A transformation of variables technique applicable to the boundary element method to simulate a special class of diffusive-advective potential problems

Abstract

This paper describes a novel Boundary Element Technique developed for application to one-dimensional and a class of two-dimensional diffusive-advective potential problems. It is based on transformation of variable procedure to establish an integral equation inverse sentence, dealing only with boundary variables, using a fundamental solution associated with a diffusive problem. To apply the technique described here, the original differential equation is rewritten and flow potential functions are employed to contract terms which appear in the original equation, giving as a result an equivalent equation expressed in terms of the derivative of the product of two functions. This new form of the governing equation, together with the proposed transformation of variables is quite convenient for the application of the boundary element methodology: a very simple discretization procedure arises; the resulting algorithms require low CPU time and the numerical results are quite accurate.