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

A boundary element method (BEM) for transient heat di usion 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 in nite ux function in order to properly capture the singular response of the ux. It is shown that the conventional nite ux BEM formulation, as well as a commercial FEM code, results in a large rst-time-step numerical error that cannot be reduced by mesh or time-step re nement. The use of the singular ux formulation for BEM demonstrates an extremely high level of accuracy for the one-dimensional case, and a signi cant 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 ux boundary are discussed