Analytical Evaluation Of Weakly Singular
Boundary Integrals For Advection-diffusion
Equation
Author(s)
Krishna M. Singh & Masataka Tanaka
Abstract
This paper addresses the analytical evaluation of weakly singular integrals arising
in the boundary element analysis of advection-diffusion equation. The kernel of
these integrals is in terms of the modified Bessel function Ko(t) which exhibits
logarithmic singularity. These integrals can be expressed in terms of the elemen-
tary integrals of the type g(n, p, a) = f£ t" exp [— pt] Ko(t) dt for straight-line
boundary elements. Closed form analytical expressions have been obtained for
these elementary integrals in terms of Bessel functions using standard recurrence
relations for the integrals of the Bessel functions, except for g(0, /?, a), p e (0, 1).
For the evaluation of g(0, p, a), p G (0, 1), approximate analytical expr
Keywords
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