A convolution model for the solution of the flow equation in multi-layered soils

In this paper the vertical flow equation in porous multi-layered soils is solved. The model makes use of the single-layer analitical solution expressed through convolution integrals. The N-layer case is solved by representing the unknown functions at the interfaces by constant piecewice approximations and setting (N-1) continuity conditions on the flow rate between two adjacent layers. A tridiagonal symmetric system of (N-1) linear equations is thus obtained and readily solved. Some numerical results are given, to show the accuracy and the efficiency of the convolution approach.