Seminario Dottorato: Numerical Solution of Richards' Equation

Wednesday 2 May 2012 - Mohammad Sayful Islam

ARGOMENTI: Seminars Ph.D. Program

Wednesday 2 May 2012 h. 15:00, room 2BC30
Mohammad Sayful Islam (Padova, Dip. Mat.)
"Numerical Solution of Richards' Equation"

As hydrological models become increasingly sophisticated (e.g., coupling with various meteorological, ecological, or biogeochemical components) and are applied in ever more computationally demanding contexts (e.g., the many realizations that are typically generated in parameter estimation, uncertainty analysis, data assimilation, or scenario studies), the need for robust, accurate, and efficient codes is greater than ever. The Richards equation for subsurface flow is highly nonlinear and requires iterative schemes for its solution. These schemes have been the subject of much research over the past two decades, but an effective all-purpose algorithm has thus far proven elusive. Ideally, rapid (quadratic as opposed to linear) and global (insensitive to initial guess) convergence is sought, in addition to applicability over a range of conditions (dry soils, storm-interstorm simulations, geological heterogeneity, 3D domains with complex boundary conditions, etc). Richards' equation can be mathematically formulated and numerically discretized in a variety of manners, and the specific form and scheme chosen will affect the mass balance behavior of the model. Using a mass conservative mixed formulation of Richards equation we implemented and tested a nested Newton-type algorithm (originally developed by Casulli and Zanolli, 2010) for solving Richards equation. Experimental results include a variable boundary condition 1D test case and a few multidimensional heterogeneous problems. The results show that judicious choice of the initial guess together with time-step adaptation ensure quadratic convergence for all tested flow regimes. We will discuss future challenges and implications in the context of modern hydrological simulators for real world applications.

Rif. int. C. Marastoni, T. Vargiolu

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