Hermitian Green element calculations of contaminant transport

A set of new discrete element equations or coefficients is herein derived for the transient 1-D contaminant transport equation, and these coefficients are based on the Green element replication of the differential equation. The cubic Hermitian interpolation functions are incorporated into the numerical model to approximate the distribution of unknown quantities. The Green element method (GEM) is a novel computational method which uses the singular boundary integral theory to solve mathematical descriptions of engineering systems. Because of the unique feature of the contaminant transport problem in which steep concentration profiles are encountered for advection-dominant cases, incorporating linear interpolation functions in GEM to approximate these profiles may be inadequate. It is for that reason that we have in this paper incorporated Hermitian interpolation functions into GEM For the contaminant transport problem to assess by how much the accuracy of the solution is enhanced. The Hermitian GEM solutions are found to be superior to the linear GEM for two numerical examples presented.