Analysis of a Fourth‐Order Scheme for a Three‐Dimensional Convection‐Diffusion Model Problem

2006 ◽  
Vol 28 (6) ◽  
pp. 2075-2094 ◽  
Author(s):  
Ashvin Gopaul ◽  
Muddun Bhuruth
Keyword(s):  
Diffusion Model ◽  
Fourth Order ◽  
Model Problem ◽  
Three Dimensional ◽  
Convection Diffusion ◽  
Order Scheme

scholarly journals Convection-Diffusion Model for Radon Migration in a Three-Dimensional Confined Space in Turbulent Conditions

2020 ◽  
Vol 16 (3) ◽  
pp. 651-663
Author(s):  
Shengyang Feng ◽  
Dongbo Xiong ◽  
Guojie Chen ◽  
Yu Cui ◽  
Puxin Chen
Keyword(s):  
Diffusion Model ◽  
Three Dimensional ◽  
Confined Space ◽  
Convection Diffusion

Analysis of a Semi-Circulant Preconditioner for a High-Order Compact Approximation of a Convection-Diffusion Model Problem

2009 ◽  
Author(s):  
R. Boojhawon ◽  
Y. D. Tangman ◽  
M. Bhuruth ◽  
M. S. Sunhaloo ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Diffusion Model ◽  
Model Problem ◽  
High Order ◽  
Convection Diffusion ◽  
Circulant Preconditioner ◽  
Compact Approximation

A Blended Compact Difference (BCD) Method for Solving 3D Convection–Diffusion Problems with Variable Coefficients

2019 ◽  
Vol 17 (06) ◽  
pp. 1950022 ◽  
Author(s):  
Tingfu Ma ◽  
Yongbin Ge
Keyword(s):  
Fourth Order ◽  
Numerical Solutions ◽  
Sixth Order ◽  
Test Problems ◽  
Convection Diffusion ◽  
Compact Difference ◽  
Second Derivatives ◽  
Order Scheme ◽  
Linear And Nonlinear ◽  
Grid Points

In this study, we present a fourth-order and a sixth-order blended compact difference (BCD) schemes for approximating the three-dimensional (3D) convection–diffusion equation with variable convective coefficients. The proposed schemes, where transport variable, its first and second derivatives are carried as the unknowns, combine virtues of compact discretization, fourth-order Padé scheme and sixth-order combined compact difference (CCD) scheme for spatial derivatives and can efficiently capture numerical solutions of linear and nonlinear convection–diffusion equations with Dirichlet boundary conditions. The fourth-order scheme requires only 7 grid points and the sixth-order scheme requires 19 grid points. The distinguishing feature of the present method is that methodologies of explicit compact difference and implicit compact difference are blended together. The truncation errors of the two difference schemes are analyzed for the interior grid points, respectively. Simultaneously, a sixth-order accuracy scheme is proposed to compute the first and second derivatives of the grid points on boundaries. Finally, the presented methods are applied to several test problems from the literature including linear and nonlinear problems. It is found that the presented schemes exhibit good performance.

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