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.

EXPONENTIAL COMPACT HIGHER-ORDER SCHEMES AND THEIR STABILITY ANALYSIS FOR UNSTEADY CONVECTION-DIFFUSION EQUATIONS

2013 ◽  
Vol 11 (01) ◽  
pp. 1350053 ◽  
Author(s):  
NACHIKETA MISHRA ◽  
Y. V. S. S. SANYASIRAJU
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Higher Order ◽  
The Other ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Unconditionally Stable ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Alternate Direction

Exponential compact higher-order schemes have been developed for unsteady convection-diffusion equation (CDE). One of the developed scheme is sixth-order accurate which is conditionally stable for the Péclet number 0 ≤ Pe ≤ 2.8 and the other is fourth-order accurate which is unconditionally stable. Schemes for two-dimensional (2D) problems are made to use alternate direction implicit (ADI) algorithm. Example problems are solved and the numerical solutions are compared with the analytical solutions for each case.

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.

scholarly journals "Approximate solution for the two-dimensional Volterra-Integro differential equation of fractional order by using Generalized Deferential Transform method "

2018 ◽  
Vol 5 (2) ◽  
pp. 1-9
Author(s):  
Mohammed G. S. AL-Safi ◽  
Wurood R. Abd AL- Hussein
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Fractional Order ◽  
Two Dimensional ◽  
Transform Method ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Differential Transform ◽  
Generalized Differential

"In this work, an efficient generalized differential transform method (GDTM) is proposed for solving the twodimensional Volterra-Integro differential equation (2-DVIDE) of fractional order. The results of the proposed method are compared with exact solution, a numerical example is considered for testing the accuracy and validity of this method."

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.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

scholarly journals Two-dimensional numerical modeling of chemical transport–transformation in fluvial rivers: formulation of equations and physical interpretation

2009 ◽  
Vol 11 (2) ◽  
pp. 106-118 ◽  
Author(s):  
Sui Liang Huang
Keyword(s):  
Sediment Transport ◽  
Chemical Transport ◽  
Transformation Model ◽  
Diffusion Equations ◽  
Desorption Kinetics ◽  
Two Dimensional ◽  
Transformation Equation ◽  
Governing Equations ◽  
Convection Diffusion ◽  
Kinetics Of

Based on previous work on the transport–transformation model of heavy metal pollutants in fluvial rivers, this paper presents the formulation of a two-dimensional model to describe chemical transport–transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics and mechanics of sediment transport and recent developments along with three very simplified test cases. The model consists of water flow governing equations, sediment transport governing equations, transport–transformation equation of chemicals and convection–diffusion equations of sorption–desorption kinetics of particulate chemical concentrations on suspended load, bed load and bed sediment. The chemical transport–transformation equation is basically a mass balance equation. It demonstrates how sediment transport affects transport–transformation of chemicals in fluvial rivers. The convection–diffusion equations of sorption–desorption kinetics of chemicals, being an extension of batch reactor experimental results, take both physical transport, i.e. convection and diffusion, and chemical reactions, i.e. sorption–desorption into account. The effects of sediment transport on chemical transport–transformation were clarified through three simple examples. Specifically, the transport–transformation of chemicals in a steady, uniform and equilibrium sediment-laden flow was calculated by applying this model, and results were shown to be rational. Both theoretical analysis and numerical simulation indicated that the transport–transformation of chemicals in sediment-laden flows with a clay-enriched riverbed possesses not only the generality of common tracer pollutants, but also characteristics of transport–transformation induced by sediment motion. Future work will be conducted to present the validation/application of the model with available data.

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