Time-splitting procedures for the numerical solution of the 2D advection-diffusion equation
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Date
Authors
Appadu, A. Rao
Gidey, H.H.
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi Publishing Corporation
Abstract
We perform a spectral analysis of the dispersive and dissipative properties of two time-splitting procedures, namely, locally onedimensional
(LOD) Lax-Wendroff and LOD (1, 5) [9] for the numerical solution of the 2D advection-diffusion equation. We solve
a 2D numerical experiment described by an advection-diffusion partial differential equation with specified initial and boundary
conditions for which the exact solution is known. Some errors are computed, namely, the error rate with respect to the L1 norm,
dispersion and dissipation errors. Lastly, an optimization technique is implemented to find the optimal value of temporal step size
that minimizes the dispersion error for both schemes when the spatial step is chosen as 0.025, and this is validated by numerical
experiments.
Description
Keywords
Numerical solution, 2D Advection-diffusion equation, Time-splitting procedures
Sustainable Development Goals
Citation
Appadu, AR & Gidey, HH 2013, 'Time-splitting procedures for the numerical solution of the 2D advection-diffusion equation', Mathematical Problems in Engineering, vol. 2013, art. 634657, pp. 1-21.art