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Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions

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  • Kim, Philsu
  • Kim, Dojin

Abstract

In this paper, we present a concrete analysis of the convergence and stability of a backward semi-Lagrangian method for a non-linear advection-diffusion equation with the Dirichlet boundary conditions. The total time derivative and the diffusion term are discretized by BDF2 and the second-order central finite difference, respectively, together with the local Lagrangian interpolation. The Cauchy problem for characteristic curves is resolved by an error correction method based on a quadratic polygon. Under the mesh restriction ▵t=O(▵x1/2) between the temporal step size △t and the spatial grid size △x, it turns out that the proposed method has the convergence order O(▵t2+▵x2+▵xp+1/▵t) in the sense of the discrete H1-norm, where p is the degree of an interpolation polynomial. Further, the unconditional stability of the method is established. Numerical tests are presented to support the theoretical analyses.

Suggested Citation

  • Kim, Philsu & Kim, Dojin, 2020. "Convergence and stability of a BSLM for advection-diffusion models with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    • Handle: RePEc:eee:apmaco:v:366:y:2020:i:c:s0096300319307362
    DOI: 10.1016/j.amc.2019.124744
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    References listed on IDEAS

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    1. Zhang, Jianying & Yan, Guangwu, 2008. "Lattice Boltzmann method for one and two-dimensional Burgers equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4771-4786.
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    Cited by:

    1. Park, Sangbeom & Kim, Philsu & Jeon, Yonghyeon & Bak, Soyoon, 2022. "An economical robust algorithm for solving 1D coupled Burgers’ equations in a semi-Lagrangian framework," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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