Preliminary Study On Transient Flow By BEM

The study on seepage problem in geotechnical engineering by using Boundary Element Method( BEM) is of engineering importance. So far, regarding boundary element analysis to the problem of seepage in geotechnical engineering, there is no commonly accepted computing method, especially for the transient flow problem, in which the time is considered. Among the current treatments of the transient flow by using BEM, the internal integration terms are included in the boundary integral equations, leading to the elevated computation. Therefore, it is proposed to simplify the computation of the internal integration terms by introducing the coordinate functions into the integrals. The study in this thesis includes the derivation of the boundary integral equation, the simplification of the internal integration terms by using coordinate functions, the discretization of the boundary integral equation and the solution of the boundary integral equation.In the process of dealing with the nonlinear integral terms in the governing equations for the problem of transient flow, the coordinate functions are proposed to express the nonlinear integral terms. Two kinds of reference points are chosen in this thesis, one kind on the boundary and the other kind both on the boundary and in the domain. Accordingly, two kinds of coordinate functions are also chosen to present the distance between the field point and the reference point. After that, the Green formula and the fundamental solution are used. The Green formula is used in the first round to simplify the flow equation, to obtain the preliminary boundary integral equation, and the Green formula is used in the second round to finalize the boundary integral equation.In the process of the discretization of the boundary integral equation, both the constant boundary element and the linear boundary element are used. In the application of the linear boundary element, meaningless coordinate matrix is encountered for the outwards normal flow at the corners. The corner treatment by assigning dual flow values to a corner node is proposed for the matrix.When the reference point is in the domain, the boundary integral equations can be classified into two categories. One is that the reference point only exist s on the boundary, while the other is that the reference point only exists on the domain. The values of the boundary nodes are obtained first. Subsequently, the boundary integral equations for the internal points are obtained. Finally, the expression of the boundary integral equation incorporating both boundary points and internal points are obtained. The conclusions are as follows:(1) The transient seepage boundary integral equations both for isotropic materials are deduced.(2) By introducing the coordinate functions, the transient seepage boundary integral equations for anisotropic materials are also deduced.(3) The corner treatment by assigning dual flow values to a corner node is proposed to deal with the meaningless in the matrix.(4) The Matlab program of transient flow by boundary element method is coded.(5) The comparison results between the results from analytical solutions and the BEM show high modeling accuracy.