用于模拟水污染传播的分区方程混合模型

Putsadee Pornphol, Porpattama Hammachukiattikul, Rajarathinam Vadivel, Salaudeen Abdulwaheed Adebayo, Saratha Sathasivam
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引用次数: 0

摘要

水污染已被确定为严重的环境问题之一,对水生动植物、陆生动植物和人类健康都有负面影响。有效的污染管理和决策需要了解我们环境中水污染的复杂动态。有许多可行的措施可以用来控制这一威胁。在数学上,水污染可以通过管理使用微分方程来模拟。为了用微分方程系统来描述水体污染,我们采用了分区模型来捕捉水体污染的动态变化。我们采用分区模型来捕捉湖泊、河流和其他水体的污染动态。该模型将各种形式的水污染分门别类,并与净化措施相结合。通过这一策略,我们展示了水污染物在不同环境中的表现,为将污染管理措施付诸实践提供了有用的知识,具体方法是使用欧拉法和 Runge-Kutta of Order 4 数值方法(RK4)求解分区模型。我们根据步长(h)的不同值(步长表示数值方法近似求解轨迹的间隔),对应用上述两种数值方法所获得结果的质量进行了质询。我们的研究结果表明,这两种数值方法都可以通过计算指定时间间隔内的区间值来求解区间方程。尽管这两种方法都很实用,但值得注意的是,与欧拉公式相比,阶次为 4 的 Runge-Kutta 数值方法在求解隔室模型时始终更为有效,尤其是当步长适中时。Runge-Kutta 方法在指定时间范围内精确逼近解的稳健性和高效性使我们得出结论,在时间步长适中的分室模型的实际应用中,Runge-Kutta 方法比欧拉方法更为可取。
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Compartmental Equations Hybrid Model for Modelling Water Pollution Transmission
Water pollution has been identified as one of serious environmental problem that has a negative impact on aquatic animals and plants, terrestrial plants and animals, and human health. Effective pollution management and decision-making require an understanding of the intricate dynamics of water contamination in our environment. There are many workable measures that can be adopted to control the menace. Mathematically, water pollution can be modelled using differential equations through management. In order to describe the pollution of water bodies using a system of differential equations. We deployed compartment models to capture the dynamic of pollution in lakes, rivers, and other water bodies. The model compartmentalizes various forms of water pollution and combines them with purification measures. With this strategy, we showed how water pollutants behave in diverse environmental contexts by providing useful knowledge for putting pollution management measures into practice by solving the compartmental model using the Euler method and the Runge-Kutta of Order 4 numerical method (RK4). The quality of results obtained by applying the two mentioned numerical methods is queried based on how they respond to different values of step size (h), which represents the interval at which the numerical methods approximate the solution trajectory. Our findings demonstrate that both numerical approaches are viable for solving compartmental equations by computing compartment values over a specified time interval. Despite the practicability of both methods, it is noteworthy that Runge-Kutta of order 4 consistently emerges as the more effective numerical method in solving our compartmental model when compared with Euler formula, particularly when step sizes are moderately large. The Runge-Kutta method's robustness and efficiency in accurately approximating solutions over the specified time range make us conclude that it is more preferable to the Euler method for practical implementations of compartmental models with moderately large time steps.
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来源期刊
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences Chemical Engineering-Fluid Flow and Transfer Processes
CiteScore
2.40
自引率
0.00%
发文量
176
期刊介绍: This journal welcomes high-quality original contributions on experimental, computational, and physical aspects of fluid mechanics and thermal sciences relevant to engineering or the environment, multiphase and microscale flows, microscale electronic and mechanical systems; medical and biological systems; and thermal and flow control in both the internal and external environment.
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