Purpose

The purpose of this study is to investigate the errors arising from the numerical treatment of model processes, paying particular attention to the impact of key system features including widely variable dispersion coefficients, spatiotemporal velocities of algal cells, and the aggregation of algae from single cells to large colonies. An advection–dispersion model has been presented to describe the vertical transport of colonial and motile harmful algae in a lake environment.

Design/methodology/approach

Model performance is examined for two different numerical treatments of the advective term: first-order upwind and quadratic upwind with a stability-preserving flux limiter (SMART). To determine how these schemes impact predictions, comparisons are made across a sequence of models with increasing complexity.

Findings

Using first-order upwinding for advection–dispersion calculations with a time oscillating velocity field leads to oscillatory numerical dispersion. Subjecting an initially uniform distribution of large-sized algal colonies to a spatiotemporal velocity creates a concentration pulse, which reaches a steady-state width at high-grid Peclet numbers when using the SMART scheme; the pulse exhibits contraction–expansion behavior throughout a velocity cycle at all Peclet numbers when using first-order upwinding. When aggregation dynamics are included with advection-dominated spatiotemporal transport, results indicate the SMART scheme predicts larger peak concentration values than those predicted by first-order upwind, but peak location and the time to large colony appearance remain largely unchanged between the two advective schemes.

Originality/value

To the best of the authors’ knowledge, this study is the first numerical investigation of a novel advection–dispersion model of vertical algal transport. In addition, a generalized expression for the effective dispersion coefficient of temporally variable flow fields is presented.

中文翻译：

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时空速度、聚集和虚假分散：群居和活动有害藻类建模的数值考虑

目的

本研究的目的是调查模型过程数值处理所产生的误差，特别关注关键系统特征的影响，包括广泛变化的离散系数、藻类细胞的时空速度以及藻类从单细胞到藻类的聚集。大的殖民地。提出了平流扩散模型来描述湖泊环境中群落和运动有害藻类的垂直运输。

设计/方法论/途径

针对平流项的两种不同数值处理来检查模型性能：一阶逆风和带有保稳通量限制器 (SMART) 的二次逆风。为了确定这些方案如何影响预测，需要对一系列复杂性不断增加的模型进行比较。

发现

使用一阶逆风进行带有时间振荡速度场的平流色散计算会导致振荡数值色散。将最初均匀分布的大型藻群置于时空速度下会产生浓度脉冲，当使用 SMART 方案时，该浓度脉冲在高网格佩克莱特数下达到稳态宽度；当使用一阶迎风时，脉冲在所有佩克莱特数的整个速度周期中表现出收缩-膨胀行为。当聚集动力学包含在平流主导的时空传输中时，结果表明 SMART 方案预测的峰值浓度值比一级迎风预测的峰值浓度值更大，但两个平流方案之间峰值位置和大群体出现的时间基本保持不变。

原创性/价值

据作者所知，这项研究是对藻类垂直输送的新型平流扩散模型的首次数值研究。此外，还提出了时变流场有效扩散系数的广义表达式。