LAUSR

A pipe is located in a semi-infinite two-dimensional porous medium partially covered by a tarp. A constant pressure gradient may be imposed at infinity on the medium while air is pumped into the pipe. The governing Laplace equation is solved by extending the famous Keldysh–Sedov formulae to doubly connected domains by reduction of the mixed problem to a Riemann–Hilbert problem with discontinuous coefficients; the solution is obtained by combining factorization and functional equations. Then, the influence of the various geometrical and flow parameters is presented and discussed.