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Compact higher order discretization of 3D generalized convection diffusion equation with variable coefficients in nonuniform grids

Author

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  • Deka, Dharmaraj
  • Sen, Shuvam

Abstract

A higher-order compact (HOC) discretization of generalized 3D convection-diffusion equation (CDE) in nonuniform grid is presented. Even in the presence of cross-derivative terms, the discretization uses only nineteen point stencil. Extension of this newly proposed discretization to semi-linear and convection-diffusion-reaction problems is seen to be straightforward and this inherent advantage is thoroughly exploited. The scheme being designed on a transformation free coordinate system is found to be efficient in capturing boundary layers and preserve the nonoscillatory property of the solution. The proposed method is tested using several benchmark linear and nonlinear problems from the literature. Additionally, problems with sharp gradients are solved. These diverse numerical examples demonstrate the accuracy and efficiency of the scheme proposed. Further, the numerical rate of convergence is seen to approach four confirming theoretical estimation.

Suggested Citation

  • Deka, Dharmaraj & Sen, Shuvam, 2022. "Compact higher order discretization of 3D generalized convection diffusion equation with variable coefficients in nonuniform grids," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    • Handle: RePEc:eee:apmaco:v:413:y:2022:i:c:s0096300321007360
    DOI: 10.1016/j.amc.2021.126652
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    References listed on IDEAS

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    1. Mohamed, N. & Mohamed, S.A. & Seddek, L.F., 2014. "Exponential higher-order compact scheme for 3D steady convection–diffusion problem," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1046-1061.
    2. Zhang, Jun & Ge, Lixin & Kouatchou, Jules, 2000. "A two colorable fourth-order compact difference scheme and parallel iterative solution of the 3D convection diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 65-80.
    3. Lin, Ji & Reutskiy, Sergiy, 2020. "A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems," Applied Mathematics and Computation, Elsevier, vol. 371(C).
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