Improving on near-surface field evaluation in the boundary-element method

A method for removing the numerical instability of the conventional Green's formula in the vicinity of the boundary surface is proposed. The approach uses a pair of Green's formulae written both inside and outside the volume of interest, even when used for solving a single-phase problem. It is shown that cancellation between the pair yields an alternative, singularity-free integral representation that is amenable to numerical calculation. The derivation of the formula is given explicitly and is accompanied by several numerical test results for validation.     

Monolithic cut finite element–based approaches for fluid-structure interaction

Cut finite element method–based approaches toward challenging fluid-structure interaction (FSI) are proposed. The different considered methods combine the advantages of competing novel Eulerian (fixed grid) and established arbitrary Lagrangian-Eulerian (moving mesh) finite element formulations for the fluid. The objective is to highlight the benefit of using cut finite element techniques for moving-domain problems and to demonstrate their high potential with regard to simplified mesh generation, treatment of large structural motions in surrounding flows, capturing boundary layers, their ability to deal with topological changes in the fluid phase, and their general straightforward extensibility to other coupled multiphysics problems. In addition to a pure fixed-grid FSI method, advanced fluid-domain decomposition techniques are also considered, leading to highly flexible discretization methods for the FSI problem. All stabilized formulations include Nitsche-based weak coupling of the phases supported by the ghost penalty technique for the flow field. For the resulting systems, monolithic solution strategies are presented. Various two- and three-dimensional FSI cases of different complexity levels validate the methods and demonstrate their capabilities and limitations in different situations.     

Extended space–time finite elements for landslide dynamics

The paper introduces a methodology for numerical simulation of landslides experiencing considerable deformations and topological changes. Within an interface capturing approach, all interfaces are implicitly described by specifically defined level‐set functions allowing arbitrarily evolving complex topologies. The transient interface evolution is obtained by solving the level‐set equation driven by the physical velocity field for all three level‐set functions in a block Jacobi approach. The three boundary‐coupled fluid‐like continua involved are modeled as incompressible, governed by a generalized non‐Newtonian material law taking into account capillary pressure at moving fluid–fluid interfaces. The weighted residual formulation of the level‐set equations and the fluid equations is discretized with finite elements in space and time using velocity and pressure as unknown variables. Non‐smooth solution characteristics are represented by enriched approximations to fluid velocity (weak discontinuity) and fluid pressure (strong discontinuity). Special attention is given to the construction of enriched approximations for elements containing evolving triple junctions. Numerical examples of three‐fluid tank sloshing and air–water‐liquefied soil landslides demonstrate the potential and applicability of the method in geotechnical investigations. Copyright © 2012 John Wiley & Sons, Ltd.