Numerical simulation of 3D unsaturated infiltration from point sources in porous media

In this paper, we present an efficient method to simulate unsaturated water flow through porous media. Our method utilizes a two-step symmetrizable finite-difference algorithm and Newton's method for the nonlinear equations. Assuming that the air pressure is equal to zero, water does not contain any salt, soil matrix is not deformable, water in soil is incompressible, and water flow depends on capillary, gradient of mixture, and evapotranspiration only, we can solve the Richards equation separately from the equation for air phase. We demonstrate the results of simulation of three-dimensional infiltration from several buried point sources described by Dirac's delta function. It is found that our approach does not generate any oscillations of solution.