Solution of Velocity at Moving Interfaces between Fresh-and Salt-Water in Aquifers

A method based on the Schwarz-Christoffcl trans-formation is developed for the solution of velocity at moving interfaces between fresh-and salt-water in aquifers. It involves the following primary steps:(1)Map the given fresh-and salt-water regions of the flow plane Z onto the upper halves of auxiliary planes t_f and t_s, respectively. (2) Use a mapping between the planestfandl,and the complex potential planes w_f and w_s to set up equations for the side-length rations of complex potential polygons,containing some geometric parameters,so that the problem becomes one of solution for the parameters. (3) Set up equations for boundary conditions, including those of fresh-water influx and material interface. (4) Solve the coupled equations for the velocity at interfaces. A main distinction between the method and common numerical methods is direct solution of the velocity without discretizing flow regions, leading to smaller error. An example shows that the method is both feasible and effective.