Browsing by Author "Ke, Guoyi"
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Item Adaptive mesh refinement for Multigrid Solver(2016-11-30) Lee, Shihyu; Aulisa, Eugenio; Bornia, Giorgio; Ke, GuoyiIn this work, we introduce the Galerkin finite element Method for Elliptic Problems. The estimates of the approximation error in both energy norm and $L^2$ are given for the variational formulation of the Poisson problem, discretized by the Galerkin finite element method. Then, the adaptive mesh refinement from Quarteroni is applied to solve the multigrid Poisson problem. This refinement is proven to be very efficient and effective compared with the uniform mesh refinement. Moreover, we propose a new estimator for the adaptive mesh refinement based on the error of approximate solution in the adjacent levels. The numerical results show that the adaptive mesh refinement with a new estimator performs much better than the one with an estimator from Quarteroni in terms of both computational time and the number of elements.Item Quantitative analysis of membrane fouling mechanisms involved in microfiltration of humic acid-protein mixtures at different solution conditions(2018) Sun, Chunyi; Zhang, Na; Li, Fazhan; Ke, Guoyi; Song, Lianfa (TTU); Liu, Xiaoqian; Liang, ShuangA systematical quantitative understanding of different mechanisms, though of fundamental importance for better fouling control, is still unavailable for the microfiltration (MF) of humic acid (HA) and protein mixtures. Based on extended Derjaguin-Landau-Verwey-Overbeek (xDLVO) theory, the major fouling mechanisms, i.e., Lifshitz-van der Waals (LW), electrostatic (EL), and acid-base (AB) interactions, were for the first time quantitatively analyzed for model HA-bovine serum albumin (BSA) mixtures at different solution conditions. Results indicated that the pH, ionic strength, and calcium ion concentration of the solution significantly affected the physicochemical properties and the interaction energy between the polyethersulfone (PES) membrane and HA-BSA mixtures. The free energy of cohesion of the HA-BSA mixtures was minimum at pH = 3.0, ionic strength = 100 mM, and c(Ca2+) = 1.0 mM. The AB interaction energy was a key contributor to the total interaction energy when the separation distance between the membrane surface and HA-BSA mixtures was less than 3 nm, while the influence of EL interaction energy was of less importance to the total interaction energy. The attractive interaction energies of membrane-foulant and foulant-foulant increased at low pH, high ionic strength, and calcium ion concentration, thus aggravating membrane fouling, which was supported by the fouling experimental results. The obtained findings would provide valuable insights for the quantitative understanding of membrane fouling mechanisms of mixed organics during MF.