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 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.

Exponential Compact Higher Order Scheme for Nonlinear Steady Convection-Diffusion Equations

2011 ◽  
Vol 9 (4) ◽  
pp. 897-916 ◽  
Author(s):  
Y. V. S. S. Sanyasiraju ◽  
Nachiketa Mishra
Keyword(s):  
Coefficient Matrix ◽  
Higher Order ◽  
Diffusion Equations ◽  
Wave Number ◽  
Two Dimensional ◽  
Thomas Algorithm ◽  
Convection Diffusion ◽  
Numerous Model ◽  
Order Scheme ◽  
Higher Order Scheme

AbstractThis paper presents an exponential compact higher order scheme for Convection-Diffusion Equations (CDE) with variable and nonlinear convection coefficients. The scheme is for one-dimensional problems and produces a tri-diagonal system of equations which can be solved efficiently using Thomas algorithm. For two-dimensional problems, the scheme produces an accuracy over a compact nine point stencil which can be solved using any line iterative approach with alternate direction implicit procedure. The convergence of the iterative procedure is guaranteed as the coefficient matrix of the developed scheme satisfies the conditions required to be positive. Wave number analysis has been carried out to establish that the scheme is comparable in accuracy with spectral methods. The higher order accuracy and better rate of convergence of the developed scheme have been demonstrated by solving numerous model problems for one and two-dimensional CDE, where the solutions have the sharp gradient at the solution boundary.

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.

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

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1735
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Diffusion Equation ◽  
Radial Basis Function ◽  
Time Domain ◽  
Basis Function ◽  
Numerical Solutions ◽  
Space Time ◽  
Diffusion Equations ◽  
Numerical Examples ◽  
Convection Diffusion ◽  
Convection Diffusion Equation

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.

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.

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