Solving Seepage Problem in Irregular Geometries Using a Moving Finite Volume Method

摘要

The main objective of this work is to develop a novel moving mesh finite-volume method capable of solv- ing the seepage problem in irregular geometries. The major difficulty in seepage problem is the location of phreatic boundary which is not known at the begin- ning of the analysis. In the current algorithm, we sup- pose an arbitrary solution domain with an hypothe- sis phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement for a cell on a curvilinear coordinate system and im- plement the known boundary conditions all over the solution domain. Defining a consistency factor, the in- consistency between the hypothesis boundary and the known boundary conditions is measured at that bound- ary. This factor is utilized to improve the phreatic boundary location and redistribute the initial mesh and cells properly. Therefore, the distributed finite vol- umes are gradually reshaped during the solution pro- cess. The process is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the new developed numerical method, a seepage problem which has been previously solved by the other investigators in the fields of finite- element and finite-difference methods is examined. Comparisons of the current results with those of oth- ers shows that the current moving grid finite-volume method essentially improves the reliability and accu- racy of the solution. Eventually, the validated code is utilized to study the seepage problem through a newly constructed earth dam.