Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation

This work is a major extension of our previous work in which we have solved a 2D nonconstant coefficient advection diffusion equation with nonconstant advection and constant diffusion terms on a square domain using the coefficient of dissipation D1=D2=0.0004{D}_{1}={D}_{2}=0.0004 using three finite...

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Main Authors: Appadu Appanah Rao, Gidey Hagos Hailu
Format: Article
Language:English
Published: De Gruyter 2025-04-01
Series:Open Physics
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Online Access:https://doi.org/10.1515/phys-2025-0137
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author Appadu Appanah Rao
Gidey Hagos Hailu
author_facet Appadu Appanah Rao
Gidey Hagos Hailu
author_sort Appadu Appanah Rao
collection DOAJ
description This work is a major extension of our previous work in which we have solved a 2D nonconstant coefficient advection diffusion equation with nonconstant advection and constant diffusion terms on a square domain using the coefficient of dissipation D1=D2=0.0004{D}_{1}={D}_{2}=0.0004 using three finite difference methods, namely, Lax–Wendroff, Du Fort–Frankel and nonstandard finite difference methods. In this current work, the first novelty is that we solve a 2D nonconstant advection diffusion equation on an irregular domain with a more complicated initial profile and considered five combinations for values of D1{D}_{1} and D2{D}_{2}. Moreover, the second novelty is the study of numerical dispersion and dissipation of Lax Wendroff scheme for the five combinations of D1{D}_{1} and D2{D}_{2}. Third, we present some numerical profiles from the three methods for the five scenario at two times: T=0.1T=0.1, 1. The fourth novelty is the plot of the modulus of the exact amplification factor, modulus of amplification factor, and relative phase error vs phase angle along xx direction vs phase angle along yy direction for the Lax–Wendroff scheme at x=y=0.5x=y=0.5 for the five scenarios.
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spelling doaj-art-07a9a1752b9d47b2bbe5febbc7395ce42025-08-20T03:11:07ZengDe GruyterOpen Physics2391-54712025-04-01231243110.1515/phys-2025-0137Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipationAppadu Appanah Rao0Gidey Hagos Hailu1Department of Mathematics, Nelson Mandela University, University Way, Summerstrand, Gqeberha, 6031, South AfricaDepartment of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana; Department of Mathematics, Aksum University, Axum, EthiopiaThis work is a major extension of our previous work in which we have solved a 2D nonconstant coefficient advection diffusion equation with nonconstant advection and constant diffusion terms on a square domain using the coefficient of dissipation D1=D2=0.0004{D}_{1}={D}_{2}=0.0004 using three finite difference methods, namely, Lax–Wendroff, Du Fort–Frankel and nonstandard finite difference methods. In this current work, the first novelty is that we solve a 2D nonconstant advection diffusion equation on an irregular domain with a more complicated initial profile and considered five combinations for values of D1{D}_{1} and D2{D}_{2}. Moreover, the second novelty is the study of numerical dispersion and dissipation of Lax Wendroff scheme for the five combinations of D1{D}_{1} and D2{D}_{2}. Third, we present some numerical profiles from the three methods for the five scenario at two times: T=0.1T=0.1, 1. The fourth novelty is the plot of the modulus of the exact amplification factor, modulus of amplification factor, and relative phase error vs phase angle along xx direction vs phase angle along yy direction for the Lax–Wendroff scheme at x=y=0.5x=y=0.5 for the five scenarios.https://doi.org/10.1515/phys-2025-0137advection diffusionlax–wendroffdu fort–frankelnonstandard finite differencenonconstant coefficientstabilityirregular domain
spellingShingle Appadu Appanah Rao
Gidey Hagos Hailu
Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
Open Physics
advection diffusion
lax–wendroff
du fort–frankel
nonstandard finite difference
nonconstant coefficient
stability
irregular domain
title Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
title_full Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
title_fullStr Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
title_full_unstemmed Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
title_short Numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
title_sort numerical solution of a nonconstant coefficient advection diffusion equation in an irregular domain and analyses of numerical dispersion and dissipation
topic advection diffusion
lax–wendroff
du fort–frankel
nonstandard finite difference
nonconstant coefficient
stability
irregular domain
url https://doi.org/10.1515/phys-2025-0137
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AT gideyhagoshailu numericalsolutionofanonconstantcoefficientadvectiondiffusionequationinanirregulardomainandanalysesofnumericaldispersionanddissipation