An Efficient High Resolution FEM for PDE Systems

Abstract

Non-physical oscillations due to numerical errors or non-uniqueness of the solution in process simulation are still a fundamental issue in fluid dynamics. This is especially true when treating equation systems of hyperbolic Partial Differential Equations (PDEs) or systems of parabolic PDEs with very large Peclet number. This work aims to find efficient Finite Element Method (FEM) approaches for a general formulation so as to solve both parabolic and hyperbolic PDEs, which leads to non-oscillation without loss of the solution accuracy, meaning mass conservation, while keeping superior sharp fronts. For this purpose, two case studies are presented. In the first case study, the Streamline Upwind/Petrov Galerkin (SUPG) method is applied on a Simulated Moving Bed (SMB) process described by an equilibrium model consisting of a parabolic PDE. The second example is a pressure swing adsorption (PSA) process, which is described as a system of hyperbolic PDEs. Applying the Galerkin FEM with Flux Corrected Transport (FCT) shows superior results. The non-oscillating sharp front still holds in case of shock phenomena and strong nonlinearities, whereas oscillations can also be reduced with the SUPG approach.