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Numerical solution of a multi-class model for batch settling in water resource recovery facilities

机译：水资源回收设施中多级沉降模型的数值解

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摘要

In Torfs et al. (2017) a new unified framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of non-linear hyperbolic-parabolic PDEs whose solutions may contain very sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit-explicit Runge-Kutta (IMEX-RK) schemes, along with the weighted essentially non-oscillatory (WENO) shock-capturing technology for the discretization of the set of equations, is advocated in this work. The versatility of the proposed unified framework is demonstrated through a set of numerical examples for batch settling occurring in both PSTs and SSTs, along with the efficiency and reliability of the numerical scheme.
机译：在Torfs等人中。 （2017）提出了一个新的统一框架来对水资源回收设施中的沉淀池进行建模，该框架提供了一组偏微分方程（PDE），用于对废水处理中的不同沉淀单元过程进行建模，例如一级和二级沉淀池（PST和SST）。扩展到处理沉淀粒子分布特性的多类框架导致了非线性双曲抛物PDE系统，其解可能包含非常尖锐的过渡。这就需要使用一致且稳健的数值方法来获得对PDE解的良好解析和可靠的近似值。在这项工作中，提倡使用隐式显式Runge-Kutta（IMEX-RK）方案以及加权的基本非振荡（WENO）震荡捕获技术来离散方程组。通过一组在PST和SST中发生的批次沉降的数值示例，以及数值方案的效率和可靠性，证明了所提出的统一框架的多功能性。

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  • 来源
    《Applied Mathematical Modelling》 |2017年第9期|415-436|共22页
  • 作者

    Raimund Burger; Stefan Diehl; M. Carmen Marti; Pep Mulet; Ingmar Nopens; Elena Torfs; Peter A. Vanrolleghem;

  • 作者单位

    Cl~2MA and Departamento de Ingenierfa Matematka, Facultad de Ciencias Flsicas y Matemiticas, Universidad de Concepcidn, Casilla 160-C Concepcidn, Chile;

    Centre for Mathematical Sciences, Lund University, P.O. Box 118, Lund S-221 00, Sweden;

    Cl~2MA and Departamento de Ingenierfa Matematka, Facultad de Ciencias Flsicas y Matemiticas, Universidad de Concepcidn, Casilla 160-C Concepcidn, Chile;

    Departament de Matematiques, Universitat de Valencia, Av. Vicent Andres Estellts, s, Burjassot £-46100, Spain;

    BIOMATH, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, Ghent B-9000, Belgium;

    modelEAU, Dfyartement de genie civil et de genie des eaux, University Laval, 1065 Av. de la Medecine, Quebec QC G1V 0A6, Canada;

    modelEAU, Dfyartement de genie civil et de genie des eaux, University Laval, 1065 Av. de la Medecine, Quebec QC G1V 0A6, Canada;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Multi-class kinematic flow model; Wastewater treatment; Convection-diffusion equation; Implicit-explicit Runge-Kutta scheme; Settling velocity distribution;

    机译：多类运动流模型;废水处理;对流扩散方程;隐式-显式Runge-Kutta方案;沉降速度分布;

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