Hans-B. Mühlhaus

Lattice Boltzmann modeling and evaluation of fluid flow in heterogeneous porous media involving multiple matrix constituents

Geomaterials are typical heterogeneous porous media involving multiple types of matrix constituents which dominate the subsurface flow behavior. An improved lattice Boltzmann method (LBM) approach is developed for analyzing the detailed flow characteristics through multiple matrix constituents, investigating sample size effects on the permeability variation, and evaluating characteristic information at the representative elementary volume (REV) scale for the macroscale reference. Applications are conducted in both 2D and 3D to numerically investigate the impact of geometric topology and matrix property on the detailed velocity field, and effects of sample sizes on the permeability for evaluating effective REV scale fluid flow parameters. The simulation results demonstrate that the improved LBM approach is able to quantitatively describe and simulate complex fluid flow through multiple-matrix constructed heterogeneous porous media, which provides more realistic simulation results for up-scaled research and engineering. Quantitative modeling of detailed heterogeneous porous media flow involving multiple permeable minerals.Investigating sample size effects on the permeability variation and the flow flux.Evaluating characteristic information at the representative element volume (REV) scale for the macroscale reference.Providing meaningful REV scale parameters for relative up-scaling research.2D/3D applications in porous flows involving quartz, clay, feldspar and cavities.

Orientation of shear bands for a rigid plastic frictional material in simple shear

The orientation of shear bands is investigated analytically and numerically for a rigid plastic frictional material in simple shear. The model is based on co-axial flow rule, incompressible deformations and a friction factor which depends on the strain history. Since we are focussing on geological timescales, the influence of elasticity is neglected. Firstly, a linear stability analysis is performed confirming Rices 1976 assertion [The localization of plastic deformation, in Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, W.T. Koiter, ed., North Holland, Amsterdam, 1976, p.207] that, in the hardening regime, bifurcation is possible at every stage. Orientation of shear bands against the less compressive principal axis lies anywhere between the Roscoe and Coulomb angles, namely between π/4+ψ/2 and π/4 + ϕ/2, where ϕ and ψ are the mobilised angles of friction and dilatancy, respectively (in our study, we assume ψ = 0). The linear stability analysis leaves open the question of which orientation will actually emerge in a boundary value problem that consider all nonlinearities. This question is addressed in a finite element study of simple shear with periodic boundary conditions in the shear direction. Our simulations show temporary inclined shear bands in the hardening regime followed by a persistent horizontal shear band. A sensitivity study with respect to geometric and constitutive parameters indicates that the height of the sample controls the orientation of the inclined shear bands. Finally, we extend our analytical and numerical studies to Cosserat plasticity. It turns out that inclined shear bands are suppressed for large values of the internal length R (narrow bands). The case of a standard continuum is gradually recovered for small R (wide bands).

Numerical Investigation of Melt Segregation Using FEM Coding Environment Escript

Understanding of melt segregation and extraction is one of the major outstanding problems of melting processes in Earths mantle. The volcanoes that lie along the Earths tectonic boundaries are fed by melt that is generated in the mantle. However, it still remains unclear how this melt is extracted and finds its way towards the volcanoes. Two important mechanisms in melt segregation and migration are reactive fluid flow and mechanical shear. Reactive fluid flow describes the formation and segregation/migration of melt significantly affected by chemical interaction between melt and rock. This reactive-infiltration instability results in melt fingering which eases the transition from porous to channelized flow and provides a key element in some of the geological phenomena on earth. The second important mechanism in melt migration is localization due to mechanical shear. Recent studies have shown that when partially molten rock is subjected to simple shear, bands of high and low porosity are formed at a particular angle to the direction of maximum extension. Thus melt distribution is also influenced by stresses in partially molten rock [2,3]. The main aim of this paper is to identify the main mechanisms inducing melt segregation and effective flow. More specifically we investigate the melt reaction instability and melt band formation in this study. Here, in addition to providing a better understanding of melting phenomena in the mantle, we also develop a numerically validated model which can be used as an active and open source for future more complicated studies. For the melt bands problem, we employ the equations of magma migration in viscous materials which was originally derived by McKenzie (1984), and for the fingering instability problem we refer to the well known equations of reactive transport [4]. We write two different numerical codes using the FEM environment “escript”. We test the codes for a set of well-understood case problems which have been studied previously by other researchers.

Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection.We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codeswas firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8]and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

On lazy evaluation as a tool to optimize the efficiency of large scale numerical simulations in Python

Scientists working on mathematical models want to concentrate on the design of models. They pay little attention to numerical methods such as the finite element method (FEM), their implementation and parallelization. The escript module in python provides an environment in which scientists can define new models using a language of partial differential equation (PDE) and spatial functions which is natural for the formulation of continuous models. This approach defines a high level of abstraction from the underlying data structures and frees modelers from issues of optimized implementation and parallelization. In its current implementation escript evaluates expressions which define PDE coefficients immediately for all nodes or elements of an FEM mesh. In the paper we will demonstrate that for complex rheologies such as the Drucker-Prager plasticity model, the memory requirements for this strategy are the limiting factor for scaling up the mesh size. The python module is backed by an escript C++ library where the processing is performed. We will discuss an new extension to the PDE coefficient handling provided by this C++ library which uses a lazy evaluation technique and will demonstrate the efficiency of this new extension in terms of compute time and memory usage for a practical engineering application, namely the simulation of elastic-plastic, saturated porous media

ACcESS: Australia's contribution to the iSERVO Institute's development

Solid earth systems simulation is now becoming feasible from the microscopic to the global scale. The ACES international cooperation has shown development of simulation capabilities for solid earth phenomena that are beyond the ability of a single group or country. Each country has different strengths, computational approaches, and laboratory and field observational systems. This range of numerical models is required to model the entire earth system, and calibration is required to ensure that results obtained using these models match with the different laboratory and field observations available in each country. For this reason, international groups have agreed to work toward establishing iSERVO to build the ACES cooperation. iSERVO aims to collaboratively develop a computational infrastructure - accessible through Web portals - that combines models developed across the international community and to conduct collaborative research to solve problems of global significance such as earthquake forecasting, green energy development, and environmental management. The new Australian Computational Earth Systems Simulator research facility provides a virtual laboratory for studying the solid Earth and its complex system behavior. The facilitys capabilities complement those developed by overseas groups, thereby creating the infrastructure for an international computational solid earth research virtual observatory.

Texture alignment in simple shear

We illustrate the flow behaviour of fluids with isotropic and anisotropic microstructure (internal length, layering with bending stiffness) by means of numerical simulations of silo discharge and flow alignment in simple shear. The Cosserat theory is used to provide an internal length in the constitutive model through bending stiffness to describe isotropic microstructure and this theory is coupled to a director theory to add specific orientation of grains to describe anisotropic microstructure. The numerical solution is based on an implicit form of the Material Point Method developed by Moresi et al. [1].