 A computational study of three numerical methods for some advection-diffusion problemsA.R. Appadu, J.K. Djoko and H.H. Gidey Applied Mathematics and Computation, 2016, vol. 272, issue P3, 629-647 Abstract: 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 L2 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. Keywords: Dispersion; Dissipation; Total variation; Oscillations; Advection-diffusion; Optimization (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:272:y:2016:i:p3:p:629-647 DOI: 10.1016/j.amc.2015.03.101 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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