Modeling, with a unified level-set representation, of the expansion of a hollow in the ground under different physical phenomena

Abstract

This paper builds on the flexibility of the level-set representation to model in a unified manner the expansion of a hollow in the ground under different physical phenomena. In particular, the dissolving action of a flow of water in a saturated soil, and that of a jet of particles of water in a nonsaturated one, are represented in a common framework. In that manner, the complex geometrical evolutions of the hollow can be followed without the need for remeshing and this approach allows for a smooth transition between saturated and non-saturated models of the soil. Implementation and numerical difficulties are discussed and two applications of industrial interest are considered. The first one describes the modeling of the piping phenomenon, and the second one the evolution of an excavation created by a leaking duct.

A stable extended FEM formulation for multi‐phase problems enforcing the accuracy of the fluxes through Lagrange multipliers

“…Authors have therefore proposed alternative approaches. Among those, the generalized and extended finite element methods (GFEM/XFEM) have been widely developed [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In these methods, the classical FEM basis, using polynomials over each element, is enriched with functions that incorporate information about the interface.…”