The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes ...The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.展开更多
The tide induced groundwater fluctuation and the seawater intrusion have important effects on hydrogeology and ecology of coastal aquifers.Among previous studies,there were few quantitative evaluations of the joint ef...The tide induced groundwater fluctuation and the seawater intrusion have important effects on hydrogeology and ecology of coastal aquifers.Among previous studies,there were few quantitative evaluations of the joint effects of the beach slope and the tide fluctuation on the groundwater dynamics.In this article,a numerical model is built by using the software FEFLOW with consideration of seawater intrusion,tide effects,density dependent flow and beach sloping effects.The simulation results are validated by laboratory experimental data in literature.More numerical scenarios are designed in a practical scale with different beach slopes.Results show that the groundwater fluctuation decays exponentially with the distance to the beach,i.e.,,and our simulation further shows that the beach slope influence can be expressed in the form of a logarithm function.While for the same location,the amplitude increases logarithmically with the beach angle in the form,where and are related with the horizontal distance（）in the form of a logarithm function.The beach slope has no influence on the phase lag,although the latter increases regularly with the distance from the sea.The beach slope effect on the seawater intrusion is investigated through the quantitative relationship among the relative intrusion length（）,the relative enhancement of the tide induced seawater intrusion（）and the beach angle（）.It is shown that the tide effects on a milder beach is much greater than on a vertical one,and both λ and κ can be expressed in logarithm functions of.The tidal effect on the flow field in the transition zone for a particular mild beach is also studied,with results showing that the tide induced fluctuation of is similar to the groundwater table fluctuation while shows a distinct variation along both directions.展开更多
基金Work sponsored by"Ministero dell' University"CNR of Italy
文摘The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.
基金supported by the Program for New Century Excellent Talents in Universities(Grant No.07-0814)
文摘The tide induced groundwater fluctuation and the seawater intrusion have important effects on hydrogeology and ecology of coastal aquifers.Among previous studies,there were few quantitative evaluations of the joint effects of the beach slope and the tide fluctuation on the groundwater dynamics.In this article,a numerical model is built by using the software FEFLOW with consideration of seawater intrusion,tide effects,density dependent flow and beach sloping effects.The simulation results are validated by laboratory experimental data in literature.More numerical scenarios are designed in a practical scale with different beach slopes.Results show that the groundwater fluctuation decays exponentially with the distance to the beach,i.e.,,and our simulation further shows that the beach slope influence can be expressed in the form of a logarithm function.While for the same location,the amplitude increases logarithmically with the beach angle in the form,where and are related with the horizontal distance（）in the form of a logarithm function.The beach slope has no influence on the phase lag,although the latter increases regularly with the distance from the sea.The beach slope effect on the seawater intrusion is investigated through the quantitative relationship among the relative intrusion length（）,the relative enhancement of the tide induced seawater intrusion（）and the beach angle（）.It is shown that the tide effects on a milder beach is much greater than on a vertical one,and both λ and κ can be expressed in logarithm functions of.The tidal effect on the flow field in the transition zone for a particular mild beach is also studied,with results showing that the tide induced fluctuation of is similar to the groundwater table fluctuation while shows a distinct variation along both directions.
