Higher-order boundary element methods for transient diffusion problems. Part II: Singular flux formulation

A boundary element method (BEM) for transient heat diffusion phenomena presented in Part I is extended to problems involving instantaneous rise of temperature on a portion of the boundary. The new boundary element formulation involves the use of an infinite flux function in order to properly capture the singular response of the flux. It is shown that the conventional finite flux BEM formulation, as well as a commercial FEM code, results in a large first-time-step numerical error that cannot be reduced by mesh or time-step refinement. The use of the singular flux formulation for BEM demonstrates an extremely high level of accuracy for the one-dimensional case, and a significant improvement in the solutions within a two-dimensional representation. The additional errors arising due to improper time interpolation of the temperature on the boundaries adjacent to the singular flux boundary are discussed.