The Application Of Moving Mesh Method For Unsteady Seepage Computations

Seepage is an key factor for structure deformation and stability analysis of hydro and geotechnical engineering. Research of unsteady seepage is one of important study for seepage. With the development of computer technology, it is growing importance to study seepage with numerical simulation method. Finite element method is most popular in the numerical methods for Seepage Computations. To efficiently, simple apply finite element method for the calculation of seepage water head, it generally require fine element in the area with large hydraulic gradient and coarse element in the area with small hydraulic gradient. However, hydraulic gradient change over time for unsteady seepage, A fixed mesh generation is difficult to meet these requirements. The mathematical model of unsteady seepage is an evolution partial differential equation, because of the feature, we can calculate the unsteady seepage with the moving mesh method. Moving grid method is one of the adaptive mesh methods. Its main idea is that it decides the size of the grid in this local area according to the characteristics scale of the local area, and it non-equidistantly distributes the grid in the area so that the calculation error is equal or approximately equal in each grid. Specifically, the mesh become smaller in the regions where the solution largely changes, and the mesh is denser in that local area; the mesh become larger in the regions where the solution sparingly changes, and the number of mesh is less in that local area. Only the location of grid nodes change, the total number of grid nodes do not change in the process of the grid changes. We calculate the unsteady seepage with the moving mesh method based on harmonic maps in this work. It delinks the PDE solver and the mesh moving algorithm and can effectively avoid the meshes tangle with this method. We first derive the basic format of finite element analysis for unsteady seepage. We introduce a reference region, and the moving of mesh is achieved by an iterative process of regional transformation. We require interpolating the solution on the newly generated mesh after the grid moving. We also construct a monitor function on gradient. It can make the mesh refined or coarsened self-fulfilling based on the change of hydraulic gradient by calculating the monitor function. So the problem is solved well.The thesis is organized as follows. In Chapter 1, we give a overview for the research of seepage calculations and adaptive finite element method at home and abroad. Chapter 2 provides some introduction to the mathematical model of seepage and it's initial conditions and boundary conditions. In Chapter 3, the basic format of finite element analysis for unsteady seepage will be investigated. Chapter 4 is devoted to the discussions of the moving mesh method based on harmonic maps. Chapter 5 presents some numerical computations for engineering. Some consluding discussions are given in Chapter 6.