Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian...

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Autores principales:	Wang Fuzhang, Zheng Kehong, Ahmad Imtiaz, Ahmad Hijaz
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	radial basis functions convection–diffusion problem interpolation function space–time distance nonlinear problems Physics QC1-999
Acceso en línea:	https://doaj.org/article/49a1dbbe8a214c7fb80b090129e9e338
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id	oai:doaj.org-article:49a1dbbe8a214c7fb80b090129e9e338
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spelling	oai:doaj.org-article:49a1dbbe8a214c7fb80b090129e9e3382021-12-05T14:11:01ZGaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena2391-547110.1515/phys-2021-0011https://doaj.org/article/49a1dbbe8a214c7fb80b090129e9e3382021-03-01T00:00:00Zhttps://doi.org/10.1515/phys-2021-0011https://doaj.org/toc/2391-5471In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.Wang FuzhangZheng KehongAhmad ImtiazAhmad HijazDe Gruyterarticleradial basis functionsconvection–diffusion probleminterpolation functionspace–time distancenonlinear problemsPhysicsQC1-999ENOpen Physics, Vol 19, Iss 1, Pp 69-76 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	radial basis functions convection–diffusion problem interpolation function space–time distance nonlinear problems Physics QC1-999
spellingShingle	radial basis functions convection–diffusion problem interpolation function space–time distance nonlinear problems Physics QC1-999 Wang Fuzhang Zheng Kehong Ahmad Imtiaz Ahmad Hijaz Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
description	In this study, we propose a simple direct meshless scheme based on the Gaussian radial basis function for the one-dimensional linear and nonlinear convection–diffusion problems, which frequently occur in physical phenomena. This is fulfilled by constructing a simple ‘anisotropic’ space–time Gaussian radial basis function. According to the proposed scheme, there is no need to remove time-dependent variables during the whole solution process, which leads it to a really meshless method. The suggested meshless method is implemented to the challenging convection–diffusion problems in a direct way with ease. Numerical results show that the proposed meshless method is simple, accurate, stable, easy-to-program and efficient for both linear and nonlinear convection–diffusion equation with different values of Péclet number. To assess the accuracy absolute error, average absolute error and root-mean-square error are used.
format	article
author	Wang Fuzhang Zheng Kehong Ahmad Imtiaz Ahmad Hijaz
author_facet	Wang Fuzhang Zheng Kehong Ahmad Imtiaz Ahmad Hijaz
author_sort	Wang Fuzhang
title	Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
title_short	Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
title_full	Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
title_fullStr	Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
title_full_unstemmed	Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
title_sort	gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/49a1dbbe8a214c7fb80b090129e9e338
work_keys_str_mv	AT wangfuzhang gaussianradialbasisfunctionsmethodforlinearandnonlinearconvectiondiffusionmodelsinphysicalphenomena AT zhengkehong gaussianradialbasisfunctionsmethodforlinearandnonlinearconvectiondiffusionmodelsinphysicalphenomena AT ahmadimtiaz gaussianradialbasisfunctionsmethodforlinearandnonlinearconvectiondiffusionmodelsinphysicalphenomena AT ahmadhijaz gaussianradialbasisfunctionsmethodforlinearandnonlinearconvectiondiffusionmodelsinphysicalphenomena
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Gaussian radial basis functions method for linear and nonlinear convection–diffusion models in physical phenomena

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