High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations

In this paper, a type of high-order compact (HOC) finite difference method is developed for solving two- and three-dimensional unsteady convection diffusion reaction (CDR) equations with variable coefficients. Firstly, an HOC difference scheme is derived to solve the two-dimensional (2D) unsteady CD...

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Bibliographic Details
Published in:Axioms 2022-03, Vol.11 (3), p.111
Main Authors: Wei, Jianying, Ge, Yongbin, Wang, Yan
Format: Article
Language:English
Subjects:
Accuracy
Burgers equation
Convection
convection diffusion reaction equation
Discretization
Error correction
Finite difference method
high-order compact difference method
Methods
Numerical analysis
Series expansion
Stability analysis
Taylor series
Truncation errors
two- and three-dimensional equations
unconditionally stable numerical method
variable coefficients
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Summary:In this paper, a type of high-order compact (HOC) finite difference method is developed for solving two- and three-dimensional unsteady convection diffusion reaction (CDR) equations with variable coefficients. Firstly, an HOC difference scheme is derived to solve the two-dimensional (2D) unsteady CDR equation. Discretization in time is carried out by Taylor series expansion and correction of the truncation error remainder, while discretization in space is based on the fourth-order compact difference formulas. The scheme is second-order accuracy in time and fourth-order accuracy in space. The unconditional stability is obtained by the von Neumann analysis method. Then, this scheme is extended to solve the three-dimensional (3D) unsteady CDR equation. It needs only a five-point stencil for 2D problems and a seven-point stencil for 3D problems. Moreover, the present schemes can solve the nonlinear Burgers equation. Finally, numerical experiments are conducted to show the good performances of the new schemes.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11030111