Adaptive Finite Element Analysis of Multi-Phase Problems



In the present thesis adaptive finite element procedures for multi-phase problems are developed and investigated. The considered multi-phase problems refer to porous soils, consisting of a soil skeleton and one or two fluid phases, in particular water and (compressed) air. Coupled formulations for soils can be applied to a broad range of geotechnical problems, covering consolidation, dewatering of soils under atmospheric conditions, as well as by means of compressed air and tunneling below the groundwater table.

An objective of an adaptive finite element analysis is the design of a spatial discretization with an optimum number of degrees of freedom, which fulfills a pre-specified level of accuracy. In general, this goal is achieved within several adaptive cycles, each of them consisting of a finite element analysis, the estimation of the error of the numerical results, mesh re-generation and - depending on the employed adaptive strategy - the transfer of data between different finite element meshes.

In this thesis two different adaptive strategies are applied. The first one is characterized by determination of error measures from incremental quantities, whereas the second one employs total quantities as the basis for the estimation of the spatial discretization error.

For the error estimation the well-known Superconvergent Patch Recovery method is employed. In the context of multi-phase problems it is applied separately to each phase. The updated mesh is generated by means of the Advancing Front Method on the basis of a mesh density function.

The application of the developed adaptive procedures is demonstrated in a numerical study, consisting of (i) the investigation of the flow of compressed air in a dry soil specimen, and (ii) the dewatering of water-saturated soil by means of compressed air.

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