A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 2: Two-Dimensional Problems

1981 ◽  
Vol 48 (2) ◽  
pp. 272-275 ◽  
Author(s):  
Rafael F. Diaz-Munio ◽  
L. Carter Wellford
Keyword(s):  
Finite Element ◽  
Variational Method ◽  
Perturbation Technique ◽  
Diffusion Equations ◽  
Galerkin Methods ◽  
Two Dimensional ◽  
Singular Perturbation Technique ◽  
Convection Diffusion ◽  
Solution Algorithms ◽  
Diffusion Problems

Approximation procedures for the solution of two-dimensional convection-diffusion problems are introduced. In these procedures finite-element techniques are utilized. The developed solution algorithms are based on a variational method of matched asymptotic expansions. When these techniques are used in conjunction with standard Galerkin methods, to solve convection-diffusion equations, highly accurate solutions are obtained. Numerical results for certain two-dimensional problems are presented to establish the accuracy of the proposed procedures.

A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 1: The One-Dimensional Case

1981 ◽  
Vol 48 (2) ◽  
pp. 265-271 ◽  
Author(s):  
Rafael F. Diaz-Munio ◽  
L. Carter Wellford
Keyword(s):  
Finite Element ◽  
Singular Perturbation ◽  
Perturbation Technique ◽  
Diffusion Equations ◽  
Shape Functions ◽  
Singular Perturbation Technique ◽  
One Dimensional ◽  
Convection Diffusion ◽  
The One ◽  
Standard Galerkin Method

Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

scholarly journals Analytical and approximate solution of two-dimensional convection-diffusion problems

2020 ◽  
Vol 10 (1) ◽  
pp. 73-77 ◽  
Author(s):  
Hatıra Günerhan
Keyword(s):  
Approximate Solution ◽  
Research Work ◽  
Convergent Series ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Transform Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Differential Transform ◽  
Diffusion Problems

In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work.

A Compact Higher-Order Scheme for Two-Dimensional Unsteady Convection–Diffusion Equations

2019 ◽  
Vol 17 (07) ◽  
pp. 1950025
Author(s):  
Yon-Chol Kim
Keyword(s):  
Stability Analysis ◽  
Numerical Study ◽  
Higher Order ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Order Scheme ◽  
Higher Order Scheme ◽  
Convection Dominated ◽  
Diffusion Problems

In this paper, we study a compact higher-order scheme for the two-dimensional unsteady convection–diffusion problems using the nearly analytic discrete method (NADM), especially, focusing on the convection dominated-diffusion problems. The numerical scheme is constructed and the stability analysis is implemented. We find the order of accuracy of scheme is [Formula: see text], where [Formula: see text] is the size of time steps and [Formula: see text] the size of spacial steps, especially, making clear the relation between [Formula: see text] and [Formula: see text] is according to the different values of diffusion parameter [Formula: see text] through von Neumann stability analysis. The obtained numerical results for several benchmark problems show that our method makes progress in the numerical study of NADM for convection–diffusion equation and is to be effective and helpful particularly in computations for the convection dominated-diffusion equations and, furthermore, valuable in the numerical treatment of many real-world problems such as MHD natural convection flow.

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