Study On Planar Linear Spline Curve Element Of FEMOL In Transient Seepage Field

Finite Element Method Of Lines(FEMOL)is a semi-analytical numerical analysis method proposed in the early 1990s.It has good adaptability to the shape of solving domain,less element division,high solving efficiency and precision.As a general numerical analysis method,FEMOL is firstly developed in the field of solid mechanics,which is the most mature field researched in FEMOL.The application of heat conduction problems has also been continuously improved by the research of our research group for many years.Some preliminary studies have also been conducted in the field of plane steady state seepage.In this paper,FEMOL is extended to the analysis of transient seepage problems and the main research work is as follows:(1)In space coordinate system,using the plane linear spline curve element to divide the whole solving area,then establishing the mapping of parameter elements based on Lagrange interpolation and cubic B-spline interpolation.Specially,in the direction of nodal line,Lagrange interpolation is used for the simple curve mapping and cubic B-spline interpolation is used for the complex curve mapping;While Linear Lagrange interpolation is used for the curve mapping of the other direction.Then mapping the plane linear spline curve element to the regular element in the interval of[-1,1].In time domain,because it's the initial study for transient seepage problem in this paper,backward difference scheme that is unconditionally stable and does not oscillate at larger time steps is adopted to discretize.Combined with the variational principle,the ordinary differential equations and the corresponding boundary conditions for solving transient seepage problems are finally formed,namely the solution format of FEMOL.(2)Using Fortran95 language,and the new version of ordinary differential equation solver-COL90,a program(TSFEMOL 1.0)for solving the transient seepage problem was developed.Users will obtain a continuous function of head in nodal line using COL90,and output any point of nodal line.The program applies to the first and second kind of boundary conditions,including the abrupt head boundaries and continuously varying head boundaries.The results of each time step are stored separately for easy viewing.(3)Writing an analytical example of transient seepage problems using the inverse solution method of elastic mechanics,and combing other analytic examples in references,then comparing the calculation results between FEMOL and analytic solution.The results show that FEMOL has a very high solving precision.Some complicated examples are constructed and compared the results of FEMOL with FEM.The results show that FEMOL is superior to FEM in the element division and calculation precision when dealing with such problems.And using the general post-processing software GID to generate the head field nephogram,realizing the visualization result display of FEMOL.