Propagation of nonlinear travelling waves in Darcy-type porous media

A wave front expansion technique is used to analyze the nonlinear wave propagation in one-dimensional, unsteady, compressible flow in a Darcy-type porous media. The analysis leads to an evolution equation for the slope of the wave front. This is an ordinary differential equation, which can be integrated to obtain a closed form solution. The solution may admit a singularity for compression waves. A general formula for the computation of shock formation distance is obtained. The effects of area variation, axial temperature gradient and porosity of the medium on the steepening of compressive wave front into a shock and the shock formation distance are investigated. Two examples highlighting these effects are also presented in the paper.