An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

Sunyoung Bu, Jingfang Huang, Treavor Boyer, Cass T. Miller

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Original languageEnglish (US)
Pages (from-to)4996-5010
Number of pages15
JournalJournal of Computational Physics
Volume229
Issue number13
DOIs
StatePublished - Jul 2010
Externally publishedYes

Fingerprint

Ion exchange
evaluation
approximation
ions
differential equations
Ordinary differential equations
ion exchange resins
formulations
drinking
water treatment
scale models
Ion exchange resins
microbalances
integral equations
Water treatment
Potable water
reactors
Integral equations
boundary conditions
Particle size

Keywords

  • Diffusion process
  • Finite element methods
  • Krylov deferred correction methods
  • Multiscale modeling
  • Semi-implicit preconditioner

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

Cite this

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process. / Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor; Miller, Cass T.

In: Journal of Computational Physics, Vol. 229, No. 13, 07.2010, p. 4996-5010.

Research output: Contribution to journalArticle

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