Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Finite element analysis of steady-state natural convection problems in fluid-saturated porous media heated from below

In this paper, a progressive asymptotic approach procedure is presented for solving the steady-state Horton-Rogers-Lapwood problem in a fluid-saturated porous medium. The Horton-Rogers-Lapwood problem possesses a bifurcation and, therefore, makes the direct use of conventional finite element methods difficult. Even if the Rayleigh number is high enough to drive the occurrence of natural convection in a fluid-saturated porous medium, the conventional methods will often produce a trivial non-convective solution. This difficulty can be overcome using the progressive asymptotic approach procedure associated with the finite element method. The method considers a series of modified Horton-Rogers-Lapwood problems in which gravity is assumed to tilt a small angle away from vertical. The main idea behind the progressive asymptotic approach procedure is that through solving a sequence of such modified problems with decreasing tilt, an accurate non-zero velocity solution to the Horton-Rogers-Lapwood problem can be obtained. This solution provides a very good initial prediction for the solution to the original Horton-Rogers-Lapwood problem so that the non-zero velocity solution can be successfully obtained when the tilted angle is set to zero. Comparison of numerical solutions with analytical ones to a benchmark problem of any rectangular geometry has demonstrated the usefulness of the present progressive asymptotic approach procedure. Finally, the procedure has been used to investigate the effect of basin shapes on natural convection of pore-fluid in a porous medium. (C) 1997 by John Wiley & Sons, Ltd.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Finite element analysis of mechanical properties in discontinuously reinforced metal matrix composites with ultrafine microstructure

This investigation focused on the finite element analyses of elastic and plastic properties of aluminium/alumina composite materials with ultrafine microstructure. The commonly used unit cell model was used to predict the elastic properties. By combining the unit cell model with an indentation model, coupled with experimental indentation measurements, the plastic properties of the composites and the associated strengthening mechanism within the metal matrix material were investigated. The grain size of the matrix material was found to be an important factor influencing the mechanical properties of the composites studied. (C) 1997 Elsevier Science S.A.

Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault

Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

Comparison of beam theory and finite-element analysis with in vivo bone strain data from the alligator cranium

The mechanical behavior of the vertebrate skull is often modeled using free-body analysis of simple geometric structures and, more recently, finite-element (FE) analysis. In this study, we compare experimentally collected in vivo bone strain orientations and magnitudes from the cranium of the American alligator with those extrapolated from a beam model and extracted from an FE model. The strain magnitudes predicted from beam and FE skull models bear little similarity to relative and absolute strain magnitudes recorded during in vivo biting experiments. However, quantitative differences between principal strain orientations extracted from the FE skull model and recorded during the in vivo experiments were smaller, and both generally matched expectations from the beam model. The differences in strain magnitude between the data sets may be attributable to the level of resolution of the models, the material properties used in the FE model, and the loading conditions (i.e., external forces and constraints). This study indicates that FE models and modeling of skulls as simple engineering structures may give a preliminary idea of how these structures are loaded, but whenever possible, modeling results should be verified with either in vitro or preferably in vivo testing, especially if precise knowledge of strain magnitudes is desired. (c) 2005 Wiley-Liss, Inc.

Biomechanics of the rostrum in crocodilians: A comparative analysis using finite-element modeling

This article reports the use of simple beam and finite-element models to investigate the relationship between rostral shape and biomechanical performance in living crocodilians under a range of loading conditions. Load cases corresponded to simple biting, lateral head shaking, and twist feeding behaviors. The six specimens were chosen to reflect, as far as possible, the full range of rostral shape in living crocodilians: a juvenile Caiman crocodilus, subadult Alligator mississippiensis and Crocodylus johnstoni, and adult Caiman crocodilus, Melanosuchus niger, and Paleosuchus palpebrosus. The simple beam models were generated using morphometric landmarks from each specimen. Three of the finite-element models, the A. mississippiensis, juvenile Caiman crocodilus, and the Crocodylus johnstoni, were based on CT scan data from respective specimens, but these data were not available for the other models and so these-the adult Caiman crocodilus, M. niger, and P. palpebrosus-were generated by morphing the juvenile Caiman crocodilus mesh with reference to three-dimensional linear distance measured from specimens. Comparison of the mechanical performance of the six finite-element models essentially matched results of the simple beam models: relatively tall skulls performed best under vertical loading and tall and wide skulls performed best under torsional loading. The widely held assumption that the platyrostral (dorsoventrally flattened) crocodilian skull is optimized for torsional loading was not supported by either simple beam theory models or finite-element modeling. Rather than being purely optimized against loads encountered while subduing and processing food, the shape of the crocodilian rostrum may be significantly affected by the hydrodynamic constraints of catching agile aquatic prey. This observation has important implications for our understanding of biomechanics in crocodilians and other aquatic reptiles.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

Large amplitude folding in finely layered viscoelastic rock structures

We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.

Analysis of steady-state heat transfer through mid-crustal vertical cracks with upward throughflow in hydrothermal systems

We conduct a theoretical analysis of steady-state heat transfer problems through mid-crustal vertical cracks with upward throughflow in hydrothermal systems. In particular, we derive analytical solutions for both the far field and near field of the system. In order to investigate the contribution of the forced advection to the total temperature of the system, two concepts, namely the critical Peclet number and the critical permeability of the system, have been presented and discussed in this paper. The analytical solution for the far field of the system indicates that if the pore-fluid pressure gradient in the crust is lithostatic, the critical permeability of the system can be used to determine whether or not the contribution of the forced advection to the total temperature of the system is negligible. Otherwise, the critical Peclet number should be used. For a crust of moderate thickness, the critical permeability is of the order of magnitude of 10(-20) m(2), under which heat conduction is the overwhelming mechanism to transfer heat energy, even though the pore-fluid pressure gradient in the crust is lithostatic. Furthermore, the lower bound analytical solution for the near field of the system demonstrates that the permeable vertical cracks in the middle crust can efficiently transfer heat energy from the lower crust to the upper crust of the Earth. Copyright (C) 2002 John Wiley Sons, Ltd.

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time-step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright (c) 2005 John Wiley & Sons, Ltd.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.