Sri Venkata Ravi Kanth ◽  
Neetu Garg
Keyword(s):  
Diffusion Equation ◽  
Convergence Analysis ◽  
Variable Coefficients ◽  
Unconditionally Stable ◽  
Stable Algorithm ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients

2018 ◽  
Vol 19 (7-8) ◽  
pp. 793-802 ◽  
Author(s):  
M. Hosseininia ◽  
M. H. Heydari ◽  
Z. Avazzadeh ◽  
F. M. Maalek Ghaini
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Main Idea ◽  
Variable Coefficients ◽  
Variable Order ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Nonlinear Advection

AbstractThis article studies a numerical scheme for solving two-dimensional variable-order time fractional nonlinear advection-diffusion equation with variable coefficients, where the variable-order fractional derivative is in the Caputo type. The main idea is expanding the solution in terms of the 2D Legendre wavelets (2D LWs) where the variable-order time fractional derivative is discretized. We describe the method using the matrix operators and then implement it for solving various types of fractional advection-diffusion equations. The experimental results show the computational efficiency of the new approach.

scholarly journals FINITE DIFFERENCE SOLUTION OF TWO-DIMENSIONAL SOLUTE TRANSPORT WITH PERIODIC FLOW IN HOMOGENOUS POROUS MEDIA

2017 ◽  
Vol 8 (2) ◽  
Author(s):  
Alexandar Djordjevich ◽  
Svetislav Savović ◽  
Aco Janićijević
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Variable Coefficients ◽  
Two Dimensional ◽  
Seepage Velocity ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

Two-dimensional advection-diffusion equation with variable coefficients is solved by the explicit finite-difference method for the transport of solutes through a homogeneous, finite, porous, two-dimensional, domain. Retardation by adsorption, periodic seepage velocity, and a dispersion coefficient proportional to this velocity are permitted. The transport is from a pulse-type point source (that ceases after a period of activity). Included are the first-order decay and zero-order production parameters proportional to the seepage velocity, periodic boundary conditions at the origin and the end of the domain. Results are compared to analytical solutions reported in the literature for special cases and a good agreement was found. The solute concentration profile is greatly influenced by the periodic velocity fluctuations. Solutions for a variety of combinations of unsteadiness of the coefficients in the advection-diffusion equation are obtainable as particular cases of the one demonstrated here. This further attests to the effectiveness of the explicit finite difference method for solving two-dimensional advection-diffusion equation with variable coefficients in a finite media, which is especially important when arbitrary initial and boundary conditions are required.

ANÁLISE DE CONVERGÊNCIA DO MÉTODO GILTT PARA PROBLEMAS EM DISPERSÃO DE POLUENTES NA ATMOSFERA

2016 ◽  
Vol 38 ◽  
pp. 182 ◽  
Author(s):  
Daniela Buske ◽  
Cláudio Zen Petersen ◽  
Régis Sperotto de Quadros ◽  
Glênio Aguiar Gonçalves ◽  
Juliana Ávila Contreira
Keyword(s):  
Diffusion Equation ◽  
Convergence Analysis ◽  
Existence And Uniqueness ◽  
Analytic Solution ◽  
Pollutant Dispersion ◽  
Analytical Representation ◽  
Multidimensional Case ◽  
The Past ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

In this paper, we present a convergence analysis of the GILTT method for pollutant dispersion problems consolidating the solution of the problem in analytical representation. There have been many advances in the GILTT technique over the past few years. The advection-diffusion equation was solved for the multidimensional case and applied to various situations, mainly in pollutant dispersion. The theorem of Cauchy-Kowalewsky guarantees the existence and uniqueness of an analytic solution for the advection-diffusion equation. In this paper, we present a convergence analysis for the GILTT method to pollutant dispersion problems. Numerical results are presented.

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