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Adaptive moving mesh methods for simulating one‐dimensional groundwater problems with sharp moving fronts
Author(s) -
Huang Weizhang,
Zheng Li,
Zhan Xiaoyong
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.482
Subject(s) - partial differential equation , interpolation (computer graphics) , advection , adaptive mesh refinement , computer science , mesh generation , grid , flow (mathematics) , mathematical optimization , mathematics , algorithm , computational science , finite element method , geometry , mathematical analysis , physics , artificial intelligence , motion (physics) , thermodynamics
Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non‐linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two‐layer mesh movement. Copyright © 2002 John Wiley & Sons, Ltd.