The Study Of Planar Linear Spline Curve Element Of FEMOL In Steady Seepage Field

Finite Element Method of Lines or FEMOL for short is a new type of numerical and analytical method whose software implementation is supported by ordinary differential equation solver.The application of this method is relatively mature in the area of solid mechanics,and it also has achieved a continuousdevelopment in the research of heat conduction,making it more and more functional in multiple areas.This thesis introduces the finite element method of lines to the study of two dimensionalsteadyseepage for the first time.The main contentsare as follows:1.Establishing a theoretical systemof the planar linear spline curve using finite element method of lines to discuss two dimensional steady seepage field.Setting up units mapping of FEMOL planar linear spline curve based on the cubic Cubic B Spline base function of interpolation and Lagrangebase function of linear interpolation.Using the.cubic B Cubic Spline interpolation as the unit connection and Lagrange linear interpolation as the unit end line,this thesis succeeds in mapping the irregular unit to a regular unit at element local coordinate within[-1,1].2.Using the variational principle,this thesis conducts the half discrete functionalvariation calculationof the two dimensional steady seepage field with the FEMOL unit of half plane linear spline curve.In order to get the ordinary differential equations(ODEs)and the corresponding boundary conditions(BCs)of the two dimensional steady seepage problem,the partial differential equation boundary value problem is converted into a functional extremum problem.3.On the theoreticalbasis of FEMOL mapping plane linear spline curve unit and the unit under the two dimensional steady seepage with functional variational calculation,this thesis uses FORTRAN 95 language to write a proprietary program SSFEM0L1.0 aiming at solving two-dimensional planar steady seepage,among which COLSYS upgraded version-COL90 is called as an ordinary differential equation solver,making this proprietary program more computationally efficient.4.According to the inverse method,this thesis writes the numerical examplerelated to two dimensional steady seepage,comparatively analyzes the solution from proprietary program SSFEMOL1.0,the analyticalsolutionand the solution from finite element method,and finally analyzes the precision and efficiency of different types of calculations.