Analytical and Numerical Aspects of Porous Media Flow

The Brinkman equations model fluid flow through porous media and are particularly interesting in regimes where viscous shear effects cannot be neglected. Two model parameters in the momentum balance function as weights for the terms related to inter-particle friction and bulk resistance. If these are not in balance, then standard finite element methods might suffer from instabilities or error estimates might deteriorate. In particular the limit case, where the Brinkman problem reduces to a Darcy problem, demands for special attention. This thesis proposes a low-order finite element method which is uniformly stable with respect to the flow regimes captured by the Brinkman model, including the Darcy limit. To that end, linear equal-order approximations are combined with a pressure stabilization technique, a grad-div stabilization, and a penalty-free non-symmetric Nitsche method. The combination of these ingredients allows to develop a robust method, which is proven to be well-posed for the whole family of problems in two spatial dimensions, even if any Brinkman parameter vanishes. An a priori error analysis reveals optimal convergence in the considered norm. A convergence study based on problems with known analytic solutions confirms the robust first order convergence for reasonable ranges of numerical (stabilization) parameters. Further, numerical investigations that partly extend the theoretical framework are considered, revealing strengths and weaknesses of the approach. An application motivated by the optimization of geothermal energy production completes the thesis. Here, the proposed method is included in a multi-physics discrete model, appropriate to describe the thermo-hydraulics in hot, sedimentary, essentially horizontal aquifers. An immersed boundary method is adopted in order to allow a flexible, automatic optimization without regenerating the computational mesh. Utilizing the developed computational framework, the optimized multi-well arrangements with respect to the net energy gain are presented and discussed for different geothermal and hydrogeological setups. The results show that taking into account heterogeneous permeability structures and variable aquifer temperatures might drastically affect the optimal configuration of the wells

A Computational model for fluid-porous structure interaction

This work utilizes numerical models to investigate the importance of poroelasticity in Fluid- Structure Interaction, and to establish a connection between the apparent viscoelastic behavior of the structure part and the intramural filtration flow. We discuss a loosely coupled computational framework for modeling multiphysics systems of coupled flow and mechanics via finite element method. Fluid is modeled as an incompressible, viscous, Newtonian fluid using the Navier-Stokes equations and the structure domain consists of a thick poroelastic material, which is modeled by the Biot system. Physically meaningful interface conditions are imposed on the discrete level via mortar finite elements or Nitsche's coupling. We further discuss the use of our loosely coupled non-iterative time-split formulation as a preconditioner for the monolithic scheme. We further investigate the interaction of an incompressible fluid with a poroelastic structure featuring possibly large deformations, where the assumption of large deformations is taken into account by including the full strain tensor. We use this model to study the influence of different parameters on energy dissipation in a poroelastic medium. The numerical results investigate the effects of poroelastic parameters on the pressure wave propagation, filtration of the incompressible fluid through the porous media, and the structure displacement

Aeronautical engineering: A cumulative index to a continuing bibliography (supplement 235)

This publication is a cummulative index to the abstracts contained in Supplements 223 through 234 of Aeronautical Engineering: A Continuing Bibliography. The bibliographic series is compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). Seven indexes are included -- subject, personal author, corporate source, foreign technology, contract number, report number and accession number