Numerical Identification of Boundary Conditions for Richards’ Equation

Abstract

A time stepping quasilinearization approach to the mixed (or coupled) form of one and two dimensional Richards’ equations is developed. For numerical solution of the linear ordinary differential equation (ODE) for 1D case and elliptic for 2D case, obtained after this semidiscretization, a finite volume method is used for direct problems arising on each time level. Next, we propose a version of the decomposition method for the numerical solution of the inverse ODE and 2D elliptic boundary problems. Computational results for some soil types and its related parameters reported in the literature are presented.

Keywords

• soil-water flow
• Richards’ equation
• inverse boundary condition problem
• ODE system
• Bellman-Kalaba quasilinearization
• decomposition of the solution