结合有限单元法运用三次样条技术求解达西速度  

Application of the cubic-spline technique with the finite element method to solving the nodal Darcian velocities

作　　者：谢一凡[1] 吴吉春[1] 薛禹群[1] 谢春红[2] 

机构地区：[1]南京大学地球科学与工程学院,江苏南京210046 [2]南京大学数学系,江苏南京210046

出　　处：《水文地质工程地质》2015年第5期1-5,共5页Hydrogeology & Engineering Geology

基　　金：国家杰出青年基金(40725010);国家自然科学基金(41030746)

摘　　要：求解含水层中溶质和热量的运移时,连续的达西速度场十分重要。传统有限单元法能够精确求解水头,但其水头一阶导数在节点上不连续,求解通过截面流量时,流入量和流出量不相等。将有限单元法与三次样条技术结合,利用三次样条函数逼近水头,保证水头一阶导数的连续性,从而利用达西公式求解出连续的达西速度场,保证流量的连续性。通过对均质和非均质介质下的二维稳定流的数值模拟,发现这种结合三次样条技术的有限单元法能够精确求解水头、达西速度与流量。The continuous velocities field is important in the simulation of transport of mass and heat. The finite element method can solve hydraulic heads with high accuracy, but cannot obtain continuous head derivatives. The velocities calculated by the finite element method are discontinuous at each node, indicating that the mass conservation is not held in the calculated flux. This paper applies the cubic-spline technique to the finite element method to ensure the continuous head derivatives, and the continuous nodal darcian velocities can be obtained. The simulation in this paper demonstrates that the proposed method can obtain accurate estimation of heads, Darcian velocities and flux.

关 键 词：三次样条法 有限单元法 地下水流模拟 速度 流量 

分 类 号：P641.2[天文地球—地质矿产勘探]