Author(s): A. J. Davies & D. Crann
The most common diffusion problems involve the description of the diffusive term
in terms of the Laplacian operator.
Such problems have been solved successfully
in a boundary element context using the Laplace transform in time together with
a dual reciprocity approach.
Some diffusion problems, e.g.
heat transfer in certain
oceanographic models and slow flow in oil films, have the diffusive term described
by the biharmonic operator.
Such problems can be written, on the introduction of
a secondary dependent variable, as a pair of coupled equations, one of Poissontype
and the other of diffusion-type.
The Laplace transform together with the dual
reciprocity method can be used to solve the resulting pair of coupled equations.
Laplace transform, boundary elements, dual reciprocity, biharmonic diffusion.
Diffusion problems in which the diffusive operator is Laplacian are welldocumented
For such problems the most common numerical approach to the
solution is to use a finite difference time-stepping process.
The Laplace transform
in time provides an alternative approach.
In both cases the parabolic problem is
reduced to an elliptic problem in the space variables and any suitable solver may
Rizzo and Shippy  first used the Laplace transform in conjunction with the
boundary integral equation method using an inversion process in terms of a prony
series of negative exponentials in time.
Stehfest’s method [3, 4], which is much
simpler to apply, was used by Moridis and Reddell .
The solution is developed
directly at one specific time value without the necessity of intermediate values.
Size: 415 kb
Paper DOI: 10.2495/BEM060251
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