A Laplace transform boundary element solution for the biharmonic diffusion equation

摘要

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 Poisson-type 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.