A new formulation of Signorini's type for seepage problems with free surfaces

• Published in: International journal for numerical methods in engineering Vol. 64; no. 1; pp. 1 - 16
• Main Authors: Zheng, H., Liu, D. F., Lee, C. F., Tham, L. G.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 07.09.2005; Wiley
• Subjects: Computational techniques; Exact sciences and technology; finite element; Flows through porous media; Fluid dynamics; free boundary problems; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Nonhomogeneous flows; Physics; seepage; variational inequality; Seepage; Singularity; free boundary problems; Solid inclusion; Signorini problem; finite element; Free boundary problem; Finite element method; Porous medium flow; Variational inequality; Variational calculus; Modelling; Surface potential; Numerical stability
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1345

A new variational inequality formulation for seepage problems with free surfaces is presented, in which a boundary condition of Signorini's type is prescribed over the potential seepage surfaces. This makes the singularity of seepage points eliminated and the location of seepage points determined easily. Compared to other variational formulations, the proposed formulation can effectively overcome the mesh dependency and significantly improve the numerical stability. A very challenging engineering example with complicated geometry and strong inhomogeneity is investigated in detail. Copyright © 2005 John Wiley & Sons, Ltd.