Fast reliable simulations of secondary settling tanks in wastewater treatment with semi-implicit time discretization

We construct approximate solutions of the initial value problem for dynamical phase transition problems via a variational scheme in one space dimension. First, we deal with a local model of phase transition dynamics which contains second and third order spatial derivatives modeling the effects of viscosity and surface tension. Assuming that the initial data are periodic, we prove the convergence of approximate solutions to a weak solution which satisfies the natural dissipation inequality. We note that this result still holds for non-periodic initial data. Second, we consider a model of phase transition dynamics with only Lipschitz continuous stress–strain function which contains a non-local convolution term to take account of surface tension. We also establish the existence of weak solutions. In both cases the proof relies on implicit time discretization and the analysis of a minimization problem at each time step.

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Efficient High Order Semi-implicit Time Discretization and Local Discontinuous Galerkin Methods for Highly Nonlinear PDEs

Journal of Scientific Computing ◽

10.1007/s10915-016-0170-4 ◽

2016 ◽

Vol 68 (3) ◽

pp. 1029-1054 ◽

Cited By ~ 7

Author(s):

Ruihan Guo ◽

Francis Filbet ◽

Yan Xu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Time Discretization ◽

High Order ◽

Nonlinear Pdes ◽

Implicit Time ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Highly Nonlinear

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Implicit time discretization

Finite Elements III - Texts in Applied Mathematics ◽

10.1007/978-3-030-57348-5_77 ◽

2021 ◽

pp. 295-304

Author(s):

Alexandre Ern ◽

Jean-Luc Guermond

Keyword(s):

Time Discretization ◽

Implicit Time

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A simple empirical model for the clarification-thickening process in wastewater treatment plants

Water Science & Technology ◽

10.2166/wst.2014.518 ◽

2014 ◽

Vol 71 (3) ◽

pp. 366-372

Author(s):

Y. K. Zhang ◽

H. C. Wang ◽

L. Qi ◽

G. H. Liu ◽

Z. J. He ◽

...

Keyword(s):

Wastewater Treatment ◽

Activated Sludge ◽

Empirical Model ◽

Wastewater Treatment Plants ◽

Volume Index ◽

Compression Zone ◽

Efficient Operation ◽

Secondary Settling ◽

Sludge Thickening ◽

Simple Empirical Model

In wastewater treatment plants (WWTPs), activated sludge is thickened in secondary settling tanks and recycled into the biological reactor to maintain enough biomass for wastewater treatment. Accurately estimating the activated sludge concentration in the lower portion of the secondary clarifiers is of great importance for evaluating and controlling the sludge recycled ratio, ensuring smooth and efficient operation of the WWTP. By dividing the overall activated sludge-thickening curve into a hindered zone and a compression zone, an empirical model describing activated sludge thickening in the compression zone was obtained by empirical regression. This empirical model was developed through experiments conducted using sludge from five WWTPs, and validated by the measured data from a sixth WWTP, which fit the model well (R2 = 0.98, p < 0.001). The model requires application of only one parameter, the sludge volume index (SVI), which is readily incorporated into routine analysis. By combining this model with the conservation of mass equation, an empirical model for compression settling was also developed. Finally, the effects of denitrification and addition of a polymer were also analysed because of their effect on sludge thickening, which can be useful for WWTP operation, e.g., improving wastewater treatment or the proper use of the polymer.

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A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

Communications in Computational Physics ◽

10.4208/cicp.290414.231214a ◽

2015 ◽

Vol 18 (1) ◽

pp. 203-229 ◽

Cited By ~ 2

Author(s):

Guoqiao You ◽

Shingyu Leung

Keyword(s):

Dynamical Systems ◽

Level Set Method ◽

Level Set ◽

Limit Cycles ◽

Time Discretization ◽

Numerical Approach ◽

Initial Guess ◽

Implicit Time ◽

Time Step ◽

Image Regularization

AbstractWe propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions. Since the derivation is based on a semi-implicit time discretization, this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method. As an interesting application of the numerical approach, we propose a new variational approach for extracting limit cycles in dynamical systems. The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles. Further, we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

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Specific cost modelling for secondary treatment of wastewater

E3S Web of Conferences ◽

10.1051/e3sconf/202126304065 ◽

2021 ◽

Vol 263 ◽

pp. 04065

Author(s):

Nikolay Makisha

Keyword(s):

Wastewater Treatment ◽

Settling Tank ◽

Membrane Bioreactors ◽

Conventional Activated Sludge ◽

Cost Modelling ◽

Cost Item ◽

Treatment Facilities ◽

Secondary Settling ◽

Technological Treatment ◽

Technological Modeling

The article is devoted to the study of model cost indicators of wastewater treatment facilities as one of the factors for ensuring sustainable development. It is noted that the greatest contribution in terms of cost formation is provided by the stage of biological wastewater treatment. As part of the study, a techno-economic simulation was conducted to compare two technological treatment schemes: conventional activated sludge scheme in aeration reactor and secondary settling tank, and treatment by means of membrane bioreactors. In the course of technological modeling, the concentrations of pollutants after treatment were obtained and compared for each of the schemes, as well as the values of possible harm to water bodies were calculated. Within the framework of cost modeling, capital and operating costs were obtained for the two variants, and key differences in their formation were analyzed. It is noted that the classical cleaning scheme requires the construction of a larger volume of structures, while for schemes with a membrane bioreactor, a significant cost item is the purchase of the actual membrane modules, but as the system performance increases, the share of these costs decreases.

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