Numerical solution of Richards’ equation remains challenging to get robust, accurate and cost-effective results, particularly for moving sharp wetting fronts. An adaptive strategy both space time is proposed deal with 2D fronts associated varying possibly vanishing diffusivity caused by nonlinearity, heterogeneity anisotropy. Adaptive stepping makes nonlinear convergence reliable backward diffe...

The non-equilibrium Richards equation is solved using a moving finite element method in this paper. The governing equation is discretized spatially with a standard finite element method, and temporally with second-order Runge-Kutta schemes. A strategy of the mesh movement is based on the work by Li et al. [R. Li, T. Tang and P. W. Zhang, A moving mesh finite element algorithm for singular probl...

In this chapter a general model for the two-phase fluid flow in porous media is presented, together with its simplified form, known as the Richards equation, which is applicable (under specific assumptions) to describe water flow in the vadose zone. In each case the governing equations are formulated at the Darcy scale, using the capillary pressure–saturation relationship and an empirical exten...

This report describes a new family of Newton-Krylov methods for solving nonlinear systems of equations arising from the solution of Richards’ equation and in fully implicit formulations in air-water systems. The basic approach is to perform secant (Broyden) updates restricted to the Krylov subspace generated by the GMRES iterative solver. This approach is introduced as Krylov-secant methods. On...