High accuracy compact difference and multigrid methods for two-dimensional time-dependent nonlinear advection-diffusion-reaction problems

We focus on high-accuracy and stable numerical methods for the time-dependent nonlinear advection-diffusion-reaction problems in this work. A novel fourth-order fully implicit compact difference scheme is derived, in which we make use of the fourth-order compact formulas to discretize the diffusion...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 100; no. 7; pp. 1552 - 1579
Main Authors: Zhang, Lin, Ge, Yongbin, Yang, Xiaojia, Zhang, Yagang
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.07.2023
Taylor & Francis Ltd
Subjects:
Accuracy
Advection
Advection-diffusion-reaction
Algorithms
Backward differencing
backward differencing formula
Energy methods
finite difference method
multigrid
Multigrid methods
nonlinear
Numerical methods
Stability analysis
Time dependence
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:We focus on high-accuracy and stable numerical methods for the time-dependent nonlinear advection-diffusion-reaction problems in this work. A novel fourth-order fully implicit compact difference scheme is derived, in which we make use of the fourth-order compact formulas to discretize the diffusion terms, the fourth-order Padé formulas to compute the nonlinear advection terms, and the fourth-order backward differencing formula to approximate the time derivative term. Convergence and stability of the new scheme are analysed by the energy method. On the basis of the novel scheme, a multigrid algorithm is established such that a time advancement algorithm for solving these nonlinear problems are obtained. We provide various numerical experiments to verify the performances of the proposed scheme including the reliability, stability and computational efficiency. And the results obtained by our method show it is more accurate than most same kind schemes reported in the literature.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160.2023.2205962