Unsteady 1d exact solutions of non-darcy flow in post-failure rock

Coal will be still the main energy in China. Hence it isstill necessary to research various problems about coalmines In general,seepage flow in post-failure wall rock in coalmines is not controlled byDarcy' Law and described as a nonlinear penetrating system of theAhmed-Sunada's non-Darcy flow. In the present paper, some simple exactanalytical solutions of the partial differential equation set of unsteady1-D Ahmed-Sunada type flow are derived with the method of separatingvariables with addition (MSVA). The MSVA was developed recently by Cai andsuccessfully applied to derive many new analytical solutions. The unknownfunction F(x,y) is assumed to be F(x,y)=f(x)\cdot g(y) in the commonmethod of separating variable, while be F(x,y)=f(x)+g(y) in MSVA. As asequence, three simple exact analytical solutions of Ahmed-Sunada'snon-Darcy flow have been successfully derived.