Journal
SYMMETRY-BASEL
Volume 14, Issue 12, Pages -Publisher
MDPI
DOI: 10.3390/sym14122616
Keywords
finite difference schemes; amplification factor; stability; relative phase error; optimization
Categories
Funding
- Nelson Mandela University Council
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In this study, three finite difference schemes were used to solve 1D and 2D convective diffusion equations. Through four numerical experiments and dispersion analysis, it was found that the Lax-Wendroff scheme was the most efficient in all cases, and the optimal value of k could minimize the errors.
In this work, we used three finite difference schemes to solve 1D and 2D convective diffusion equations. The three methods are the Kowalic-Murty scheme, Lax-Wendroff scheme, and nonstandard finite difference (NSFD) scheme. We considered a total of four numerical experiments; in all of these cases, the initial conditions consisted of symmetrical profiles. We looked at cases when the advection velocity was much greater than the diffusion of the coefficient and cases when the coefficient of diffusion was much greater than the advection velocity. The dispersion analysis of the three methods was studied for one of the cases and the optimal value of the time step size k, minimizing the dispersion error at a given value of the spatial step size. From our findings, we conclude that Lax-Wendroff is the most efficient scheme for all four cases. We also show that the optimal value of k computed by minimizing the dispersion error at a given value of a spacial step size gave the lowest l(2) and l(infinity) errors.
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