A novel vertex-centered finite volume method for solving Richards' equation and its adaptation to local mesh refinement

DOI10.1016/J.JCP.2024.112766MaRDI QIDQ6126553

Xiaoping Zhang, Alberto Guadagnini, Yan Zhu, Yingzhi Qian, Jiesheng Huang, Lili Ju

Publication date: 9 April 2024

Published in: Journal of Computational Physics (Search for Journal in Brave)

zbMATH Keywords

nonmatching gridsRichards' equationvertex-centered finite volume methodsoil water movementlocally refined meshes

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Flows in porous media; filtration; seepage (76Sxx)

Cites Work

• An open source massively parallel solver for Richards equation: mechanistic modelling of water fluxes at the watershed scale
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• A multiscale finite element method for elliptic problems in composite materials and porous media
• A study on iterative methods for solving Richards' equation
• A mortar mixed finite volume method for elliptic problems on non-matching multi-block triangular grids
• A vertex-centered and positivity-preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids
• Vertex-centered linearity-preserving schemes for nonlinear parabolic problems on polygonal grids
• Relationship between the vertex-centered linearity-preserving scheme and the lowest-order virtual element method for diffusion problems on star-shaped polygons
• A fully interior penalty discontinuous Galerkin method for variable density groundwater flow problems
• Multiphase flow in heterogeneous porous media: A classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach
• CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS
• A vertex‐centered and positivity‐preserving scheme for anisotropic diffusion equations on general polyhedral meshes

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