generation of coarse scale continuum flow models from detailed fracture characterizations 1 a procedure for developing coarse scale continuum models from detailed fracture descriptions is developed and applied the coarse models are in the form of a generalized dual porosity representation in which matrix rock and fractures exchange fluid locally while large scale flow occurs through the fracture network the methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse scale parameters describing fracture fracture matrix fracture and matrix matrix flow the geometry of the local subgrids as well as the required parameters for the coarse scale model are determined from local flow solutions using the underlying discrete fracture model the method is applied to two and three dimensional single phase and two phase flow problems and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations for the cases considered it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations and speedups of about a factor of 100 are achieved

numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media a numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented the method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield upon appropriate averaging of the fine scale velocity field the coarse scale or equivalent grid block permeability when the region over which this coarse scale permeability is computed constitutes a representative elementary volume rev the resulting equivalent permeability may be interpreted as the effective permeability of the region solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle based finite element numerical procedure which allows for the modeling of geometrically complex features the specification of periodic boundary conditions is shown to yield symmetric positive definite equivalent permeability tensors in all cases the method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields the applicability and limitations of the method for these more general heterogeneity fields are discussed

localization and regularization behavior of mixed finite elements for 2d structural problems with damaging material abstract a class of lagrangian mixed finite elements is presented for applications to 2d structural problems based on a damage constitutive model attention is focused on localization and regularization issues as compared with the correspondent behavior of lagrangian displacement based elements a non local regularization procedure of integral type is adopted a predictor corrector technique is used to solve the evolution problem of the damage variable the proposed elements show superior performances for typical structural applications

generation of complex bipartite graphs by using a preferential rewiring process it is important in computer science sociology and so on to investigate complex bipartite graphs from a viewpoint of statistical physics we propose a model to generate complex bipartite graphs without growing the bipartite graphs are assumed to have two sets of the fixed numbers of nodes and a fixed number of edges between nodes belonging to different sets of nodes in this model essential ingredients are a preferential rewiring process and a fitness distribution function by using the preferential rewiring process we confirm that a bipartite graph reaches a stationary state after a sufficiently long time has passed we find that the obtained bipartite graph has a scale free like property when a suitable fitness distribution is used it turns out that a condensation of edges takes place in the cases of certain fitness distributions

compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification abstract the paper deals with the numerical solution of a compositional model describing compressible two phase flow of a mixture composed of several components in porous media with species transfer between the phases the mathematical model is formulated by means of the extended darcy s laws for all phases components continuity equations constitutive relations and appropriate initial and boundary conditions the splitting of components among the phases is described using a new formulation of the local thermodynamic equilibrium which uses volume temperature and moles as specification variables the problem is solved numerically using a combination of the mixed hybrid finite element method for the total flux discretization and the finite volume method for the discretization of transport equations a new approach to numerical flux approximation is proposed which does not require the phase identification and determination of correspondence between the phases on adjacent elements the time discretization is carried out by the backward euler method the resulting large system of nonlinear algebraic equations is solved by the newton raphson iterative method we provide eight examples of different complexity to show reliability and robustness of our approach

adaptive implicit finite element methods for multicomponent compressible flow in heterogeneous and fractured porous media this work presents adaptive implicit first order and second order discontinuous galerkin dg methods for the transport of multicomponent compressible fluids in heterogeneous and fractured porous media discretized by triangular quadrilateral and hexahedral grids the adaptive implicit method aim combines the advantages of purely explicit or implicit methods in time in grid cells with high fluxes or low pore volumes the transport update is done implicitly to alleviate the courant friedrichs lewy cfl time step constraints of the conditionally stable explicit approach grid cells with a large cfl condition are updated explicitly combined this allows higher efficiency than explicit methods but it reduces the penalty of implicit methods which exhibit high numerical dispersion and are more computationally and storage expensive per time step the advantages of aim are modest for uniform grids and rock properties however in heterogeneous or fractured reservoirs explicit methods may become impractical while a fully implicit approach introduces unnecessary numerical dispersion and is overkill for low permeability layers and matrix blocks in such applications aim is shown to be significantly more efficient and accurate the division between explicit and implicit grid cells is made adaptively in space and time this allows for a high level of explicitness and can also adapt to high fluxes caused by e g viscous and gravitational flow instabilities numerical examples demonstrate the powerful features of aim to model e g solute transport carbon sequestration in saline aquifers and miscible gas injection in fractured oil and gas reservoirs

a mixed multiscale finite element method for elliptic problems with oscillating coefficients the recently introduced multiscale finite element method for solving elliptic equations with oscillating coefficients is designed to capture the large scale structure of the solutions without resolving all the fine scale structures motivated by the numerical simulation of flow transport in highly heterogeneous porous media we propose a mixed multiscale finite element method with an over sampling technique for solving second order elliptic equations with rapidly oscillating coefficients the multiscale finite element bases are constructed by locally solving neumann boundary value problems we provide a detailed convergence analysis of the method under the assumption that the oscillating coefficients are locally periodic while such a simplifying assumption is not required by our method it allows us to use homogenization theory to obtain the asymptotic structure of the solutions numerical experiments are carried out for flow transport in a porous medium with a random log normal relative permeability to demonstrate the efficiency and accuracy of the proposed method

modeling the large scale dynamics of saturated groundwater flow using spatial filtering theory 1 theoretical development we develop a model and a framework for understanding the explicitly resolved large scale dynamics of groundwater flow in fully saturated heterogeneous porous media the approach is based upon the large eddy simulation les methodology from geophysical fluid dynamics the idea behind the les approach is to explicitly resolve the larger scales of flow and provide a closure model for the effect of subgrid scales upon resolved scales the technical foundation of the method rests on a spatial filtering operation which allows one to precisely define the scale of the model we spatially filter darcy s law and the continuity equation to produce a model for the resolved scale dynamics we develop les approximations for the resulting flow equations and a closure model for unresolved subgrid scale terms we model the subgrid terms using resolved scale quantities only and thus do not require subgrid scale information the accuracy of these closure models depends upon the scale at which hydraulic conductivity is measured by field tests we characterize the approximations used to model subgrid scale effects asymptotically with a small parameter the dimensionless filter width defined as the ratio of the filter width to the dominant length scale of the explicitly resolved variables

convergence of a nonconforming multiscale finite element method the multiscale finite element method msfem t y hou x h wu and z cai math comp 1998 to appear t y hou and x h wu j comput phys 134 1997 pp 169 189 has been introduced to capture the large scale solutions of elliptic equations with highly oscillatory coefficients this is accomplished by constructing the multiscale base functions from the local solutions of the elliptic operator our previous study reveals that the leading order error in this approach is caused by the resonant sampling which leads to large error when the mesh size is close to the small scale of the continuous problem similar difficulty also arises in numerical upscaling methods an oversampling technique has been introduced to alleviate this difficulty t y hou and x h wu j comput phys 134 1997 pp 169 189 a consequence of the oversampling method is that the resulting finite element method is no longer conforming here we give a detailed analysis of the nonconforming error our analysis also reveals a new cell resonance error which is caused by the mismatch between the mesh size and the wavelength of the small scale we show that the cell resonance error is of lower order our numerical experiments demonstrate that the cell resonance error is generically small and is difficult to observe in practice

a residual based a posteriori error estimator for single phase darcy flow in fractured porous media in this paper we develop an a posteriori error estimator for a mixed finite element method for single phase darcy flow in a two dimensional fractured porous media the discrete fracture model is applied to model the fractures by one dimensional fractures in a two dimensional domain we consider raviart thomas mixed finite element method for the approximation of the coupled darcy flows in the fractures and the surrounding porous media we derive a robust residual based a posteriori error estimator for the problem with non intersecting fractures the reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm numerical results verifying the robustness of the proposed a posteriori error estimator are given moreover our numerical results indicate that the a posteriori error estimator also works well for the problem with intersecting fractures

discontinuous galerkin finite element convergence for incompressible miscible displacement problems of low regularity in this article we analyze the numerical approximation of incompressible miscible displacement problems with a combined mixed finite element and discontinuous galerkin method under minimal regularity assumptions the main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem in order to deal with the nonconformity of the method and to avoid overpenalization of jumps across interelement boundaries the careful construction of a reflexive subspace of the space of bounded variation which compactly embeds into l 2 omega and of a lifting operator which is compatible with the nonlinear diffusion coefficient are required an equivalent skew symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows us to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method numerical experiments underline the robustness of the proposed algorithm

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

physics based preconditioners for flow in fractured porous media discrete fracture models are an attractive alternative to upscaled models for flow in fractured media as they provide a more accurate representation of the flow characteristics a major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large scale simulations in this work two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations first the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there this assures good scalability of the preconditioners in terms of problem size and permeability contrast for fracture dominated problems numerical examples show that such geometric preconditioners are comparable or preferable when compared to state of the art algebraic multigrid preconditioners the robustness of the physics based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy second the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions this facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates and without sacrificing basic physical modeling principles with the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers

numerically consistent regularization of force based frame elements recent advances in the literature regularize the strain softening response of force based frame elements by either modifying the constitutive parameters or scaling selected integration weights although the former case maintains numerical accuracy for strain hardening behavior the regularization requires a tight coupling of the element constitutive properties and the numerical integration method in the latter case objectivity is maintained for strain softening problems however there is a lack of convergence for strain hardening response to resolve the dichotomy between strain hardening and strain softening solutions a numerically consistent regularization technique is developed for force based frame elements using interpolatory quadrature with two integration points of prescribed characteristic lengths at the element ends owing to manipulation of the integration weights at the element ends the solution of a vandermonde system of equations ensures numerical accuracy in the linear elastic range of response comparison of closed form solutions and published experimental results of reinforced concrete columns demonstrates the effect of the regularization approach on simulating the response of structural members copyright 2008 john wiley sons ltd

growing network with local rules preferential attachment clustering hierarchy and degree correlations the linear preferential attachment hypothesis has been shown to be quite successful in explaining the existence of networks with power law degree distributions it is then quite important to determine if this mechanism is the consequence of a general principle based on local rules in this work it is claimed that an effective linear preferential attachment is the natural outcome of growing network models based on local rules it is also shown that the local models offer an explanation for other properties like the clustering hierarchy and degree correlations recently observed in complex networks these conclusions are based on both analytical and numerical results for different local rules including some models already proposed in the literature

local rewiring rules for evolving complex networks abstract the effects of link rewiring are considered for the class of directed networks where each node has the same fixed out degree we model a network generated by three mechanisms that are present in various networked systems growth global rewiring and local rewiring during a rewiring phase a node is randomly selected one of its out going edges is detached from its destination then re attached to the network in one of two possible ways either globally to a randomly selected node or locally to a descendant of a descendant of the originally selected node although the probability of attachment to a node increases with its connectivity the probability of detachment also increases the result is an exponential degree distribution with a small number of outlying nodes that have extremely large degree we explain these outliers by identifying the circumstances for which a set of nodes can grow to very high degree

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

a high order fully coupled upwind compact discontinuous galerkin method for modeling of viscous fingering in compressible porous media abstract we present a new approach for high fidelity compressible porous media simulations our method is based on a fully coupled upwind high order discontinuous galerkin formulation of the equations of miscible displacement transport a key feature of the proposed method is the high level of flexibility to compute complex subsurface geometries maintaining full order of accuracy the present formulation solves pressure and transport equations in a fully coupled fashion and as a result can capture the strong interaction between pressure and concentrations of injected components in highly compressible media the proposed method also shows very low sensitivity to mesh orientation in contrast with classical finite volume approximations used in porous media flow simulations the robustness and accuracy of the method are demonstrated in a number of challenging compressible and incompressible multiphase flow problems numerical simulations also reveal interesting phenomena associated with high pore compressibility such as the reduction of the growth rate of viscous fingers and the alteration of flow patterns near impermeable obstacles additional computations performed with an anisotropic permeability tensor reveal that somewhat against intuition viscous fingers have a preferential growth along the direction of low permeability

a fully coupled upwind discontinuous galerkin method for incompressible porous media flows high order computations of viscous fingering instabilities in complex geometry we present a new approach to the simulation of viscous fingering instabilities in incompressible miscible displacement flows in porous media in the past high resolution computational simulations of viscous fingering instabilities have always been performed using high order finite difference or fourier spectral methods which do not posses the flexibility to compute very complex subsurface geometries our approach instead by means of a fully coupled nonlinear implementation of the discontinuous galerkin method possesses a fundamental differentiating feature in that it maintains high order accuracy on fully unstructured meshes in addition the proposed method shows very low sensitivity to mesh orientation in contrast with classical finite volume approximation used in porous media flow simulations the robustness and accuracy of the method are demonstrated in a number of challenging computational problems

a new approach to simulating flow in discrete fracture networks with an optimized mesh natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels fractures are by themselves heterogeneous objects of broadly distributed sizes shapes and orientations that are interconnected in large correlated networks with little field data and evidence numerical modeling can provide important information on the underground hydraulic phenomena however it must overcome several barriers first the complex network structure produces a structure difficult to mesh second the absence of a priori homogenization scale along with the double fracture and network heterogeneity levels requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains to tackle these two related issues we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental geological and geometrical characteristics we show that the flow properties are marginally affected while the problem complexity i e memory capacity and resolution time can be divided by orders of magnitude the goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures the principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision

implementation of higher order methods for robust and efficient compositional simulation numerical simulation of two phase multicomponent flow in permeable media with species transfer between the phases often requires use of higher order methods unlike first order methods higher order methods may be very sensitive to problem formulation the sensitivity to problem formulation and lack of recognition have hindered the widespread use of higher order methods in various problems including improved oil recovery and sequestration from co 2 injection in this work we offer proper formulation of species balance equations and boundary conditions which overcome problems of formulations used previously that were detrimental to the efficiency of higher order methods we also present proper approximation of phase fluxes in the mixed finite element method our proposals remove major deficiencies in using higher order methods in two phase multicomponent flow numerical examples are presented to demonstrate robustness and efficiency of our approach

efficient finite element formulation for the analysis of localized failure in beam structures this paper presents a finite element formulation for the analysis of localized failures in beam structures each member is considered to be a prismatic body that in case of a localized failure is divided by a singular surface into two elastic bulks the fracture process on this surface is described by the cohesive crack concept using a traction separation law a plane cross section is assumed which implies a link between the continuous and the structural classical beam theory description of the beam for the numerical treatment of the model a finite beam element exhibiting an internal interface is proposed whereas the strong discontinuities are approximated by means of additional degrees of freedom that are placed at the centroid of the singular surface hence each bulk can be described individually by a common beam element with the normal set of nodal degrees of freedom whereas the singular surface is described layer wise the residuum vector and the symmetric stiffness matrix of the resulting element are obtained by assembling the contributions of the two bulks and the singular surface and afterwards by eliminating the additional degrees of freedom by a static condensation the formulation which does not change the global degrees of freedom is numerically very efficient especially in the case of extensive beam structures and can easily be implemented in any conventional finite element code several numerical examples are provided to demonstrate the effectiveness and the robustness of the proposed method the equilibrium iterations show an optimal convergence rate even if many cracks emerge simultaneously the results do not exhibit any artificial mesh dependencies or artificial stress locking effects copyright 2007 john wiley sons ltd

an efficient multi point flux approximation method for discrete fracture matrix simulations we consider a control volume discretization with a multi point flux approximation to model discrete fracture matrix systems for anisotropic and fractured porous media in two and three spatial dimensions inspired by a recently introduced approach based on a two point flux approximation we explicitly account for the fractures by representing them as hybrid cells between the matrix cells as well as simplifying the grid generation our hybrid approach excludes small cells in the intersection of the fractures and hence avoids severe time step restrictions associated with small cells excluding the small cells also reduces the condition number of the discretization matrix for examples involving realistic anisotropy ratios in the permeability numerical results show significant improvement compared to existing methods based on two point flux approximations we also investigate the hybrid method by studying the convergence rates for different apertures and fracture matrix permeability ratios finally the effect of removing the cells in the intersections of the fractures are studied together these examples demonstrate the efficiency flexibility and robustness of our new approach

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a fully mass conservative iterative impec method for multicomponent compressible flow in porous media abstract in this paper we consider efficient and fully mass conservative numerical methods for the multicomponent compressible single phase darcy flow in porous media compared with the classical implicit pressure explicit concentration impec scheme by which one of the components may be not mass conservative the new scheme enjoys an appealing feature that the conservation of mass is retained for each of the components the pressure velocity system is obtained by the summation of the discrete conservation equation for each component multiplying an unknown parameter which is nonlinearly dependent of the molar concentrations this approach is quite different from the conventional method which is used in the classical impec scheme we utilize a fully mass conservative iterative impec method to solve the nonlinear system for molar concentration pressure and velocity fields the upwind mixed finite element methods are used to solve the pressure velocity system although the peng robinson equation of state eos is utilized to describe the pressure as a function of the molar concentrations our method is suitable for any type of eos under some reasonable conditions the iterative scheme can be proved to be convergent and the molar concentration of each component is positivity preserving several interesting examples of multicomponent compressible flow in porous media are presented to demonstrate the robustness of the new algorithm

a plastic nonlocal damage model abstract in the present paper a plastic nonlocal damage model is proposed for studying the mechanical response of structural elements made of cementitious materials a new isotropic damage model which is able to describe the behavior of a wide class of cementitious materials is presented a regularization technique based on the introduction of the damage laplacian in the damage limit function is adopted to overcome the analytical and computational problems induced by the softening constitutive law a drucker prager type of plastic limit function is proposed considering isotropic hardening a numerical procedure based on an implicit backward euler technique for the time integration of the plastic and damage evolution equations is presented to solve each nonlinear step a predictor corrector iterative method is developed within the splitting method in particular the damage evolution is determined solving a constrained minimization problem of a convex functional the proposed algorithm is implemented in a finite element code and it is used to study the structural behavior of elements made of masonry materials

control volume method for numerical simulation of two phase immiscible flow in two and three dimensional discrete fractured media 1 we provide a numerical procedure for the simulation of two phase immiscible and incompressible flow in two and three dimensional discrete fractured media the concept of cross flow equilibrium is used to reduce the fracture dimension from n to n 1 in the calculation of flow in the fractures this concept which is often referred to as the discrete fracture model has a significant effect on the reduction of computational time the spatial discretization is performed with the control volume method this method is locally conservative and allows the use of unstructured grids to represent complex geometries such as discrete fracture configurations the relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes which is consistent with the physics of fluid flow the system of partial differential equations is decoupled and solved using the implicit pressure explicit saturation impes approach the algorithm has been successfully tested in two and three dimensional numerical simulations of wetting phase fluid injection such as water in discrete fractured media saturated by a nonwetting phase such as nonaqueous phase liquid or oil with mild to high nonlinearity in relative permeability and capillary pressure to the best of our knowledge results for simulations of two phase immiscible and incompressible flow in three dimensional discrete fractured media including capillary and gravity effects are the first to appear in the literature

multiscale finite element for problems with highly oscillatory coefficients in this paper we study a multiscale finite element method for solving a class of elliptic problems with finite number of well separated scales the method is designed to efficiently capture the large scale behavior of the solution without resolving all small scale features this is accomplished by constructing the multiscale finite element base functions that are adaptive to the local property of the differential operator the construction of the base functions is fully decoupled from element to element thus the method is perfectly parallel and is naturally adapted to massively parallel computers we present the convergence analysis of the method along with the results of our numerical experiments some generalizations of the multiscale finite element method are also discussed

scaling of weighted spectral distribution in deterministic scale free networks abstract scale free networks are abundant in the real world in this paper we investigate the scaling properties of the weighted spectral distribution in several deterministic and stochastic models of evolving scale free networks first we construct a new deterministic scale free model whose node degrees have a unified format using graph structure features we derive a precise formula for the spectral metric in this model this formula verifies that the spectral metric grows sublinearly as network size i e the number of nodes grows additionally the mathematical reasoning of the precise formula theoretically provides detailed explanations for this scaling property finally we validate the scaling properties of the spectral metric using some stochastic models the experimental results show that this scaling property can be retained regardless of local world node deleting and assortativity adjustment

a critical comparison of nonlocal and gradient enhanced softening continua continuous models of material degradation may cease to produced meaningful results in the presence of high strain gradients these gradients may occur for instance in the propagation of waves with high wave numbers and at stress concentrators adding nonlocal or gradient terms to the constitutive modelling may enhance the ability of the models to describe such situations the effect of adding nonlocal or gradient terms and the relation between these enhancements are examined in a continuum damage setting a nonlocal damage model and two different gradient damage models are considered in one of the gradient models higher order deformation gradients enter the equilibrium equations explicitly while in the other model the gradient influence follows in a more implicit way from an additional partial differential equation the latter implicit gradient formulation can be rewritten in the integral format of the nonlocal model and can therefore be regarded as truly nonlocal this is not true for the explicit formulation in which the nonlocality is limited to an infinitesimal volume this fundamental difference between the formulations results in quite different behaviour in wave propagation localisation and at crack tips this is shown for the propagation of waves in the models their localisation properties and the behaviour at a crack tip the responses of the nonlocal model and the implicit gradient model agree remarkably well in these situations while the explicit gradient formulation shows an entirely different and sometimes nonphysical response

a discontinuous galerkin method for gravity driven viscous fingering instabilities in porous media we present a new approach to the simulation of gravity driven viscous fingering instabilities in porous media flow these instabilities play a very important role during carbon sequestration processes in brine aquifers our approach is based on a nonlinear implementation of the discontinuous galerkin method and possesses a number of key features first the method developed is inherently high order and is therefore well suited to study unstable flow mechanisms secondly it maintains high order accuracy on completely unstructured meshes the combination of these two features makes it a very appealing strategy in simulating the challenging flow patterns and very complex geometries of actual reservoirs and aquifers this article includes an extensive set of verification studies on the stability and accuracy of the method and also features a number of computations with unstructured grids and non standard geometries

multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media 1 a discrete fracture model for the flow of compressible multicomponent fluids in homogeneous heterogeneous and fractured media is presented in single phase in the numerical model we combine the mixed finite element mfe and the discontinuous galerkin dg methods we use the cross flow equilibrium concept to approximate the fractured matrix mass transfer the discrete fracture model is numerically superior to the single porosity model and overcomes limitations of the dual porosity models including the use of a shape factor the mfe method provides a direct and accurate approximation for the velocity field which is crucial for the convective terms in the flow equations the dg method associated with a slope limiter is used to approximate the species balance equations this method can capture the sharp moving fronts the calculation of the fracture fracture flux across three and higher intersecting fracture branches is a challenge in this work we provide an accurate approximation of these fluxes by using the mfe formulation numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

multi scale finite volume method for elliptic problems in subsurface flow simulation in this paper we present a multi scale finite volume msfv method to solve elliptic problems with many spatial scales arising from flow in porous media the method efficiently captures the effects of small scales on a coarse grid is conservative and treats tensor permeabilities correctly the underlying idea is to construct transmissibilities that capture the local properties of the differential operator this leads to a multi point discretization scheme for the finite volume solution algorithm transmissibilities for the msfv have to be constructed only once as a preprocessing step and can be computed locally therefore this step is perfectly suited for massively parallel computers furthermore a conservative fine scale velocity field can be constructed from the coarse scale pressure solution two sets of locally computed basis functions are employed the first set of basis functions captures the small scale heterogeneity of the underlying permeability field and it is computed in order to construct the effective coarse scale transmissibilities a second set of basis functions is required to construct a conservative fine scale velocity field the accuracy and efficiency of our method is demonstrated by various numerical experiments

memory and burstiness in dynamic networks a discrete time random process is described which can generate bursty sequences of events a bernoulli process where the probability of an event occurring at time t is given by a fixed probability x is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding t for small values of x the interevent time distribution follows a power law with exponent 2 x we consider a dynamic network where each node forms and breaks connections according to this process the value of x for each node depends on the fitness distribution x from which it is drawn we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions and for both cases where the memory effect either is or is not present this work can potentially lead to methods to uncover hidden fitness distributions from fast changing temporal network data such as online social communications and fmri scans

minimum structural controllability problems of complex networks abstract controllability of complex networks has been one of the attractive research areas for both network and control community and has yielded many promising and significant results in minimum inputs and minimum driver vertices however few studies have been devoted to studying the minimum controlled vertex set through which control over the network with arbitrary structure can be achieved in this paper we prove that the minimum driver vertices driven by different inputs are not sufficient to ensure the full control of the network when the associated graph contains the inaccessible strongly connected component which has perfect matching and propose an algorithm to identify a minimum controlled vertex set for network with arbitrary structure using convenient graph and mathematical tools and the simulation results show that the controllability of network is correlated to the number of inaccessible strongly connected components which have perfect matching and these results promote us to better understand the relationship between the network s structural characteristics and its control

a mixed finite element technique based on implicit discretization of faults for permeability upscaling in fault damage zones 1 natural fault damage zones fdzs are often composed of complex arrays containing many thin faults to account for fdzs in large scale models it is necessary to represent the flow effects of these many small faults by some form of upscaling the explicit discretization of the geometry and topology of these thin faults and of the rock matrix typically leads to meshes comprising large numbers of elements making it difficult to solve the flow equations efficiently this paper proposes a practical technique based on the mixed finite element method mfem permitting the permeability upscaling in two dimensional fault damage zones that contain thin and isotropic low permeability faults this technique utilizes an implicit discretization scheme that is similar in principle to those used for discrete fracture networks the scheme described here treats flow across faults accurately but unlike the schemes used for fractures it neglects the flow along the faults because intrafault volumetric flow in thin faults is very small this approach allows for a simpler numerical discretization and a reduction in numerical calculation effort the scheme can be readily implemented in a standard mixed finite element code compared with the same mfem based on an explicit discretization scheme the two techniques are shown to produce results that agree closely the implicit technique is shown to be more efficient than the explicit technique for a typical fault damage zone model this technique is readily extendable to three dimensions

application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity selected groundwater flow scenarios are used in a two way comparison between the mixed hybrid finite element method and the standard finite element method also called the conforming finite element method the simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists the basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element by contrast the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential the conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity the mixed hybrid finite element method provides velocities everywhere in the field as well as potentials at the center of each element and each edge moreover the normal component of the velocity field is continuous between adjacent elements the results of the simulations are presented in the form of streamlines to avoid the problem of velocity discontinuity the method of cordes and kinzelbach 1992 is used it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method the comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy it is also superior to the conforming method in terms of computational effort the potential fields obtained by the mixed hybrid and the conforming finite element methods are the same

analytical and variational numerical methods for unstable miscible displacement flows in porous media the miscible displacement of one fluid by another in a porous medium has received considerable attention in sub surface environmental and petroleum engineering applications when a fluid of higher mobility displaces another of lower mobility unstable patterns referred to as viscous fingering may arise their physical and mathematical study has been the object of numerous investigations over the past century the objective of this paper is to present a review of these contributions with particular emphasis on variational methods these algorithms are tailored to real field applications thanks to their advanced features handling of general complex geometries robustness in the presence of rough tensor coefficients low sensitivity to mesh orientation in advection dominated scenarios and provable convergence with fully unstructured grids this paper is dedicated to the memory of dr jim douglas jr for his seminal contributions to miscible displacement and variational numerical methods

equilibrium based iterative solutions for the non linear beam problem summary the paper describes a procedure for the non linear analysis of structures which are an assemblage of beams with material non linearities of general type the approach uses the equilibrium integrals and a consistent iterative formulation at the element level within the general framework of the displacement method for the solution of the global structural problem the application of dierent approaches to the non linear beam problem is presented and discussed including the traditional stiness and exibility approach and some mixed formulations the proposed equilibrium based approach is shown to be more accurate and more robust than the traditional compatibility based approach on which most of the non linear beam elements available today are based similar advantages are also found with respect to an approach based on the three eld mixed assumed strain method the paper presents a new approach to the numerical static or dynamic analysis of structures made up of an assemblage of non linear beam elements with spread material non linearities an essential step in the numerical incremental solution of such a problem within the usual framework of the displacement method at the global level consists in nding for each individual element the end forces which correspond to given end displacements together with the associated generalized strains and stresses at the dierent sections along the element this step is often referred to as element state determination for simplicity in the following the beam element will be considered as partially constrained at the ends so that no rigid body displacement is allowed and as a consequence we shall refer to end deformations q rather than to end displacements and to the associated end forces or generalized stresses p the standard stiness and exibility approaches will be briey reviewed before going into the presentation of the proposed algorithms after that a review of some mixed approaches is carried out showing the application of two and three eld formulation to the non linear beam problem pointing out dierences and similarities with the proposed algorithms finally numerical examples are presented so as to compare the behaviour of the various approaches when implemented in a non linear nite element beam used in a standard displacement based finite element fe code

a regularized force based beam element with a damage plastic section constitutive law a new beam finite element is presented with a generalized section constitutive law based on damage mechanics and plasticity to analyse the cyclic structural response of plane frames both displacement based and force based fb approaches are used and compared to demonstrate the significant advantages of the fb formulation in the presence of material non linearity in order to overcome the analytical problems and the pathological mesh dependency of the numerical response in the presence of strain softening post peak behaviour a classical non local regularization procedure is adopted first based on the integral definition of the associated variable governing the damaging evolution process subsequently for the fb element a new simple regularization technique is proposed based on a selected integration procedure along the element length which predefines the location of the gauss points in the beam region where the localization phenomena take place as for the other computational aspects an iterative element state determination is adopted for the fb formulation and a local predictor corrector algorithm is used to solve the incremental evolution problems of the damage and plastic internal variables finally some examples are shown on simple beams and frames subjected to monotonically increasing and cyclic loading conditions copyright 2006 john wiley sons ltd