Unsaturated Flow Simulation with Modified Transformation Methods

The chief goal of this research is to develop robust and practical numerical methods for solving the highly nonlinear partial differential equation describing unsaturated flow in porous media. A new combination approach consisting of a rational function transformation and a common under-relaxation technique is proposed to solve the finite element formulation of h-based form of Richards equation. Numerical studies show that this combination method outperforms previous numerical schemes in the sense that it can use larger time-steps and mesh sizes to produce acceptable results and also converge to a stable solution quickly in each time-step. Furthermore, the superiority of proposed approach is also identified when combined with different time stepping schemes in terms of efficiency that it takes less run time to produce solutions satisfying the requirements in accuracy. This book should be of special interest to researchers, civil engineers who will deal with unsaturated flow simulations.