مدلسازی عددی انتقال آلودگی در محیط متخلخل در حالت جریان ناپایدار با استفاده از روش حجم محدود

آب زیرزمینی یک منبع آب شیرین حائز اهمیت است، که در مقایسه با آب سطحی کمتر مستعد آلودگی بوده و دسترسی به این منبع با ارزش، مقرون به صرفه می باشد. این مسائل باعث می شود آب زیرزمینی به عنوان یک منبع کارآمد در کمبود آب سطحی مانند خشکسالی به ویژه در کشورهای خشک و نیمه خشک شناخته شود. در این تحقیق معادله انتقال آلودگی در آب زیرزمینی با استفاده از روش نوین حجم محدود  ddfv مدلسازی شده که با استفاده از این روش  غلظت آلودگی در مرکز و رئوس هر المان بدست می آید. مدل ارائه شده بر روی مش مثلثی ساختارنیافته اعمال شده است که برای مدلسازی مرزهای هندسی پیچیده مناسب می‌باشد. در حالت جریان ناپایدار، معادله جریان با معادله انتقال همبسته گردید و نتایج مدل عددی با نتایج مدل مادفلو صحت‌سنجی شد. در ادامه مدل هم بسته جریان و انتقال در محیط با غیرهمگنی بالا مورد استفاده قرار گرفته که نتایج نشان از پایداری مدل مورد نظر می دهد. همچنین با استفاده از مدل عددی مورد نظر نتایج معادلات جریان و انتقال آلودگی عاری از هر گونه نوسانات عددی می باشد.  

numerical modeling of contamination transport equation in porous media for transient flow regime by finite volume method

groundwater is an essential source of fresh water, which is less prone to pollution in comparison to surface water, and access to this valuable resource is affordable. these issues make groundwater a viable source during surface water shortages such as drought, especially in arid and semi-arid countries. hence, groundwater flow and contaminant transport modeling is an efficient tool in monitoring the aquifers. since the analytical methods are limited to the simplified cases, the numerical models are applied to assess the quality and quantity of groundwater in real aquifers. therefore, in this research, the equation of contamination transport is modeled by a novel dual discrete finite volume method (ddfvm). the solution domain for this study is two-dimensional, anisotropic, heterogeneous and saturated. the mechanisms considered in the solute transport equation include advection, diffusion and dispersion with no chemical reactions. contrary to the classical finite volume methods using two points to approximate fluxes across the element’s interfaces, in the method proposed in this study, the values of hydraulic head and contamination concentrations are obtained at the center and vertices of each element. this numerical method is considered as a cell centered fvm which preserves local mass conservation. this model has been applied to an unstructured triangular mesh that could be fitted to complex geometric boundaries. for the transient flow regimes, the flow equation has been coupled with the contaminant transport problem, and the results of the numerical model are validated with the model of modflow. for this purpose, first the flow equation is solved to obtain the hydraulic head and seepage velocity. subsequently, the dispersion coefficients are calculated for the solution of transport equation at each time step. in the first example, the one-dimensional flow has been considered for the verification of flow and transport equation. to solve this problem the confined aquifer is discretized with the mesh size of 0.5 m and 0.001 day. the second problem includes the two-dimensional domain in which the north and west boundaries are the first type boundary condition, and the east and south boundaries are no-flow boundary conditions, respectively. the mesh size and time step in this problem are similar to the first example. in the third example, two-dimensional aquifer with the prescribed flux boundary condition have been discretized into 3777 nodes and 7312 elements. in these three problems, the results for the two parameters of hydraulic head and solute concentration at different time lapses, show excellent agreement between the ddfv method and the model of modflow. since the numerical schemes usually suffer from numerical oscillations and instabilities in the heterogenous domain, in the last problem the flow and transport fv coupled model has been applied in a porous media with strong heterogeneity. the log-normal distribution has been assumed for the permeability map with the average value of 8􀀁 10􀀂􀀃􀀄 m􀀄, correlation length of 5 m and variance of 10􀀂􀀃􀀅 and different permeability maps were generated randomly. the free-oscillation solutions for the two parameters of hydraulic head and pollutant concentration demonstrate the stability of the model.