A NEW APPROACH FOR THE TREATMENT OF DIFFUSIVE TERMS OF THE CONVECTIVE-DIFFUSIVE TRANSPORT EQUATION IN THE DISCONTINUOUS GALERKIN METHOD

The models that are being used to solve convection-diffusion problems in engineering are normally based on Fick's law. In some applications the use of linear Fick's law is accurate enough in spite of predicting all infinite speed of propagation. However, there are many other applications where a model that predicts a finite speed of propagation is mandatory(1). A number of models have been proposed so far to eliminate the infinite speed paradox. The linear model that has been most commonly accepted by scientist and engineers is the one proposed initially by Cattaneo in 1948(2.3), Cattaneo's law was originally proposed for pure-diffusive problems. However, in the context of most engineering applications it is important to consider both, diffusion and convection, phenomena, since neither of these transport processes call be ignored. For this reason; the authors have recently proposed a generalization of Cattaneo's law that call be used ill connective-diffusive problems. This constitutive equation, together with the mass conservation equation; leads to a hyperbolic model for convection-diffusion''. On the other hand, ill the framework of the discontinuous Galerkin methods, the discretization of the diffusive terms is by no means trivial and the rise of hybrid methods is standard. However, the discontinuos Galerkin method is more appropriate for the discretization of the hyperbolic model. For this reason, we present herein a discontinuous Galerkin scheme for the hyperbolic convection-diffusion model. The numerical results are compared with those of the parabolic model solved by discontinuous Galerkin methods for parabolic problems.