An Adaptive Method of Lines Approach for Modeling Flow Transport in Rivers

Abstract. The process of formation of cloud droplets on an ensemble of aerosol particles is modelled by numerous investigators using the method of lines (MOL). The method involves discretization of the aerosol size spectrum into bins whose position and width evolve with time. One of the drawbacks of the method is its poor representation of the aerosol spectrum shape in the region between the unactivated aerosol mode and the activated cloud-droplet mode. An adaptive spectrum refinement procedure that improves the performance of the method is introduced and tested. A model of drop formation on multi-component aerosol is formulated for the purpose of the study. Model formulation includes explicit treatment of the drop temperature evolution. Several examples of the model set-up are used to demonstrate model capabilities. Model results are compared to those without adaptivity, and are compared to the Twomey's formul\\ae. A C++ implementation of the model is available as an electronic supplement of the paper.

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TRANSIENT SIMULATION OF LARGE SCALE GAS TRANSMISSION NETWORKS USING AN ADAPTIVE METHOD OF LINES

Computational Methods in Sciences and Engineering 2003 ◽

10.1142/9789812704658_0138 ◽

2003 ◽

Author(s):

E.S. TENTIS ◽

D.P. MARGARIS ◽

D.G. PAPANIKAS

Keyword(s):

Large Scale ◽

Method Of Lines ◽

Adaptive Method ◽

Transient Simulation ◽

Transmission Networks

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An adaptive method of lines solution of the Korteweg-de Vries equation

Computers & Mathematics with Applications ◽

10.1016/s0898-1221(98)00093-5 ◽

1998 ◽

Vol 35 (12) ◽

pp. 13-25 ◽

Cited By ~ 15

Author(s):

P. Saucez ◽

A.Vande Wouwer ◽

W.E. Schiesser

Keyword(s):

Vries Equation ◽

Method Of Lines ◽

Adaptive Method ◽

De Vries

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Simulation of Membrane Separations Using a Modified Maxwell-Stefan Model

Chemical Product and Process Modeling ◽

10.2202/1934-2659.1314 ◽

2009 ◽

Vol 4 (4) ◽

Author(s):

Paulo Brito ◽

Licínio M. Gando-Ferreira ◽

António Portugal

Keyword(s):

Method Of Lines ◽

Cross Flow ◽

Adaptive Method ◽

Polysulfone Membrane ◽

Membrane Pore ◽

Adaptive Resolution ◽

Resolution Algorithm ◽

Model Equations ◽

Observed Rejection ◽

High Rejection

In this work, a modified Maxwell-Stefan model, which considers both the concentration polarization and the transport through the membrane, is tested for the simulation of Dextran T70 aqueous solutions filtration. Numerical simulations by solving the model equations with an adaptive resolution algorithm, based on the Adaptive Method of Lines, determined the concentration profiles in the polarization layer and inside the membrane pore. It is shown that the formation of significant solute accumulation at the membrane/polarization interface leads to high levels of apparent rejection. A tubular cross-flow ultrafiltration module, containing a tubular polysulfone membrane with a molecular weight cut-off of 50 kDa, was used to perform the experiments. The model is able to successfully simulate data in the high rejection/low flux region using an equilibrium constant Keq of 0.25, but does not reproduce the observed rejection drop/pressure build-up which occurs for increased fluxes, which may be due to limitations of the model itself.

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Adaptive method of lines for multi-component aerosol condensational growth and CCN activation

Geoscientific Model Development ◽

10.5194/gmd-4-15-2011 ◽

2011 ◽

Vol 4 (1) ◽

pp. 15-31 ◽

Cited By ~ 11

Author(s):

S. Arabas ◽

H. Pawlowska

Keyword(s):

Method Of Lines ◽

Cloud Droplet ◽

Adaptive Method ◽

Size Spectrum ◽

Grid Refinement ◽

Cloud Droplets ◽

Adaptive Grid Refinement ◽

Refinement Procedure ◽

Set Up ◽

Condensational Growth

Abstract. The process of formation of cloud droplets on an ensemble of aerosol particles is modelled by numerous investigators using the method of lines (MOL). The method involves discretisation of the aerosol size spectrum into bins whose positions evolve with time. One of the drawbacks of the method is its poor representation of the aerosol spectrum shape in the region between the unactivated aerosol mode and the activated droplet mode. An adaptive grid refinement procedure is introduced. The procedure splits any overly wide bins into several narrower ones during integration. The number of new bins added is a function of particle concentration in the bin being split. Application of the grid refinement procedure results in suppression of the sensitivity of the computed cloud droplet spectrum characteristics such as droplet number concentration or effective radius to the initial grid choice. A model of droplet formation on multi-component aerosol is formulated for the purpose of the study. Model formulation includes explicit treatment of the droplet temperature evolution. Several examples of the model set-up are used to demonstrate model capabilities. Model results are compared to those without adaptivity. A C++ implementation of the model is available as an electronic supplement of the paper.

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