Reaction-Diffusion in a Two-Dimensional Catalyst Pellet
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Consider the reaction-diffusion in a two-dimensional catalyst pellet with governing equations and boundary condition:
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Contributed by: Housam Binousand Brian G. Higgins (May 2013)
Open content licensed under CC BY-NC-SA
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Details
In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind,
.
The Chebyshev derivative matrix at the quadrature points is an
matrix
given by
,
,
for
, and
for
,
, and
,
where for
and
.
The discrete Laplacian is given by where
is the
identity matrix,
is the Kronecker product operator,
, and
is
without the first row and first column.
References
[1] P. Moin, Fundamentals of Engineering Numerical Analysis, Cambridge, UK: Cambridge University Press, 2001.
[2] L. N. Trefethen, Spectral Methods in MATLAB, Philadelphia: SIAM, 2000.
[3] T. R. Marchant and M. I. Nelson,"Semi-analytical Solutions for One- and Two-Dimensional Pellet Problems," Proceedings of the Royal Society A, 460(2048), 2004 pp. 2381–2394. doi:10.1098/rspa.2004.1286.
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