A dynamic, adaptive, locally conservative and nonconforming solution strategy for transport phenomena in chemical engineering

A family of discontinuous Galerkin (DG) methods are formulated and applied to chemical engineering problems. They are the four primal discontinuous Galerkin schemes for the space discretization: Symmetric Interior Penalty Galerkin, Oden-Baumann-Babuska DG formulation, Nonsymmetric Interior Penalty Galerkin and Incomplete Interior Penalty Galerkin. Numerical examples of DG to solve typical chemical engineering problems, including a diffusion-convection-reaction system in a catalytic particle, a problem of heat transfer in a fixed bed and a contaminant transport problem in porous media, are presented. This paper highlights the substantial advantages of DG on adaptive mesh modification over traditional methods. In particular, we formulate and study the dynamic mesh modification strategy for DG guided by mathematically sound a posteriori error estimators.