Comparison of Finite Difference Schemes for Fluid Flow in Unsaturated Porous Medium (Soil)

Water movement in an unsaturated porous medium (soil) can be expressed by Richards equation with the mass conservation law and Darcy-Buckingham's law. This equation can be expressed in three different forms as pressure head-based, moisture content based and mixed from. In this study, we solve one dimensional Richards Equation in mixed form numerically using finite difference method with various time-stepping schemes: Forward Euler, Backward Euler, Crank-Nicolson and a Stabilized Runge-Kutta-Legendre Super Time-Stepping and we compare their performances using Dirichlet boundary condition on an isotropic homogeneous vertical soil column.