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A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems

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  • Lin, Ji
  • Reutskiy, Sergiy

Abstract

In this work, a new cubic B-spline-based semi-analytical algorithm is presented for solving 3D anisotropic convection-diffusion-reaction (CDR) problems in the inhomogeneous medium. The mathematical model is expressed by the quasi-linear second-order elliptic partial differential equations (EPDE) with mixed derivatives and variable coefficients. The final approximation is obtained as a sum of the rough primary solution and the modified spline interpolants with free parameters. The primary solution mathematically satisfies boundary conditions. Thus, the free parameters of interpolants are chosen to satisfy the governing equation in the solution domain. The numerical examples demonstrate the high accuracy of the proposed method in solving 3D CDR problems in single- and multi-connected domains.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309361
    DOI: 10.1016/j.amc.2019.124944
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    References listed on IDEAS

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    1. Korkmaz, Alper & Dağ, Idris, 2016. "Quartic and quintic B-spline methods for advection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 208-219.
    2. Sharifi, Shokofeh & Rashidinia, Jalil, 2016. "Numerical solution of hyperbolic telegraph equation by cubic B-spline collocation method," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 28-38.
    3. Lin, Ji & Reutskiy, S.Y. & Lu, Jun, 2018. "A novel meshless method for fully nonlinear advection–diffusion-reaction problems to model transfer in anisotropic media," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 459-476.
    4. Dhawan, S. & Bhowmik, Samir Kumar & Kumar, Sheo, 2015. "Galerkin-least square B-spline approach toward advection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 128-140.
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    Citations

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    Cited by:

    1. Lin, Ji & Zhang, Yuhui & Reutskiy, Sergiy & Feng, Wenjie, 2021. "A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems," Applied Mathematics and Computation, Elsevier, vol. 398(C).
    2. Heng Cheng & Zebin Xing & Yan Liu, 2023. "The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
    3. 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).
    4. Fengxin Sun & Jufeng Wang & Xiang Kong & Rongjun Cheng, 2021. "A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems," Mathematics, MDPI, vol. 9(19), pages 1-15, October.
    5. Farzaneh Safari & Qingshan Tong & Zhen Tang & Jun Lu, 2022. "A Meshfree Approach for Solving Fractional Galilei Invariant Advection–Diffusion Equation through Weighted–Shifted Grünwald Operator," Mathematics, MDPI, vol. 10(21), pages 1-18, October.

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