A study concerning the solution of advection–diffusion problems by the Boundary Element Method

Cunha, Cynara de Lourdes da Nóbrega; Carrer, J. A. M.; Oliveira, Marcelo Franco de; Costa, Vera Lúcia Anunciação

doi:10.1016/j.enganabound.2016.01.002

Cited by 21 publications

(7 citation statements)

References 25 publications

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“…Due to the combination of two effects, diffusive and advective the explicit method is sensitive for the choice of t  . The relationship between these two effects is named as Péclet Number (Cunha C. , Carrer, Oliveira, & Viviane, 2016).…”

Section: Fdm Formulationmentioning

confidence: 99%

A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem

Oliveira

Thoaldo²,

Dias³

2022

J. Eng. Exact Sci.

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This paper is concerned with the development of a formulation of the Finite Difference Method, in the solution of the transient diffusion-advection equation. In this approach, a weighting function with respect to time is used in the fundamental differential equation. By assuming a linear variation in some time interval, a time integration is performed. This integration reduces the order of time derivative in the basic equation and the initial conditions can be taken into account directly in consequence. Three pollutant transport problems are presented in order to verify the stability and accuracy of the proposed approach. The results for this approach are compared with the Boundary Element Methods results. The comparisons of numerical results show a good agreement between the furnished results for the proposed approach and the boundary element method results assumed here as reference results. By analyzing the results one can conclude that the formulation presented in this paper is capable of producing accurate results for the problem.

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Section: Fdm Formulationmentioning

confidence: 99%

A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem

Oliveira

Thoaldo²,

Dias³

2022

J. Eng. Exact Sci.

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“…Numerical simulation is the only possible way to solve the ADREs with the nonlinear terms or the non-constant coefficients and twoor three-dimensional domains with complicated geometry (Guo et al, 2012). In general, the ADREs have been solved via various numerical methods, such as the finite element method (FEM) (Araya et al, 2005(Araya et al, , 2007Franca and Valentin, 2000;Idelsohn et al, 1996), the discontinuous Galerkin method (Eshaghi et al, 2019), the boundary element method (Cunha et al, 2016;Singh and Tanaka, 2000), spectral method , the finite volume HFF 32,2 method (Phongthanapanich and Dechaumphai, 2010;Ramos, 2007) and the finite difference method (Anguelov et al, 2003;Clavero et al, 2005;Kojouharov and Chen, 2000;Mickens, 1994Mickens, , 2000Mukherjee and Natesan, 2009).…”

Section: Introductionmentioning

confidence: 99%

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Mesgarani

Kermani

Abbaszadeh

2021

HFF

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Purpose The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients. Design/methodology/approach The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well. Findings Several test problems are provided to confirm the validity and efficiently of the proposed method. Originality/value For the first time, some famous examples are solved by using the proposed high-order technique.

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“…The convection-diffusion equation is a combination of diffusion and convection processes that are referred to as substance diffusion and concentration change, respectively. Numerical solutions for the convection-diffusion equation have been applied extensively by using conventional mesh-based approaches, such as the finite difference method (FDM) [4][5][6], finite volume method [7], finite element method (FEM) [8], and boundary element method (BEM) [9]. The Lattice Boltzmann method, which does not involve the use of a mesh, was adopted to simulate fluid flow in an elliptical honeycomb monolith reactor [10].…”

Section: Introductionmentioning

confidence: 99%

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

Xiao

Liu

2020

Mathematics

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This article proposes a space–time meshless approach based on the transient radial polynomial series function (TRPSF) for solving convection–diffusion equations. We adopted the TRPSF as the basis function for the spatial and temporal discretization of the convection–diffusion equation. The TRPSF is constructed in the space–time domain, which is a combination of n–dimensional Euclidean space and time into an n + 1–dimensional manifold. Because the initial and boundary conditions were applied on the space–time domain boundaries, we converted the transient problem into an inverse boundary value problem. Additionally, all partial derivatives of the proposed TRPSF are a series of continuous functions, which are nonsingular and smooth. Solutions were approximated by solving the system of simultaneous equations formulated from the boundary, source, and internal collocation points. Numerical examples including stationary and nonstationary convection–diffusion problems were employed. The numerical solutions revealed that the proposed space–time meshless approach may achieve more accurate numerical solutions than those obtained by using the conventional radial basis function (RBF) with the time-marching scheme. Furthermore, the numerical examples indicated that the TRPSF is more stable and accurate than other RBFs for solving the convection–diffusion equation.

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A study concerning the solution of advection–diffusion problems by the Boundary Element Method

Cited by 21 publications

References 25 publications

A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem

A finite difference method formulation based on the time integral domain for the solution of Transient diffusion-advection problem

Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

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