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

Transport phenomena play a dominant role in chemical engineering processes, e.g., distillation process in a packed column. A family of discontinuous Galerkin (DG) methods are formulated and applied to chemical engineering problems. They are the four primal DG 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. Numerical results show the capability of DG to solve a set of rather diverse time-dependent problems in chemical engineering. For mass transfer simulation, DG treats both the convection-dominated and the diffusion-dominated systems very well. For heat transfer simulation, DG is effective for both the convection-dominated and the conduction-dominated problems. DG has less numerical diffusions compared with other classic algorithms. DG possesses substantial advantages on adaptive mesh modification over finite difference methods, finite volume methods, and classic finite element methods. Adaptive strategies, especially the dynamic mesh modification, are formulated and studied for DG methods guided by mathematics-based and physics-driven a posteriori error estimators. The proposed dynamic strategy performs very well for transient problems with a long period of simulation time in aspects of both the accuracy and the computational cost. This is an abstract of a paper presented at the AIChE Annual Meeting (Austin, TX 11/7-12/2004).