the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

on the modelling of incompressibility in linear and non linear elasticity with the master slave approach this is the pre peer reviewed version of the following article munoz jose j on the modelling of incompressibility in linear and non linear elasticity with the master slave approach international journal for numerical methods in engineering abril 2008 vol 74 num 2 p 269 293 which has been published in final form at http www3 interscience wiley com journal 116323442 abstract

numerical modelling of the propagation of fast landslides using the finite element method this paper proposes a two dimensional 2d model for the analysis of the propagation of fast landslides involving a fluidized material such as debris and mud flows flowslides and avalanching flows the model is based on the navier stokes depth integrated equations to incorporate the effect of steep slopes and centrifugal forces due to the high velocities characterizing the flowslides and the bed curvature a curvilinear system of reference is used the corresponding equations of motion are complemented by depth averaged constitutive equations and bed friction laws the resulting set of differential equations are solved using the two step taylor galerkin algorithm this algorithm has been used by the authors to solve hydraulic and dam break problems using the finite element method owing to the importance of the source term compared to the advection component the proposed algorithm follows a splitting scheme using a fourth order runge kutta method for integrating the friction and slope components the performance of the overall approach has been checked in a number of examples the analysis of the results provides insights into the key elements of the model and shows the adequacy of the method to solve real problems where merging and splitting of the flow occur copyright 2004 john wiley sons ltd

parallel spectral element solution of the stokes problem abstract in this paper we present a high efficiency medium grained parallel spectral element method for numerical solution of the stokes problem in general domains the method is based upon naturally concurrent uzawa and jacobi preconditioned conjugate gradient iterative methods geometry based data parallel distribution of work amongst processors nearest neighbor sparsity and high order substructuring for minimum communication general locally structured globally unstructured parallel constructs and efficient embedding of vector reduction operations for inner product and norm calculation an analysis is given for the computational complexity of the algorithm on a native medium grained parallel processor and the potential communication superiority of high order discretizations is described lastly the method is implemented on the fast intel vector hypercube and the performance of this algorithm architecture coupling is evaluated in a technical and economic framework that reflects the true advantages of parallel solution of partial differential equations

the complexity of the homeomorphism relation between compact metric spaces abstract we determine the exact complexity of classifying compact metric spaces up to homeomorphism more precisely the homeomorphism relation on compact metric spaces is borel bi reducible with the complete orbit equivalence relation of polish group actions consequently the same holds for the isomorphism relation between separable commutative c algebras and the isometry relation between c k spaces

development of a stabilised petrov galerkin formulation for conservation laws in lagrangian fast solid dynamics a stabilised second order finite element methodology is presented for the numerical simulation of a mixed conservation law formulation in fast solid dynamics the mixed formulation where the unknowns are linear momentum deformation gradient and total energy can be cast in the form of a system of first order hyperbolic equations the difficulty associated with locking effects commonly encountered in standard pure displacement formulations is addressed by treating the deformation gradient as one of the primary variables the formulation is first discretised in space by using a stabilised petrov galerkin pg methodology derived through the use of variational work conjugate principles the semi discretised system of equations is then evolved in time by employing a total variation diminishing runge kutta tvd rk time integrator the formulation achieves optimal convergence e g second order with linear interpolation with equal orders in velocity or displacement and stresses in contrast with the displacement based approach this paper defines a set of appropriate stabilising parameters suitable for this particular formulation where the results obtained avoid the appearance of non physical spurious zero energy modes in the solution over a long term response we also show that the proposed pg formulation is very similar and under certain conditions identical to the well known two step taylor galerkin 2tg a series of numerical examples are presented in order to assess the performance of the proposed algorithm the new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios

stabilized low order finite elements for failure and localization problems in undrained soils and foundations abstract geomaterials in general and soils in particular are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water in the limit of zero compressibility of water and soil grains and zero permeability which correspond to the classical undrained assumption of soil mechanics the functions used to interpolate displacements and pressures must fulfill either the babuska brezzi conditions or the much simpler patch test proposed by zienkiewicz and taylor these requirements exclude the use of elements with equal order interpolation for pressures and displacements for which spurious oscillations may appear the simplest elements with continuous pressures which can be used in 2d are the quadratic triangle and quadrilateral with linear and bilinear pressures respectively the purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures t3p3 and bilinear quadrilaterals q4p4 the proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist

a general explicit or semi explicit algorithm for compressible and incompressible flows this note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases it is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided the algorithm permits the use of equal interpolation for all variables by avoiding the need for the babuska brezzi constraints in regions where the flow is nearly incompressible the success of the algorithm which here is written for the non conservative equation form is demonstrated on several examples ranging from nearly incompressible through transonic regions to supersonic flows up to mild shocks such as those occurring in the examples presented in this paper no artificial viscosity is added at any stage the algorithm extends some concepts introduced in an earlier paper

on using linear elements in incompressible plane strain problems a simple edge based approach for triangles in this paper a simple iterative method is presented for finite element solution of incompressible plane strain problems using linear elements instead of using a mixed formulation approach we use an equivalent displacement velocity approach in an iterative manner control volumes are taken for regions which are to exhibit incompressible behaviour for triangular elements the control volume is chosen as the area built on the parts of each pair of elements at the sides of an edge in this case elements are let to exchange volume it is shown that the proposed edge based approach removes the deficiency of the linear triangular elements i e locking effect similar edge based approach is applied to the linear quadrilateral elements however if the control volume is chosen as the element volume the formulation gives similar results as the discontinuous mixed formulation using one pressure point without exhibiting instability behaviour the formulation is based on decomposition of the displacement velocity field into deviatoric and volumetric parts the volumetric part is iteratively eliminated without confronting locking or instability phenomenon the iterative procedure is very cheap and simple to be implemented in any fem code several examples are given to demonstrate the performance of the procedure copyright 2004 john wiley sons ltd

one step taylor galerkin methods for convection diffusion problems third and fourth order taylor galerkin schemes have shown to be efficient finite element schemes for the numerical simulation of time dependent convective transport problems by contrast the application of higher order taylor galerkin schemes to mixed problems describing transient transport by both convection and diffusion appears to be much more difficult in this paper we develop two new taylor galerkin schemes maintaining the accuracy properties and improving the stability restrictions in convection diffusion we also present an efficient algorithm for solving the resulting system of the finite element method finally we present two numerical simulations that confirm the properties of the methods

substructuring preconditioners for the q_1 mortar element method the q 1 mortar element method is a non conforming finite element method with q 1 elements based on domain decomposition for the laplace equation it yields an ill conditioned linear system for solving the linear system the so called preconditioned conjugate gradient method in a subspace is used preconditioners are proposed and estimates on condition numbers and arithmetical complexity are given finally numerical experiments are presented

average trajectories and fluctuations from noisy nonlinear maps the average trajectories and fluctuations around them resulting from an ensemble of noisy nonlinear maps are analyzed the bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically this equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points the scaling properties of the average value and of the variance are obtained with the help of this equation

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

the patch test for mixed formulations this paper presents a simple extension of the patch test to mixed formulations to provide the necessary and sufficient conditions for convergence the general algebraic conditions of babuska and brezzi are given a simple form and a conceptual application of the patch tests serves to point out the instability of several well known formulations for incompressible problems the test is also applied to mixed displacement strain formulations of elasticity and limiting formulations are noted

turbulence orbit equivalence and the classification of nuclear c algebras we bound the borel cardinality of the isomorphism relation for nuclear simple separable c algebras it is turbulent yet borel reducible to the action of the automorphism group of the cuntz algebra o2 on its closed subsets the same bounds are obtained for affine homeomorphism of metrizable choquet simplexes as a by product we recover a result of kechris and solecki namely that homeomorphism of compacta in the hilbert cube is borel reducible to a polish group action these results depend intimately on the classification theory of nuclear simple c algebras by k theory and traces both of necessity and in order to lay the groundwork for further study on the borel complexity of c algebras we prove that many standard c algebra constructions and relations are borel and we prove borel versions of kirchberg s o2 stability and embedding theorems we also find a c algebraic witness for a k hard equivalence relation the authors dedicate this article to the memory of greg hjorth

numerical algorithms for strong discontinuities in elastic plastic solids abstract in this paper the implementation of second order godunov methods for dynamic wave propagation in one dimensional elastic plastic solids is investigated first the lagrangian form of the algorithm is reviewed and then the algorithm is extended to the eulerian frame of reference this extension requires additional evolution equations to handle the history of the material along particle paths both the lagrangian and eulerian versions of the algorithm require appropriately accurate approximations to the solution of riemann problems in order to represent the interaction of waves at cell boundaries two inexpensive approximations to the solution of the riemann problem are constructed and the resulting algorithms are tested against the analytic solution of the riemann problem for longitudinal motion in an elastic plastic bar these approximations to the riemann problem are shown to work well even for strong discontinuities finally the numerical experience gained from the simple longitudinal bar problem is used to design an algorithm for strong shocks predicted by a realistic soil model

1d wave propagation in saturated viscous geomaterials improvement and validation of a fractional step taylor galerkin finite element algorithm abstract this paper tackles the numerical simulation of 1d wave propagation in saturated viscous porous media and especially in soil like geomaterials for this purpose an improved fractional step taylor galerkin algorithm is first formulated and then validated on the basis of a new analytical solution the algorithm based on a stress velocity pressure formulation of the hydro mechanical problem combines an explicit taylor galerkin method with a fractional time stepping while an accurate runge kutta type integrator is introduced to treat the viscosity of the porous skeleton the overall algorithm results in an efficient stabilized scheme allowing for linear equal interpolation of field variables even when the so called undrained incompressible limit is approached the accuracy and stability of the method are verified with reference to a 1d benchmark problem concerning the propagation of p waves along a saturated viscoelastic soil stratum for this problem a frequency domain analytical solution is derived assuming incompressible interstitial fluid and soil grains the assumption of maxwell viscoelastic soil skeleton is analytically convenient to preserve the linearity of the problem while the same rheology of a more realistic elasto viscoplastic non linear behaviour is maintained the performance of the fractional step taylor galerkin algorithm is explored simulating the dynamic response of the stratum to harmonic impulsive and seismic input excitations in particular parametric analyses are performed to confirm the effectiveness of the method in reproducing fully undrained responses as well as in dealing with weakly viscous materials

wavelet stabilization of the lagrange multiplier method we propose here a stabilization strategy for the lagrange multiplier formulation of dirichlet problems the stabilization is based on the use of equivalent scalar products for the spaces h 1 2 partial omega and h 1 2 partial omega which are realized by means of wavelet functions the resulting stabilized bilinear form is coercive with respect to the natural norm associated to the problem a uniformly coercive approximation of the stabilized bilinear form is constructed for a wide class of approximation spaces for which an optimal error estimate is provided finally a formulation is presented which is obtained by eliminating the multiplier by static condensation this formulation is closely related to the nitsche s method for solving dirichlet boundary value problems

an introduction to finite element methods for transient advection problems abstract an introduction is presented to time accurate finite element methods recently developed for solving unsteady problems governed by linear and nonlinear advection equations this includes methods making an explicit use of the characteristic curves methods based on the taylor series in time and least squares methods

crises and hysteresis in coupled logistic maps a new type of crisis is found in coupled logistic maps in this crisis several chaotic attractors undergo cyclic collisions with their basin boundaries and merge into a bigger one whose chaotic dynamical behavior exhibits cyclic transitions among its components with a well defined overall period

an analysis of time discretization in the finite element solution of hyperbolic problems abstract the problem of the time discretization of hyperbolic equations when finite elements are used to represent the spatial dependence is critically examined a modified equation analysis reveals that the classical second order accurate time stepping algorithms i e the lax wendroff leap frog and crank nicolson methods properly combine with piecewise linear finite elements in advection problems only for small values of the time step on the contrary as the courant number increases the numerical phase error does not decrease uniformly at all wavelengths so that the optimal stability limit and the unit cfl property are not achieved these fundamental numerical properties can however be recovered while still remaining in the standard galerkin finite element setting by increasing the order of accuracy of the time discretization this is accomplished by exploiting the taylor series expansion in the time increment up to the third order before performing the galerkin spatial discretization using piecewise linear interpolations as a result it appears that the proper finite element equivalents of second order finite difference schemes are implicit methods of incremental type having third and fourth order global accuracy on uniform meshes taylor galerkin methods numerical results for several linear examples are presented to illustrate the properties of the taylor galerkin schemes in one and two dimensional calculations

a taylor galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua abstract this paper presents a taylor galerkin algorithm formulated in terms of velocities and stresses which can be applied to solid dynamics problems requiring good resolution of small wavelengths such as propagation of shocks the proposed model is both fast as it uses simple linear elements triangles in 2d and tetrahedra in 3d and accurate it mitigates locking and mesh alignment problems and therefore can be applied to localized failure computations without the limitations exhibited by the classical displacement formulations

flow rate boundary problems for an incompressible fluid in deformable domains formulations and solution methods in this paper we consider the numerical solution of the interaction of an incompressible fluid and an elastic structure in a truncated computational domain as well known in this case there is the problem of prescribing realistic boundary data on the artificial sections when only partial data are available this problem has been investigated extensively for the rigid case in this work we start considering the compliant case by focusing on the flow rate conditions for the fluid we propose three formulations of this problem different algorithms for its numerical solution and carry out several 2d numerical simulations with the aim of comparing the performances of the different algorithms

shallow water problems a general explicit formulation this paper gives a general formulation for shallow water equations which is capable of solving problems of induced harbour oscillation tidal flow tsunami propagation dispersion of pollutant etc the shallow water equations are written in a novel fully conservative form the solution algorithm is based on an explicit time integration procedure which exploits the conservative properties of the governing equations and incorporates accurate treatment of convective terms without introduction of artificial damping its accuracy and low cost of computation make it attractive with regard to existing procedures

high order taylor galerkin and adaptive h p methods for second order hyperbolic systems application to elastodynamics a new family of high order taylor galerkin schemes is presented for the analysis of second order hyperbolic systems the use of such schemes within an adaptive h p finite element strategy for spatial approximation in two dimensional problems is described numerical results are presented to demonstrate performance of these methods

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

coupling finite element and spectral methods first results a poisson equation on a rectangular domain is solved by coupling two methods the domain is divided in two squares a finite element approximation is used on the first square and a spectral discretization is used on the second one two kinds of matching conditions on the interface are presented and compared in both cases error estimates are proved

on the classification of positions and complex structures in banach spaces abstract a topological setting is defined to study the complexities of the relation of equivalence of embeddings or position of a banach space into another and of the relation of isomorphism of complex structures on a real banach space the following results are obtained a if x is not uniformly finitely extensible then there exists a space y for which the relation of position of y inside x reduces the relation e 0 and therefore is not smooth b the relation of position of l p inside l p or inside l p p 2 reduces the relation e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group c the relation of position of a space inside another can attain the maximum complexity e max d there exists a subspace of l p 1 p 2 on which isomorphism between complex structures reduces e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

fractal and riddled basins arithmetic signatures in the parameter space of two coupled quadratic maps we investigate the parameter space of two coupledquad ratic logistic maps of special interest is the analytical characterization of the precursors leading to riddled basins we delimit stability domains for orbits with the two lowest periods in addition we study the singularities of the phase space surfaces obtainedby eliminating all parameters from the equations of motion c 2001 elsevier science b v all rights reserved

polish groupoids and functorial complexity we introduce and study the notion of functorial borel complexity for polish groupoids such a notion aims to measure the complexity of classifying the objects of a category in a constructive and functorial way in the particular case of principal groupoids such a notion coincides with the usual borel complexity of equivalence relations our main result is that on one hand for polish groupoids with an essentially treeable orbit equivalence relation functorial borel complexity coincides with the borel complexity of the associated orbit equivalence relation on the other hand for every countable equivalence relation e that is not treeable there are polish groupoids with different functorial borel complexity both having e as orbit equivalence relation in order to obtain such a conclusion we generalize some fundamental results about the descriptive set theory of polish group actions to actions of polish groupoids answering a question of arlan ramsay these include the becker kechris results on polishability of borel g spaces existence of universal borel g spaces and characterization of borel g spaces with borel orbit equivalence relations

an improved finite element flux corrected transport algorithm an improved finite element flux corrected transport fe fct method for the numerical solution of hydrodynamic conservation equations is described based on the method developed by lohner and his collaborators to solve conservation equations in fluid mechanics and its application is extended to gas discharge problems the high and low order schemes used are the ones proposed by lohner who adds diffusion to the high order scheme by subtracting the lumped mass matrix from the consistent mass matrix to give the low order scheme the diffusion coefficient is adjusted globally a variable diffusion coefficient is introduced it is assumed to be constant in each element and is shown to transform the high order solution to a scheme equivalent to an upwind scheme which has minimal diffusion but ensures positive results this avoids the complexity of upwinding in fe especially in two dimensions it is also shown that the correct amount of real diffusion may be easily added to the algorithm when required for example for electrons results are presented which show that the high order scheme reduces to the upwind difference scheme when the new diffusion is used the proposed fct scheme is shown to give similar results in comparison with a fourth order fd fct algorithm finally the new method is applied to a streamer propagation problem in one dimension and the results obtained are shown to agree well with previously published results

wave propagation and localization problems in saturated viscoplastic geomaterials this paper presents an improved algorithm to deal with wave propagation and localization problems in saturated viscoplastic geomaterials it consists of a mixed formulation in terms of effective stress velocity and pore pressure that uses a fractional step algorithm allowing the use of equal order of interpolation for the three variables and the simplest element such as the linear triangle the viscoplastic model used is of modified cam clay type viscoplasticity results in a strong source term that deteriorates the accuracy of the two step taylor galerkin algorithm therefore a runge kutta splitting scheme has been used to deal with the source terms resulting in a better accuracy of the method copyright 2006 john wiley sons ltd

a stabilized fractional step runge kutta taylor sph algorithm for coupled problems in geomechanics abstract failure of geomaterials with pores filled with fluids is an important research area in both civil and geological engineering many finite element formulations for coupled problems present difficulties such as overestimating failure loads or mesh alignment dependence resulting on spurious failure mechanisms moreover the spaces where field variables are approximated have to fulfill additional requirements ensuring stability stress velocity pore pressure formulations in fe analysis provide accurate results for wave propagation and failure analysis however finite elements present important limitations when deformations are large the purpose of this paper is to present a stabilized fractional step sph algorithm which combines the advantages of the sph method for large deformation problems with those of the taylor galerkin algorithm used within the finite element framework

modifications to the lax wendroff scheme for hyperbolic systems with source terms for wave phenomena in one spatial dimension governed by hyperbolic partial differential equations with source terms the standard lax wendroff scheme leads to oscillations at discontinuous wavefronts even if the courant friedrich lewy cfl number is set equal to unity we modify the lax wendroff scheme for hyperbolic systems with source terms based on characteristic analysis to preserve the wave profile correctly when the cfl number is set equal to 1 the new scheme can be used as easily as the original lax wendroff scheme since the calculation of the characteristics is not introduced in the new scheme thus additional computations of characteristics are not necessary we also extend our method for higher spatial dimensions and illustrate our approach by numerical examples copyright 1999 john wiley sons ltd

completeness of the isomorphism problem for separable c algebras this paper studies the descriptive set theoretical complexity of the isomorphism problem for separable c algebras we prove that the isomorphism problem for separable simple ai c algebras is complete in the class of orbit equivalence relations this means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple separable ai c algebras

time accurate solution of advection diffusion problems by finite elements abstract the taylor galerkin method recently proposed for the spatial and temporal discretization of hyperbolic equations is employed to derive accurate and efficient numerical schemes for the solution of time dependent advection diffusion problems two distinct numerical strategies are discussed the first is suitable for evolutionary problems while the second is appropriate for situations in which a steady state is eventually reached for purely evolutionary problems the taylor galerkin method is applied to the complete advection diffusion equation and through modifications of the standard mass matrix is shown to generate an incremental form of the crank nicolson time stepping method such an incremental form also lends itself to the derivation of computationally simple but accurate explicit algorithms to deal with transient situations which evolve towards a highly convective steady state the global taylor galerkin method is found to be ineffective since it reduces to the standard galerkin formulation as the temporal term vanishes for such cases we suggest the use of a splitting up method in which advection and diffusion are treated separately by appropriate taylor galerkin methods the proposed methods are illustrated first for linear constant coefficient equations they are successively extended to deal with nonlinear and multi dimensional problems numerical applications indicate their effectiveness

application of level set approach to moving interfaces and free surface problems in flow through porous media abstract the level set technique introduced by osher and sethian has been widely used in computational fluid dynamics problems involving two or more immiscible fluids with sharp interfaces this paper presents an application of the level set to unconfined seepage problems where a free surface or a sharp interface exists it is based on considering the movement of both fluids introducing a smooth indicator function with a level set describing the interface position the proposed method can be applied to other flow in porous media problems involving immiscible fluids such as oil recovery applications

incompressibility without tears how to avoid restrictions of mixed formulation the severe restrictions of the babuska brezzi stability criteria permit only a limited number of interpolations for velocities displacements and pressure to be used for incompressible behaviour these restrictions preclude the use of many useful elements we show in this paper how such difficulties can be side stepped by seeking the steady state solution through the use of various time marching schemes this permits a simple iterative approach to incompressible or nearly incompressible problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow etc

a two steps time discretization scheme using the sph method for shock wave propagation the smoothed particle hydrodynamics sph is a meshfree method which has been applied to a wide range of problems in the present work a new time integration algorithm using a corrected sph spatial discretization for small deformations is applied to solve the propagation of shock waves in viscoplastic continua in the method presented herein the equations are formulated in terms of stress and velocity a corrected lagrangian kernel is employed and two different sets of particles are used for the time discretization numerical instabilities are not present when using this new sph formulation the method proposed here has been proved to be efficient and it provides solutions of good accuracy

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

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

an eulerian mixed formulation for viscoplastic materials abstract this paper presents an eulerian mixed formulation for viscoplastic materials the algorithm is formulated in terms of deviatoric stress velocity and hydrostatic pressure using a fractional step algorithm that allows the use of equal order of interpolation for the three variables the constitutive law is based on the viscoplasticity theory of perzyna with the von mises yield criterion the jaumann rate of cauchy stress tensor is used to ensure the objectivity of the constitutive law a splitting scheme based on a two step taylor galerkin algorithm for the advective terms plus a fourth order runge kutta scheme for the sources has been used to improve the accuracy of the method

high order taylor galerkin methods for linear hyperbolic systems a new family of high order taylor galerkin schemes is presented for the analysis of first order linear hyperbolic systems the schemes are unconditionally stable which makes them very attractive to use in conjunction with adaptive hp finite element methods for spatial approximation

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100