Comparison of Strongly-Convergent Solution Schemes for Sharp-Front InfiltrationProblems

摘要

Accurate and economical numerical solution of sharp-front problems remainfundamental concerns in water resources. Richards' equation (RE) was considered as a test problem for media properties and auxiliary conditions that resulted in the development and propagation of a sharp-front through a domain. Conventional modified Picard iteration (MPI) and Newton-Raphson iteration (NRI) methods were found to be unreliable, yielding non-convergent solutions for many discretization schemes. Strongly-convergent schemes were formulated based upon modifications to the NRI method, including method of lines formulations based upon ordinary differential equation or differential algebraic equation forms of the problem. Strongly-convergent methods were found to be much more robust than MPI or NRI methods. A model formulation based upon a transformed equation approach, which reduced the original nonlinearity present in the system, was found to offer further advantages over conventional approaches for some situations. (AN).