TY - JOUR

T1 - A computational study of three numerical methods for some advection-diffusion problems

AU - Appadu, A.R.

AU - Djoko, J.K.

AU - Gidey, H.H.

PY - 2016/1

Y1 - 2016/1

N2 - © 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.

AB - © 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.

UR - https://www.mendeley.com/catalogue/fc331ad8-0517-3086-8ade-a1e4dab5fed4/

U2 - 10.1016/j.amc.2015.03.101

DO - 10.1016/j.amc.2015.03.101

M3 - Article

SN - 0096-3003

VL - 272

SP - 629

EP - 647

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -