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problem computationally challenging to solve. Moreover, initialization of thousands of variables simultaneously also presents a significant challenge. Hence, after solving with the CD approach with fewer nodes, we verify the accuracy of the results with a more accurate MOL approach for our case studies. We present a brief description of the spatial and the temporal discretization schemes used in this work in the subsequent sections. 2.5.1 Spatial Discretization PSA processes are convection dominated and finding accurate discretization scheme that re- solves sharp adsorption fronts is an additional challenge. Although higher-order methods accurately predict behaviour for smooth regions, they introduce unrealistic oscillations around steep zones in the spatial profile. First-order methods can be inherently bounded and can ensure no oscillatory behavior for steep zones. However, due to low order accuracy, fronts lose their sharpness (numerical smearing) unless hundreds of spatial nodes are used. Therefore, high-resolution methods are utilized for convection dominated processes which ensure second or higher order accuracy for smooth regions together with low order accuracy without oscil- lations for steep regions and discontinuities in the spatial profile [124, 70]. In particular, we use the finite volume method with flux limiters in this work since it not only avoids these aforementioned issues but also is well suited to model hyperbolic conservation laws, given its inherent conservative property [58, 114, 124]. Finite volume methods with flux limiters utilize the theory of flux-corrected transport (FCT) which incorporates anti-diffusion to negate the effects of excessive smearing. FCT removes numerical dispersion from the discretized equations to keep the fronts sharp ensuring no oscillations [32]. On the other hand, finite volume methods with a flux limiter conceptually are exact opposite of FCT. In other words, they introduce additional numerical dispersion around steep zones to avoid oscillations. However, the theory of flux limiters has been derived from FCT [91, 125]. 2.5 Simulation Methodologies Chapter 2. Pressure Swing Adsorption 29PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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