galerkin projected residual method applied to diffusion reaction problems a stabilized finite element method is presented for scalar and linear second order boundary value problems the method is obtained by adding to the galerkin formulation multiple projections of the residual of the differential equation at element level these multiple projections allow the generation of appropriate number of free stabilization parameters in the element matrix depending on the local space of approximation and on the differential operator the free parameters can be determined imposing some convergence and or stability criteria or by postulating the element matrix with the desired stability properties the element matrix of most stabilized methods such as gls and ggls methods can be obtained using this new method with appropriate choices of the stabilization parameters we applied this formulation to diffusion reaction problems optimal rates of convergency are numerically observed for regular solutions

an analysis of the time integration algorithms for the finite element solutions of incompressible navier stokes equations based on a stabilised formulation abstract this work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the navier stokes equations the stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes particular attention is given to the generalised method and the linear discontinuous in time finite element scheme the time integration schemes are first applied to two model problems represented by a first order differential equation in time and the one dimensional advection diffusion equation and subjected to a detailed mathematical analysis based on the fourier series expansion in order to establish the accuracy and efficiency of the time integration schemes for the navier stokes equations a detailed computational study is performed of two standard numerical examples unsteady flow around a cylinder and flow across a backward facing step it is concluded that the semi discrete generalised method provides a viable alternative to the more sophisticated and expensive space time methods for simulations of unsteady flows of incompressible fluids governed by the navier stokes equations

a parallelized meshfree method with boundary enrichment for large scale cfd a parallel computational implementation of a meshfree method the reproducing kernel particle method rkpm is used for 3 d implicit cfd analysis a novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions this technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations many of which involve inherently serial steps this is important because the expense of meshfree computations makes parallelization crucial for large size problems the performance of the parallelization technique and the accuracy of the implicit cfd algorithm are demonstrated in two example problems

bounded renormalization with continuous penalization for level set interface capturing methods in this work a reinitialization procedure oriented to regularize the level set ls function field is presented in ls approximations for two fluid flow simulations a scalar function indicates the presence of one or another phase and the interface between them in general the advection of such function produces a degradation of some properties of the ls function such as the smoothness of the transition between phases and the correct position of the interface the methodology introduced here denominated bounded renormalization with continuous penalization consists of solving by the finite element method a partial differential equation with certain distinguishing properties with the aim of keeping the desirable properties of the ls function the performance of the strategy is evaluated for several typical cases in one two and three dimensional domains for both the advection and the renormalization stages copyright 2010 john wiley sons ltd

an optimal control of water level considering time delay system this paper presents a numerical application of the optimal control considering time delay system to the flood control with drainage basin the optimal control theory is used to obtain the control values which satisfies the state equation and minimizes performance function feature of this study is application of time delay system to control problems two kinds of control values which has time difference can be introduced those are quantity of water intake and release in drainage basin these control values are correlated with each other which can be modeled by the time delay system the sakawa shindo method is employed for the minimization algorithm to calculate the water flow phenomenon the shallow water equation is employed the clank nicolson method is applied to temporal discretization and the stabilized bubble function method is applied to spatial discretization as the numerical model the flood flow in the tsurumi river which locates in yokohama city is represented

on inf sup stabilized finite element methods for transient problems we consider the behavior of inf sup stabilization in the context of transient problems with multiple time scales our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process we show that for algorithms defined through a process wherein spatial and temporal discretizations are separated the coupling of implicit time integration with spatial inf sup stabilization may lead to anomalous pressure behavior including the onset of spurious oscillations for very small time steps effectively this coupling introduces a stability criterion resulting in a dependence between the spatial grid size and the time step we illustrate our theoretical results by numerical examples that demonstrate the stability criterion 2004 elsevier b v all rights reserved

use of finite element methods in frequency domain aeroacoustics the linearized euler equations are used widely in many aerodynamic noise prediction schemes the linearized euler equations also support instability waves which can obscure the acoustic solution an approach to suppress the instability waves is to solve the linearized euler equations in the frequency domain also the frequency domain approach is far less expensive compared to the time domain approach in terms of the computational time though only a single frequency can be computed at one time the application and comparison of two unstructured grid methods for the solution of aeroacoustic problems in the frequency domain are presented algorithms are developed using the discontinuous galerkin and the streamline upwind petrov galerkin finite element methods in two spatial dimensions on conforming triangular meshes using nodal polynomial basis sets unlike other existing frequency domain solvers no assumption is made regarding the nature of the mean flow the application of the two methods to a two dimensional benchmark problem involving the suppression of instability waves is presented the two methods are compared in terms of the computational cost it is concluded that the discontinuous galerkin method is prohibitively more expensive compared to the streamline upwind petrov galerkin method for aeroacoustic applications in the frequency domain using conforming meshes and nodal polynomials

supg finite element computation of compressible flows with the entropy and conservation variables formulations abstract supg stabilized finite element formulations of compressible euler equations based on the conservation and entropy variables are investigated and compared the formulation based on the conservation variables consists of the formulation introduced by tezduyar and hughes plus a shock capturing term the formulation based on the entropy variables is the same as the one by hughes franca and mallet which has a shock capturing term built in these formulations are tested on several subsonic transonic and supersonic compressible flow problems it is shown that the stabilized formulation based on the conservation variables gives solutions which are just as good as those obtained with the entropy variables furthermore the solutions obtained using the two formulations are very close and in some cases almost indistinguishable consequently it can be deduced that the relative merits of these two formulations will continue to remain under debate

on continuum immersed strategies for fluid structure interaction abstract continuum immersed strategies are widely used these days for the computational simulation of fluid structure interaction problems the principal characteristic of such immersed techniques is the representation of the immersed solid via a momentum forcing source in the navier stokes equations in this paper the immersed finite element method ifem introduced by zhang et al 2004 41 for the analysis of deformable solids immersed in an incompressible newtonian viscous fluid is further enhanced by means of three new improvements a first update deals with the modification of the conservation of mass equation in the background fluid in order to account for non isochoric deformations within the solid phase a second update deals with the incompressibility constraint for the solid phase in the case of isochoric deformations where an enhanced evaluation of the deformation gradient tensor is introduced in a multifield hu washizu variational sense in order to overcome locking effects the third update is focussed on the improvement of the robustness of the overall scheme by introducing an implicit one step time integration scheme with enhanced stability properties in conjunction with a consistent newton raphson linearisation strategy for optimal quadratic convergence the resulting monolithic methodology is thoroughly studied for a range of lagrangian and nurbs based shape finite element functions for a series of numerical examples with the purpose of studying the effect of the spatial semi discretisation in the solution comparisons are also established with the newly developed immersed structural potential method ispm by gil et al 2010 7 for benchmarking and assessment of the quality of the new formulation

simple stabilizing matrices for the computation of compressible flows in primitive variables the key ingredient that balances stability and accuracy in stabilized formulations is the parameter of intrinsic time scales for multi dimensional hyperbolic systems of equations this parameter is a matrix and the available expressions for its computation involve the solution of an eigenvalue problem which can be tedious or cpu time consuming thus for formulations based on primitive variables including pressure a couple of simple stabilizing matrices are presented which are easy to implement and cpu economic numerical evaluations show the performance of the various choices

space time finite element techniques for computation of fluid structure interactions we describe the space time finite element techniques we developed for computation of fluid structure interaction fsi problems among these techniques are the deforming spatial domain stabilized space time dsd sst formulation and its special version and the mesh update methods including the solid extension mesh moving technique semmt also among these techniques are the block iterative quasi direct and direct coupling methods for the solution of the fully discretized coupled fluid and structural mechanics equations we present some test computations for the mesh moving techniques described we also present numerical examples where the fluid is governed by the navier stokes equations of incompressible flows and the structure is governed by the membrane and cable equations overall we demonstrate that the techniques we have developed have increased the scope and accuracy of the methods used in computation of fsi problems 2005 elsevier b v all rights reserved

a unified finite element formulation for compressible and incompressible flows using augmented conservation variables abstract a unified approach to computing compressible and incompressible flows is proposed the governing equation for pressure is selected based on the local mach number in the incompressible limit the divergence free constraint on velocity field determines the pressure while it is the equation of state that governs the pressure solution for the compressible flows stabilized finite element formulations based on the space time and semi discrete methods with the augmented conservation variables are employed the augmented conservation variables consist of the usual conservation variables and pressure as an additional variable the formulation is applied to various test problems involving steady and unsteady flows over a large range of mach and reynolds numbers

a stabilized and coupled meshfree meshbased method for the incompressible navier stokes equations part i stabilization abstract a stabilized meshfree galerkin method is employed for the approximation of the incompressible navier stokes equations in eulerian or arbitrary lagrangian eulerian ale formulation equal order interpolations for velocities and pressure are used it is well known from the meshbased context i e from finite volume and finite element methods that in convection dominated flow problems in eulerian or ale formulation stabilization is a crucial requirement for reliable solutions also stabilization is needed in order to enable equal order interpolations of the incompressible navier stokes equations standard stabilization techniques developed in a meshbased context are extended to meshfree methods it is found that the same structure of the stabilization schemes may be used however the aspect of the stabilization parameter weighting the stabilization terms has to be reconsidered in part ii of this work the resulting stabilized meshfree galerkin method is coupled with a stabilized finite element method the resulting coupled method employs the comparatively costly meshfree galerkin method only where it is needed i e in areas of the domain where a mesh is difficult to maintain and the efficient meshbased finite element method is used in the rest of the domain the fluid solver resulting from this technique is able to solve complex flow problems involving large deformations of the physical domain and or moving and rotating obstacles

extended space time finite elements for landslide dynamics summary the paper introduces a methodology for numerical simulation of landslides experiencing considerable deformations and topological changes within an interface capturing approach all interfaces are implicitly described by specifically defined level set functions allowing arbitrarily evolving complex topologies the transient interface evolution is obtained by solving the level set equation driven by the physical velocity field for all three level set functions in a block jacobi approach the three boundary coupled fluid like continua involved are modeled as incompressible governed by a generalized non newtonian material law taking into account capillary pressure at moving fluid fluid interfaces the weighted residual formulation of the level set equations and the fluid equations is discretized with finite elements in space and time using velocity and pressure as unknown variables non smooth solution characteristics are represented by enriched approximations to fluid velocity weak discontinuity and fluid pressure strong discontinuity special attention is given to the construction of enriched approximations for elements containing evolving triple junctions numerical examples of three fluid tank sloshing and air water liquefied soil landslides demonstrate the potential and applicability of the method in geotechnical investigations copyright 2012 john wiley sons ltd

improving stability of stabilized and multiscale formulations in flow simulations at small time steps abstract the objective of this paper is to show that use of the element vector based definition of stabilization parameters introduced in t e tezduyar computation of moving boundaries and interfaces and stabilization parameters int j numer methods fluids 43 2003 555 575 t e tezduyar y osawa finite element stabilization parameters computed from element matrices and vectors comput methods appl mech engrg 190 2000 411 430 circumvents the well known instability associated with conventional stabilized formulations at small time steps we describe formulations for linear advection diffusion and incompressible navier stokes equations and test them on three benchmark problems advection of an l shaped discontinuity laminar flow in a square domain at low reynolds number and turbulent channel flow at friction velocity reynolds number of 395

ale supg finite element method for convection diffusion problems in time dependent domains conservative form a streamline upwind petrov galerkin supg finite element method for a convection dominated transient convection diffusion reaction equation in time dependent domains is proposed the time dependent domain is handled by the arbitrary lagrangian eulerian ale approach whereas the supg method is used for the spatial discretization further the first order modified backward euler and the second order modified crank nicolson methods are used for the temporal discretization it is shown that the stability of the semi discrete continuous in time conservative ale supg equation is independent of the mesh velocity whereas the stability of the fully discrete scheme with the implicit euler time discretization is unconditionally stable and is only conditionally stable time step depends on mesh velocity with the crank nicolson method numerical results are presented to support the stability estimates and to show the influence of the supg stabilization parameter in a time dependent domain further the proposed numerical scheme is applied to a boundary layer problem in a time dependent domain c 2017 elsevier inc all rights reserved

algebraic approximation of sub grid scales for the variational multiscale modeling of transport problems abstract variational multiscale vms finite element methods fems are robust for the development of general formulations for the solution of multiphysics and multiscale transport problems to obtain a tractable and computationally efficient model vms methods often rely on a residual based algebraic approximation of the sub grid scales small or unresolved features of the solution field not captured by the discretization using a so called intrinsic time scales matrix which depends on the problem s overall differential operator and represents the main model parameter a novel technique for approximating the intrinsic time scales matrix for generic transport problems in a relatively inexpensive manner e g does not rely on eigenvalue computations is presented the method is denoted transport equivalent scaling tes and is based on the monolithic casting of the transport problem as a system of transient advective diffusive reactive tadr equations and a subsequent scaling of the coefficient matrices such to preserve each type of transport flux an algebraic vms formulation incorporating the tes method is complemented with a discontinuity capturing dc approach and implemented within a fem solver for the solution of tadr problems the solution of the global discrete system is accomplished using a generalized alpha time stepper together with a globalized inexact newton krylov nonlinear solver the effectiveness of the tes formulation is verified with the simulation of benchmark incompressible compressible and magnetohydrodynamic flow problems the results demonstrate that the tes method seamlessly handles incompressible compressible flows in a unified manner e g without assessing the compressibility of the flow the convergence process using the tes approach and a more standard approximation for the intrinsic time scales as well as the effect of the dc approach are also investigated analysis of the intrinsic time scales for a one dimensional incompressible flow model reveals the similitudes and differences between the tes formulation and other conventional methods

a stabilized mlpg method for steady state incompressible fluid flow simulation in this paper the meshless local petrov galerkin mlpg method is extended to solve the incompressible fluid flow problems the streamline upwind petrov galerkin supg method is applied to overcome oscillations in convection dominated problems and the pressure stabilizing petrov galerkin pspg method is applied to satisfy the so called babuska brezzi condition the same stabilization parameter t t s u p email protected p s p g is used in the present method the circle domain of support linear basis and fourth order spline weight function are applied to compute the shape function and bubnov galerkin method is applied to discretize the pdes the lid driven cavity flow backward facing step flow and natural convection in the square cavity are applied to validate the accuracy and feasibility of the present method the results show that the stability of the present method is very good and convergent solutions can be obtained at high reynolds number the results of the present method are in good agreement with the classical results it also seems that the present method which is a truly meshless is very promising in dealing with the convection dominated problems

a maximum principle preserving finite element method for scalar conservation equations this paper introduces a first order viscosity method for the explicit approximation of scalar conservation equations with lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension provided the lumped mass matrix is positive definite the method is shown to satisfy the local maximum principle under a usual cfl condition the method is independent of the cell type for instance the mesh can be a combination of tetrahedra hexahedra and prisms in three space dimensions

a stabilized finite element method based on sgs models for compressible flows abstract we present an appropriate extension of the stabilized finite element formulation introduced in a corsini f rispoli a santoriello a variational multiscale high order finite element formulation for turbomachinery flow computations comput methods appl mech engrg 194 2005 4797 4823 for the prediction of incompressible flows aimed at compressible flows the stabilized formulation is the so called variable subgrid scale method v sgs based on an approximation of the class of subgrid scale models sgs derived from the hughes variational multiscale method hughes vms introduced in t j r hughes multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods comput methods appl mech engrg 127 1995 387 401 it is characterized by a variable stabilization parameter within the domain of element we also propose an innovative procedure for computing the stabilization parameter by using the one dimensional element green s functions corresponding to an advective diffusive differential operator the stabilization parameter is defined as the sum of two components the first providing its mean value and the second its element wise space dependency on this basis the present work proposes the stabilization matrix for the multidimensional advective diffusive system of equations governing compressible flows the procedure developed for computing the stabilization parameter can be applied to other differential operators as it has been shown in a corsini f rispoli a santoriello a variational multiscale high order finite element formulation for turbomachinery flow computations comput methods appl mech engrg 194 2005 4797 4823 the proposed stabilization device is validated by simulation of inviscid and viscous supersonic flow configurations

a mortar approach for fluid structure interaction problems immersed strategies for deformable and rigid bodies abstract this paper proposes a new fluid structure interaction immersed computational framework the coupling between an underlying incompressible fluid and an embedded solid is formulated by means of the overlapping domain decomposition method in conjunction with a mortar approach leading to a variationally consistent scheme which is capable of unifying a range of methodologies currently available in the literature this novel framework provides great flexibility and enables the modelling of immersed deformable solids compressible and incompressible as well as rigid bodies through the use of a weak director based formulation a novel null space reduction scheme is employed in order to enhance the conditioning of the resulting system of equations and reduce the computational cost an implicit structure preserving time integration algorithm is used to yield extra stability and robustness and the use of a segmentation technique near the boundary between fluid and solid also leads to enhanced accuracy the methodology is benchmarked against results obtained by using alternative boundary fitted methodologies

correct energy evolution of stabilized formulations the relation between vms supg and gls via dynamic orthogonal small scales and isogeometric analysis i the convective diffusive context this paper presents the construction of novel stabilized finite element methods in the convective diffusive context that exhibit correct energy behavior classical stabilized formulations can create unwanted artificial energy our contribution corrects this undesired property by employing the concepts of dynamic as well as orthogonal small scales within the variational multiscale framework vms the desire for correct energy indicates that the large and small scales should be h 0 1 orthogonal using this orthogonality the vms method can be converted into the streamline upwind petrov galerkin supg or the galerkin least squares gls method incorporating both large and small scales in the energy definition asks for dynamic behavior of the small scales therefore the large and small scales are treated as separate equations two consistent variational formulations which depict correct energy behavior are proposed i the galerkin least squares method with dynamic small scales glsd and ii the dynamic orthogonal formulation do the methods are presented in combination with an energy decaying generalized time integrator numerical verification shows that dissipation due to the small scales in classical stabilized methods can become negative on both a local and a global scale the results show that without loss of accuracy the correct energy behavior can be recovered by the proposed methods the computations employ nurbs based isogeometric analysis for the spatial discretization

interface tracking and interface capturing techniques for finite element computation of moving boundaries and interfaces we provide an overview of some of the interface tracking and interface capturing techniques we developed for finite element computation of flow problems with moving boundaries and interfaces this category of flow problems includes fluid particle fluid object and fluid structure interactions free surface and two fluid flows and flows with moving mechanical components both classes of techniques are based on stabilized formulations the interface tracking techniques are based on the deforming spatial domain stabilized space time dsd sst formulation where the mesh moves to track the interface the interface capturing techniques developed primarily for free surface and two fluid interface flows are formulated typically over non moving meshes using an advection equation in addition to the flow equations the advection equation governs the evolution of an interface function that marks the location of the interface we also highlight some of the methods we developed to increase the scope and accuracy of these two classes of techniques

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

finite element stabilization parameters computed from element matrices and vectors abstract we propose new ways of computing the stabilization parameters used in the stabilized finite element methods such as the streamline upwind petrov galerkin supg and pressure stabilizing petrov galerkin pspg formulations the parameters are computed based on the element level matrices and vectors which automatically take into account the local length scales advection field and the reynolds number we describe how we compute these parameters in the context of first a time dependent advection diffusion equation and then the navier stokes equations of unsteady incompressible flows

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

a space time formulation and improved spatial reconstruction for the divide and conquer multiscale method abstract a time discontinuous space time formulation for the divide and conquer multiscale method is presented this multiscale method aims at stable and accurate solutions of transient convection diffusion reaction problems the method is constituted by a time discontinuous space time finite element method on the fine scale level an explicit procedure for advancing the coarse scale solution on the respective level and inter scale operators providing the data transfer between the coarse and fine scale level in both directions the results from three numerical test cases show that for both problematic flow regimes that is the regime of dominant convection and the regime of dominant convection and absorption the proposed method provides completely stable solutions which are not achieved by standard stabilized methods particularly for the later regime for remedying a still to be noted shortcoming of the proposed method that is a too smooth resolution of sharp gradient regions in the solution field considerable improvement can be provided by the use of cubic spline interpolation as the spatial reconstruction i e the spatial coarse to fine inter scale operator

a second order maximum principle preserving lagrange finite element technique for nonlinear scalar conservation equations this paper proposes an explicit at least second order maximum principle sat isfying lagrange finite element method for solving nonlinear scalar conservation equations the technique is based on a new viscous bilinear form introduced in guermond and nazarov com put methods appl mech engrg 272 2014 pp 198 213 a high order entropy viscosity method and the boris book zalesak flux correction technique the algorithm works for arbitrary meshes in any space dimension and for all lipschitz fluxes the formal second order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems

adaptive time step with anisotropic meshing for incompressible flows this paper presents a method of combining anisotropic mesh adaptation and adaptive time stepping for computational fluid dynamics cfd first we recall important features of the anisotropic meshing approach using a posteriori estimates relying on the length distribution tensor approach and the associated edge based error analysis then we extend the proposed technique to contain adaptive time advancing based on a newly developed time error estimator the objective of this paper is to show that the combination of time and space anisotropic adaptations with highly stretched elements can be used to compute high reynolds number flows within reasonable computational and storage costs in particular it will be shown that boundary layers flow detachments and all vortices are well captured automatically by the mesh the time step is controlled by the interpolation error and preserves the accuracy of the mesh adapted solution a variational multiscale vms method is employed for the discretization of the navier stokes equations numerical solutions of some benchmark problems demonstrate the applicability of the proposed space time error estimator an important feature of the proposed method is its conceptual and computational simplicity as it only requires from the user a number of nodes according to which the mesh and the time steps are automatically adapted

a stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics a novel numerical method for solving three dimensional two phase flow problems is presented this method combines a quadrature free discontinuous galerkin method for the level set equation with a pressure stabilized finite element method for the navier stokes equations the main challenge in the computation of such flows is the accurate evaluation of surface tension forces this involves the computation of the curvature of the fluid interface in the context of the discontinuous galerkin method we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results a more robust second order least squares computation of the curvature that filters out the high frequencies and produces converged results is presented this whole numerical technology allows to simulate a wide range of flow regimes with large density ratios to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation

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

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

modeling incompressible flows at low and high reynolds numbers via a finite calculus finite element approach we present a formulation for incompressible flows analysis using the finite element method fem the necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus fic method the stabilization terms introduced by the fic formulation allow to solve a wide range of fluid flow problems for low and high reynolds numbers flows without the need for a turbulence model examples of application of the fic fem formulation to the analysis of 2d and 3d incompressible flows with moderate and large reynolds numbers are presented

finite element methods for linear hyperbolic problems abstract we give a survey of some recent work by the authors on finite element methods for convectiondiffusion problems and first order linear hyperbolic problems

unified adaptive variational multiscale method for two phase compressible incompressible flows in this paper we present a new stabilized finite element method to solve the two phase compressible incompressible fluid flow problems using the level set method an anisotropic mesh adaptation with a regularized interface is adopted to deal with the high discontinuity in the material properties the coupling between the pressure and the flow velocity is ensured by introducing mass conservation terms in the momentum equation therefore the same set of primitive unknowns and equations is described for both phases the unified system is solved using a new derived variational multiscale stabilized finite element method it is tested on three time dependent liquid gas interface problems the numerical results show good stability and accuracy properties permitting also to deal with important compressibility effect high density ratio and extremely stretched anisotropic elements

stabilized finite element method for incompressible flows with high reynolds number in the following paper we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3d time dependent incompressible navier stokes equations the proposed method starts by the use of a finite element variational multiscale vms method which consists in here of a decomposition for both the velocity and the pressure fields into coarse resolved scales and fine unresolved scales this choice of decomposition is shown to be favorable for simulating flows at high reynolds number we explore the behaviour and accuracy of the proposed approximation on three test cases first the lid driven square cavity at reynolds number up to 50 000 is compared with the highly resolved numerical simulations and second the lid driven cubic cavity up to re 12 000 is compared with the experimental data finally we study the flow over a 2d backward facing step at re 42 000 results show that the present implementation is able to exhibit good stability and accuracy properties for high reynolds number flows with unstructured meshes

solution techniques for the fully discretized equations in computation of fluid structure interactions with the space time formulations we provide an overview of the solution techniques we have developed for the fully discretized equations encountered at every time step in computation of fluid structure interactions with the space time techniques these coupled nonlinear equations are generated from the finite element discretization of the governing equations for the fluid mechanics structural mechanics and the motion of the fluid mechanics mesh the fluid mechanics equations are discretized with the deforming spatial domain stabilized space time formulation the mesh motion is governed by the equations of elasticity with the smaller elements stiffened in the finite element formulation the coupled fully discretized equations are solved with the block iterative quasi direct and direct coupling methods we present numerical examples with incompressible flows and membrane and cable structures 2005 elsevier b v all rights reserved

shape optimization of a body in compressible inviscid flows abstract the objective of this paper is to determine the optimal shape of a body a two dimensional elliptical cylinder in this study located in a compressible inviscid flow governed by the euler equations such that the pressure acting on the surface of the body is minimized the formulation to obtain the optimal shape is based on optimal control theory the optimal state is defined as the state in which the performance function the integration of the square sum of the traction on the surface of the body is minimized due to a reduction in pressure on the body the compressible euler equations are treated as constraint equations that is the optimal shape of the body is considered to be that shape that minimizes the pressure acting on the body under the constraint of the euler equations a gradient of the performance function is computed by using the adjoint variables the weighted gradient method is used as the minimization algorithm the volume of the body is assumed to be constant for the discretization of both the state and adjoint equations the mixed interpolation method based on the bubble function interpolation presented previously by the authors is employed both the structured mesh around the surface and the smoothing procedure are employed for the gradient as numerical studies the shape optimization of a body in a uniform flow field is carried out the initial shape of the body is assumed to be an ellipse the shape is updated by minimizing the pressure on the surface finally the shape of the body should be almost a flat line stable optimal shape determination of a body in a compressible inviscid flow is obtained by using the presented method

locally conservative stabilized finite element methods for variably saturated flow standard galerkin finite element methods for variably saturated groundwater flow have several deficiencies for instance local oscillations can appear around sharp infiltration fronts without the use of mass lumping and velocity fields obtained from differentiation of pressure fields are discontinuous at element boundaries here we consider conforming finite element discretizations based on a multiscale formulation along with recently developed local postprocessing schemes the resulting approach maintains the basic flexibility and appeal of traditional finite element methods while controlling nonphysical oscillations and producing element wise mass conservative velocity fields accuracy and efficiency of the proposed schemes are evaluated through a series of steady state and transient variably saturated groundwater flow problems in homogeneous as well as heterogeneous domains the schemes are formulated for a generic nonlinear advection diffusion equation and are thus applicable to many other flow models

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers since the mid of the 1980s a number of methods have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers the paper gives a review and state of the art of these methods discusses their derivation proposes some alternative choices of parameters in the methods and categorizes them some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods

finite element formulation for convective diffusive problems with sharp gradients using finite calculus abstract a finite element method fem for steady state convective diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented the necessary stabilization of the numerical solution is provided by the finite calculus fic approach the fic method is based in the solution by the galerkin fem of a modified set of governing equations which include characteristic length parameters it is shown that the fic balance equation for the multidimensional convection diffusion problem written in the principal curvature axes of the solution introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients the dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach

stabilization and shock capturing parameters in supg formulation of compressible flows abstract the streamline upwind petrov galerkin supg formulation is one of the most widely used stabilized methods in finite element computation of compressible flows it includes a stabilization parameter that is known as typically the supg formulation is used in combination with a shock capturing term that provides additional stability near the shock fronts the definition of the shock capturing term includes a shock capturing parameter in this paper we describe for the finite element formulation of compressible flows based on conservation variables new ways for determining the and the shock capturing parameter the new definitions for the shock capturing parameter are much simpler than the one based on the entropy variables involve less operations in calculating the shock capturing term and yield better shock quality in the test computations

time accurate consistently stabilized mesh free methods for convection dominated problems this is the pre peer reviewed version of the following article huerta a fernandez s time accurate consistently stabilized mesh free methods for convection dominated problems international journal for numerical methods in engineering gener 2003 vol 56 num 9 p 1225 1242 which has been published in final form at http www3 interscience wiley com journal 102522343 abstract

isogeometric fluid structure interaction analysis with emphasis on non matching discretizations and with application to wind turbines abstract in this paper we develop a framework for fluid structure interaction fsi modeling and simulation with emphasis on isogeometric analysis iga and non matching fluid structure interface discretizations we take the augmented lagrangian approach to fsi as a point of departure here the lagrange multiplier field is defined on the fluid structure interface and is responsible for coupling of the two subsystems thus the fsi formulation does not rely on the continuity of the underlying function spaces across the fluid structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains however in deriving the final fsi formulation the interface lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables avoiding the use of lagrange multipliers adds efficiency to the proposed formulation as an added benefit the ability to employ non matching grids for multi physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for iga we show an application of the proposed fsi formulation to the simulation of the nrel 5 mw offshore wind turbine rotor where the aerodynamics domain is modeled using volumetric quadratic nurbs while the rotor structure is modeled using a cubic t spline based discretization of a rotation free kirchhoff love shell we conclude the article by showing fsi coupling of a t spline shell with a low order finite element method fem discretization of the aerodynamics equations this combined use of iga and fem is felt to be a good balance between speed robustness and accuracy of fsi simulations for this class of problems

objectivity tests for navier stokes simulations the revealing of non physical solutions produced by laplace formulations abstract laplace formulations are weak formulations of the navier stokes equations commonly used in computational fluid dynamics in these schemes the viscous terms are given as a function of the laplace diffusion operator only despite their popularity recently it has been proven that they violate a fundamental principle of continuum mechanics the principle of objectivity it is remarkable that such flaw has not being noticed before neither detected in numerical experiments in this work a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments through the tests it is shown how for slip boundaries or free surfaces laplace formulations generate non physical solutions which widely depart from the real fluid dynamics these tests can be easily reproduced not requiring complex simulation tools furthermore they can be used as benchmarks to check consistency of developed or commercial software the article is closed with a discussion of the mathematical aspects involved including the issues of boundary conditions and objectivity

on the stabilized finite element method for steady convection dominated problems with anisotropic mesh adaptation in this work we combine the use of the streamline upwind petrov galerkin supg method with anisotropic mesh adaptation to obtain accurate solutions for steady convection dominated problems the anisotropic mesh adaptation framework is introduced in the context of a local mesh generation method based on a mesh topology modification and a minimal volume principle a new route to get a metric field directly at the node of the mesh is highlighted using the length distribution tensor and an edge based error analysis an a posteriori error estimation is applied to the stabilized finite element solution detecting automatically all sharp gradients inner and boundary layers the numerical examples show that the use of the anisotropic mesh adaptation algorithm allows the recovery of the global convergence order of the numerical schemes while producing accurate and oscillation free numerical solutions

a diffuse interface method for the navier stokes darcy equations perfusion profile for a patient specific human liver based on mri scans abstract we present a diffuse interface method for coupling free and porous medium type flows modeled by the navier stokes and darcy equations its essential component is a diffuse geometry model generated from the phase field solution of a separate initial boundary value problem that is based on the allen cahn equation phase field approximations of the interface and its gradient are then employed to transfer all interface terms in the coupled variational flow formulation into volumetric terms this eliminates the need for an explicit interface parametrization between the two flow regimes we illustrate accuracy and convergence for a series of benchmark examples using standard low order stabilized finite element discretizations our diffuse interface method is particularly attractive for coupled flow analysis on imaging data with complex implicit interfaces where procedures for deriving explicit surface parametrizations constitute a significant bottleneck we demonstrate the potential of our method to establish seamless imaging through analysis workflows by computing a perfusion profile for a full scale 3d human liver based on mri scans

solution of high reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing the objective of this paper is to show that anisotropic meshes with highly stretched elements can be used to compute high reynolds number flows in particular it will be shown that boundary layers flow detachments and all vortices are well captured automatically by the mesh we present an anisotropic meshing based on a posteriori estimation for the incompressible navier stokes equations the proposed a posteriori estimate is based on the length distribution tensor approach and the associated edge based error analysis the finite element flow solver is based on a variational multiscale vms method which consists in here of decomposing both the velocity and the pressure fields into coarse resolved and fine unresolved scales this choice of decomposition is shown to be efficient for simulating flows at high reynolds number the stabilization parameters are determined taking into account the anisotropy of the mesh using a directional element diameter the adaptation algorithm is applied to high reynolds number flows inside the 2d and 3d lid driven cavities and compared to accurate reference solutions

quadratic finite elements and incompressible viscous flows pressure stabilization methods are applied to higher order velocity finite elements for application to viscous incompressible flows both a standard pressure stabilizing petrov galerkin pspg method and a new polynomial pressure projection stabilization ppps method have been implemented and tested for various quadratic elements in two dimensions a preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed galerkin finite element approximations to the navier stokes equations the preconditioner is demonstrated for bb stable elements with discontinuous pressure approximations in two and three dimensions

enhanced approximation linear solution technique ealst abstract the enhanced discretization and solution techniques are among the advanced computational methods we rely on in simulation and modeling of complex flow problems including those with moving boundaries and interfaces the set of enhanced discretization and solution techniques includes those based on enhancement in spatial discretization enhancement in time discretization and enhancement in iterative solution of nonlinear and linear equation systems the enhanced approximation linear solution technique ealst was introduced to increase the performance of the iterative technique used in solution of the linear equation systems when some parts of the computational domain may offer more of a challenge for the iterative method than the others the ealst can be used for computations based on semi discrete or space time formulations

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

functions and sequences generated by reaction systems the paper investigates formal properties of reaction systems introduced by ehrenfeucht and rozenberg a reaction system defines a function from the set 2 s of subsets of a finite set s into 2 s itself we investigate properties of such functions and characterize situations when the function is total we also introduce and characterize the property of functional completeness function classes defined by different types of reaction systems are compared comparisons are carried out also between different methods of generating long sequences and cycles

on solving the sum of ratios problem this paper addresses the development of efficient global search methods for fractional programming problems such problems are in general nonconvex with numerous local extremums and belong to a class of global optimization problems first we reduce a rather general fractional programming problem with d c functions to solving an equation with a vector parameter that satisfies some nonnegativity assumption this theorem allows the justified use of the generalized dinkelbachs approach for solving fractional programming problems with a d c goal function based on solving of some d c minimization problem we developed a global search algorithm for fractional programming problems which was tested on a set of low dimensional test problems taken from the literature as well as on randomly generated problems with up to 200 variables or 200 terms in the sum

a plausible extension of standard penalty streamline upwind and immersed boundary techniques to the improved element free galerkin based solution of incompressible navier stokes equations abstract the present work has been conducted in order to propose the extension of standard penalty and stabilization techniques to the improved element free galerkin iefg method for the numerical solution of incompressible fluid flow problems in principle the numerical procedures to be implemented in this communication have been conceived for finite element method fem based solutions and these include the reduced integration penalty method ripm the streamline upwind petrov galerkin supg scheme and a penalty based immersed boundary method pbibm for the imposition of essential boundary conditions along internal fluid solid interfaces the linear momentum balance and mass conservation equations have been coupled via the ripm in order to obtain a global weak formulation where the iefg model is entirely developed in terms of improved moving least squares imls approximations of the velocity field a detailed explanation concerning the appropriate extension of both the ripm and supg procedures to the context of iefg formulations has also been provided the resulting formulation has been applied to the solution of two well known benchmark problems i lid driven square cavity flow and ii flow past a fixed cylinder regarding the flow past a fixed cylinder benchmark problem the fluid solid interaction has been imposed as an internal immersed boundary condition via the pbibm the feasibility and reliability of implementing the ripm supg and pbibm procedures in the iefg formulation have been proven by comparison with experimental and mesh based numerical results reported in the literature the results obtained in this study have revealed that a proper extension of the aforementioned penalty and stabilization techniques to the iefg formulation allows the achievement of accurate and stable numerical results during the solution of incompressible fluid dynamics problems

two dimensional shape optimization using partial control and finite element method for compressible flows abstract the objective of this study is to determine the two dimensional shape of a body located in a compressible viscous flow where the applied fluid force is minimized the formulation to obtain the optimal shape is based on an optimal control theory an optimal state is defined as a state in which the performance function defined as the integration of the square sum of the applied fluid forces is minimized due to a reduction in the applied fluid forces compressible navier stokes equations are treated as constraint equations in other words the body is considered to have a shape that minimizes the fluid forces under the constraint of the navier stokes equations the gradient of the performance function is computed using the adjoint variables a weighted gradient method is used as the minimization algorithm the volume of the body is assumed to be the same as that of the initial body in the case of the algorithm used in this study both the creation of a structured mesh around the surface of the body and the smoothing procedure are employed for the computation of gradient in this study a remeshing technique based on the structured mesh around the body changing its configuration in the iteration cycle is employed for the correction to keep the volume constant the surface coordinates are moved along the radial direction for the discretization of both the state and adjoint equations the efficient bubble function interpolation presented previously by the authors 18 is employed the algorithm which is known as the partial control algorithm is applied to the numerical procedure to determine the movement of the coordinates in the case of the gradient method in order to avoid the convergence of the final shape to the local minimum shape the new algorithm which is called the partial control algorithm is presented in this study in numerical studies the shape determination of a body in a uniform flow field is carried out in 2d domains the initial shape of the body is assumed to be an elliptical cylinder the shape is modified by minimizing the applied fluid forces finally the desired shape of a body whose performance function is reduced and converged to a constant value is obtained by carrying out a procedure that involves the use of the partial control algorithm the desired shape of a body whose performance function is reduced further is obtained stable shape determination of a body in a compressible viscous flow is carried out by using the presented method it is indicated that the optimal shape can be obtained by using the partial control algorithm

calculation of the advective limit of the supg stabilization parameter for linear and higher order elements abstract we investigate for linear and higher order elements various ways of calculating the advective limit of the stabilization parameter used in the streamline upwind petrov galerkin supg formulation of flow problems in the context of a pure advection test problem we compare the ugn based element matrix based and element node based calculations of the advective limit of the our investigation shows that the performances of the ugn based and element matrix based definitions are comparable with the element matrix based definition yielding somewhat lower values we also show that for both definitions as the polynomial orders increase the values decrease as they should

a lagrangian finite element approach for the analysis of fluid structure interaction problems a lagrangian finite element method for the analysis of incompressible newtonian fluid flows based on a continuous re triangulation of the domain in the spirit of the so called particle finite element method is here revisited and applied to the analysis of the fluid phase in fluid structure interaction problems a new approach for the tracking of the interfaces between fluids and structures is proposed special attention is devoted to the mass conservation problem it is shown that despite its lagrangian nature the proposed combined finite element particle method is well suited for large deformation fluid structure interaction problems with evolving free surfaces and breaking waves the method is validated against the available analytical and numerical benchmarks copyright 2010 john wiley sons ltd

a stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows a numerical method for the simulation of three dimensional incompressible two phase flows is presented the proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two phase flow problems with a level set method implemented with a quadrature free discontinuous galerkin dg method e marchandise j f remacle n chevaugeon a quadrature free discontinuous galerkin method for the level set equation journal of computational physics 212 2006 338 357 the use of a fast contouring algorithm n chevaugeon e marchandise c geuzaine j f remacle efficient visualization of high order finite elements international journal for numerical methods in engineering permits us to localize the interface accurately by doing so we can compute the discontinuous integrals without neither introducing an interface thickness nor reinitializing the level set the capability of the resulting algorithm is demonstrated with large scale numerical examples free surface flows dam break sloshing and small scale ones two phase poiseuille rayleigh taylor instability