Arash Mohajeri

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.

Coupled Mechanical-Hydrological-Chemical Problems in Elasto-plastic Saturated Soils and Soft Rocks Using escript

The understanding of chemical effects on mechanical behavior of porous media is a key element in the solution of problems in geology, mining, soil, rock and environmental engineering. In order to develop this understanding, the current work employs a new set of equations to numerically investigate the coupled mechanical-hydrological-chemical (MHC) problem for soils and soft rocks. The objectives of this research are to observe the soil and soft rock behavior under mechanical loading and chemical erosion and also to validate the application of our solver algorithm written in a finite element programming environment “escript”.

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