A computational study of three numerical methods for some advection-diffusion problems

  • Appadu A
  • Djoko J
  • Gidey H
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© 2015 Elsevier Inc.Three numerical methods have been used to solve two problems described by advection-diffusion equations with specified initial and boundary conditions. The methods used are the third order upwind scheme [5], fourth order upwind scheme [5] and non-standard finite difference scheme (NSFD) [10]. We considered two test problems. The first test problem we considered has steep boundary layers near x = 1 and this is challenging problem as many schemes are plagued by non-physical oscillation near steep boundaries [16]. Many methods suffer from computational noise when modeling the second test problem. We compute some errors, namely L 2 and L ∞ errors, dissipation and dispersion errors, total variation and the total mean square error for both problems. We then use an optimization technique [1] to find the optimal value of the time step at a given value of the spatial step which minimizes the dispersion error and this is validated by numerical experiments.




Appadu, A. R., Djoko, J. K., & Gidey, H. H. (2016). A computational study of three numerical methods for some advection-diffusion problems. Applied Mathematics and Computation, 272, 629–647. https://doi.org/10.1016/j.amc.2015.03.101

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