ﺗﻮﺳﻌﻪ ﯾﮏ ﻣﺪل ﻋﺪدي ﺟﺪﯾﺪ ﺑﺮ ﻣﺒﻨﺎي ﮔﺎﻟﺮﮐﯿﻦ ﻧﺎﭘﯿﻮﺳﺘﻪ ﺑﺮاي ﺷﺒﯿﻪ ﺳﺎزي ﺗﻬﺎﺟﻢ آب ﺷﻮر درﯾﺎ ﺑﻪ آﺑﺨﻮان ﻫﺎي ﺳﺎﺣﻠﯽ

A new numerical method based on discontinuous galerkin for simulation of seawater intrusion into coastal aquifers

ﺳﺎﺑﻘﻪ و ﻫﺪف: آﺑﺨﻮانﻫﺎي ﺳﺎﺣﻠﯽ از ﻣﻬﻢﺗﺮﯾﻦ ﻣﻨﺎﺑﻊ ﺗﺎﻣﯿﻦ آب ﺷﯿﺮﯾﻦ در ﺑﺴﯿﺎري از ﮐﺸﻮرﻫﺎي ﺟﻬﺎن، ﺑﻪ ﺧﺼﻮص در ﻧﻮاﺣﯽ ﺧﺸﮏ و ﻧﯿﻤﻪﺧﺸﮏ ﺑﻪﺷﻤﺎر ﻣﯽرود. ﺑﻪ دﻟﯿﻞ ﻣﺠﺎورت و ارﺗﺒﺎط آﺑﺨﻮانﻫﺎي ﺳﺎﺣﻠﯽ ﺑﺎ آب ﺷﻮر درﯾﺎ و ﺗﻬﺪﯾﺪ ﻧﺎﺷﯽ از آﻟﻮده ﺷﺪن آنﻫﺎ ﺑﻪ واﺳﻄﻪ ﭘﯿﺶروي آب شور، مديريت و حفاظت اين منابع آب شيرين ساحلي امري كاملا ضروري است.بنابراين هدف از پژوهش حاضر، توسعه يك مدل عددي جديد براي شبيه سازي انتقال آلودگي در آبخوان هاي ساحلي ( تهاجم آب شور دريا به آبخوان هاي ساحلي ) با استفاده از روش عددي گالركين ناپيوسته مي باشد. ﻣﻮاد و روش ﻫﺎ: در اﯾﻦ ﭘﮋوﻫﺶ روشﻫﺎي ﮔﺎﻟﺮﮐﯿﻦﻧﺎﭘﯿﻮﺳﺘﻪ ﮐﻪ ﮐﻢ ، ﺗﺮ در ﻣﺴﺎﺋﻞ ﻣﻬﻨﺪﺳﯽ ﮔﺴﺘﺮش ﭘﯿﺪا ﮐﺮده اﺳﺖ ﺑﺮاي ﺷﺒﯿﻪﺳﺎزي ﺟﺮﯾﺎنﻫﺎي واﺑﺴﺘﻪ ﺑﻪ ﭼﮕﺎﻟﯽ آب زﯾﺮزﻣﯿﻨﯽ (ﻣﺎﻧﻨﺪ ﻫﺠﻮم آب ﺷﻮر درﯾﺎ ﺑﻪ آﺑﺨﻮانﻫﺎي ﺳﺎﺣﻠﯽ)ﺑﻪ ﮐﺎر ﮔﺮﻓﺘﻪ ﺷﺪ. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر ﻣﻌﺎدﻻت ﻏﯿﺮﺧﻄﯽ ﺣﺎﮐﻢ ﺑﺮ ﺟﺮﯾﺎن و اﻧﺘﻘﺎل ﺷﻮري در ﯾﮏ ﻣﺤﯿﻂ آﺑﺨﻮان اﺷﺒﺎع ﺑﺎ اﺳﺘﻔﺎده از روش ﮔﺎﻟﺮﮐﯿﻦ ﻧﺎﭘﯿﻮﺳﺘﻪ ﻣﻨﻘﻄﻊﺳﺎزي ﮔﺮدﯾﺪ و از روش ﺿﻤﻨﯽ ﺑﺮاي ﻣﻨﻘﻄﻊﺳﺎزي زﻣﺎﻧﯽ اﺳﺘﻔﺎده ﺷﺪ. ﭘﺲ از اﻋﻤﺎل روش ﭘﯿﮑﺎرد اﺻﻼح ﺷﺪه ﺑﺮاي ﺧﻄﯽﺳﺎزي ﻣﻌﺎدﻻت ﺟﺒﺮي ﺣﺎﺻﻠﻪ ﺑﻪ ،ﺷﺮاﯾﻂ ﻣﺮزي و اوﻟﯿﻪ ﮐﺎر ﮔﺮﻓﺘﻪ ﺷﺪ ﮐﻪ ﺑﺮاي از ﺑﯿﻦ ﺑﺮدن ﻧﻮﺳﺎﻧﺎت ﻏﯿﺮﻓﯿﺰﯾﮑﯽ در ﺣﻞ ﻋﺪدي از ﻣﺤﺪودﮐﻨﻨﺪه ﺷﯿﺐ ﭼﺎوﻧﺖ- ﺟﺎﻓﺮي اﺳﺘﻔﺎد ﺷﺪ. ﺎﻓﺘﻪ ﻫﺎ: ﺑﻪ ﻣﻨﻈﻮر ارزﯾﺎﺑﯽ و ﺻﺤﺖ ، ﺳﻨﺠﯽ ﻣﺪل ﭘﻨﺞ ﻣﺴﺄﻟﻪ ﺷﺎﻣﻞ ﻣﺴﺄﻟﻪ اﺳﺘﺎﻧﺪارد ﻫﻨﺮي، دو ﻣﺴﺄﻟﻪ اﺻﻼح ﺷﺪه ﻫﻨﺮي ﻣﺴﺄﻟﻪ اﻟﺪر و در ﻧﻬﺎﯾﺖ ﻣﺴﺄﻟﻪ آزﻣﺎﯾﺸﮕﺎﻫﯽ ﮔﺎﺳﻮاﻣﯽ- ﺳﻠﻤﻨﺖ در ﺳﻪ ﻓﺎز ﻣﺘﻔﺎوت ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار ﮔﺮﻓﺖ. ﺑﺮاي ﺗﻤﺎﻣﯽ ﻣﺴﺎﺋﻞ ﻧﺘﺎﯾﺞ ﺑﺎ ﺳﺎﯾﺮ ﺣﻞﻫﺎي اراﺋﻪ ﺷﺪه ﺑﺮاي آن ﻣﺴﺎﺋﻞ ﻣﻘﺎﯾﺴﻪ ﮔﺮدﯾﺪ ﺗﺎ دﻗﺖ ﻣﺪل ﻗﺎﺑﻞ ارزﯾﺎﺑﯽ ﺑﺎﺷﺪ. ﻫﻤﮕﺮاﯾﯽ روش ﺑﺎ رﯾﺰ ﮐﺮدن ﺷﺒﮑﻪ ﺣﻞ در ﻣﺴﺄﻟﻪ اﺳﺘﺎﻧﺪارد ﻫﻨﺮي ﻧﺸﺎن داده ﺷﺪ. ﻣﺤﺪودﮐﻨﻨﺪه ﺷﯿﺐ ﭼﺎوﻧﺖ- ﺟﺎﻓﺮ ﺑﺮاي ﮐﻨﺘﺮل ﻧﻮﺳﺎﻧﺎت ﻏﯿﺮﻓﯿﺰﯾﮑﯽ در ﺣﻞ ﻣﺴﺄﻟﻪ آزﻣﺎﯾﺸﮕﺎﻫﯽ ﺑﻪﻃﻮر ﻣﻮﻓﻘﯿﺖآﻣﯿﺰي ﺑﻪ ﮐﺎر ﮔﺮﻓﺘﻪ ﺷﺪ ﮐﻪ ﻧﺘﺎﯾﺞ رﺿﺎﯾﺖ ﺑﺨﺸﯽ از آن ﺑﻪ دﺳﺖ آﻣﺪ. ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ دﻗﺖ ﻣﺪل را در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﺳﺎﯾﺮ روشﻫﺎي ﻋﺪدي ﺑﻪﺧﻮﺑﯽ ﻧﺸﺎن داده اﺳﺖ. ﻧﺘﯿﺠﻪ ﮔﯿﺮي: ﻣﺪل ﺑﺎ اﺳﺘﻔﺎده از ﻣﺴﺎﺋﻞ ﻣﺬﮐﻮر ﻣﻮرد ﺻﺤﺖ ﺳﻨﺠﯽ و ارزﯾﺎﺑﯽ ﻗﺮار ﮔﺮﻓﺖ ﮐﻪ ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ در ﺗﻤﺎﻣﯽ ﻣﺜﺎل ﻫﺎ ﺑﯿﺎﻧﮕﺮ دﻗﺖ ﺑﺴﯿﺎر ﺑﺎﻻي اﯾﻦ روش دارد. در ﻣﮑﺎن ﻫﺎﯾﯽ از داﻣﻨﻪ ﺣﻞ ﮐﻪ ﺳﺮﻋﺖ ﺟﺮﯾﺎن ﺑﺎﻻﺳﺖ، ﻧﺸﺎن داده ﺷﺪ اﯾﻦ روش در ﻣﻘﺎﯾﺴﻪ ﺑﺎ ﺑﺮﺧﯽ روش ﻫﺎ ﻫﻤﺎﻧﻨﺪ ﺗﻔﺎﺿﻞ ﻣﺤﺪود ﻧﻮﺳﺎﻧﺎت ﻏﯿﺮﻓﯿﺰﯾﮑﯽ از ﺧﻮد ﺑﺮوز ﻧﻤﯽدﻫﺪ. ﻋﻼوه ﺑﺮ اﯾﻦ ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽدﻫﺪ ﮐﻪ اﯾﻦ روش ﻧﺴﺒﺖ ﺑﻪ روشﻫﺎي ﻋﺪدي دﯾﮕﺮ ﻫﻢ ﭼﻮن روش اﺣﺠﺎم ﻣﺤﺪود ﭘﺨﺶ ﻋﺪدي ﮐﻢ ﺗﺮي را ﺑﺮوز ﻣﯽ دﻫﺪ. ﻫﻤﯿﻦ ﻃﻮر اﺳﺘﻔﺎده از اﯾﻦ روش ﺑﺮاي ﺷﺒﯿﻪﺳﺎزي ﻣﺴﺄﻟﻪ آزﻣﺎﯾﺸﮕﺎﻫﯽ ﺟﻨﺒﻪ ﮐﺎﻣﻼً ﻋﻤﻠﯽ اﯾﻦ ﻣﺪل را ﻧﺸﺎن ﻣﯽ دﻫﺪ.

Background and Objectives: Coastal aquifers are of the most important freshwater resources in many countries, especially in arid and semi-arid zones. Due to the proximity and contact with the sea and thus the threat of contamination because of the seawater intrusion, management and protection of these freshwater resources are quite necessary. Therefore, the main goal of the present study is to develop a new numerical model for simulation of the contaminant transport in coastal aquifers (Materials and Methods: In this study, Discontinuous Galerkin methods which have been less developed in engineering problems were applied for discretization of the coupled nonlinear system of flow and solute transport equations in a saturated porous medium and a fully implicit backward Euler scheme was applied for temporal discretization. The primal DGs have been developed successfully for density-dependent flows by applying initial and boundary conditions to the coupled equations. Then, to linearize the resulting nonlinear systems, Picard iterative technique was applied and Chavent-Jaffre slope limiter was used to eliminate the nonphysical oscillations appeared in the solution. seawater intrusion) using discontinuous Galerkin method. Results: Five benchmark problems including standard Henry problem together with its two modified versions, Elder problem and Goswami-Clement experimental problem in three distinct phases were simulated for validation and verification of the numerical code. For all the benchmark problems, the results were compared against other solutions in order to assess the model accuracy. The solution convergence was proved for the standard henry problem. Applying the Chavent-Jaffre slope limiter to the experimental test showed a satisfactory results obtained from the simulations. In comparison with other numerical solutions, the present model revealed a good accuracy for all the problems. Conclusion: The DG model were verified and evaluated using the above-mentioned problems. The results from simulations showed a good accuracy for DG method. In portions of the domain where the velocity is high, it was indicated that the DG methods in comparison with other numerical methods e.g. finite difference, do not emerge non-physical oscillations. Also, the results show a less numerical dispersion in comparison with other numerical methods such as finite volume methods. In addition, simulating the experimental problem with the current model shows the practical aspects of the developed model based on discontinuous Galerkin.