Direct Finite Element Computation of Periodic Adsorption Processes

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Abstract
This article presents a direct method for computing time-periodic solutions of adsorption processes as an alternative to prolonged dynamic simulation of the natural evolution to periodicity. Direct computation of periodicity is established by discretization on a two-dimensional space-time grid that is periodic in time. Petrov-Galerkin (SUPG) finite element approximation is applied for consistent stabilization of convective terms in the governing hyperbolic equations. Newton iteration with Gaussian elimination (frontal method) is used to solve the resulting set of nonlinear algebraic equations. Computations match exact solutions on simple adsorption cycles, and capture shock layers with as few as two elements. In its present form, the direct method is more efficient than dynamic simulation when the natural evolution to periodicity extends over hundreds of cycles, and will likely be even faster with superior discretization and solution techniques.

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