dwork s conjecture on unit root zeta functions annals of mathematics 150 1999 867 927 arxiv math 9911270v1 math nt 1 nov 1999 dwork s conjecture on unit root zeta functions by daqing wan 1 introduction in this article we introduce a systematic new method to investigate the conjectural p adic meromorphic continuation of professor bernard dwork s unit root zeta function attached to an ordinary family of algebraic varieties defined over a finite field of characteristic p after his pioneer p adic investigation of the weil conjectures on the zeta function of an algebraic variety over a finite field dwork went on to study the p adic analytic variation of a family of such zeta functions when the variety moves through an algebraic family in the course of doing so he was led to a new zeta function called the unit root zeta function which goes beyond the reach of the existing theory he conjectured 8 that such a unit root zeta function is p adic meromorphic everywhere these unit root zeta functions contain important arithmetic information about a family of algebraic varieties they are truly p adic in nature and are transcendental functions sometimes seeming quite mysterious in fact no single nontrivial example has been proved to be true about this conjecture other than the trivial overconvergent or log convergent case for which dwork s classical p adic theory already applies see 6 11 26 for various attempts in this article we introduce a systematic new method to study such unit root zeta functions our method can be used to prove the conjecture in the case when the involved unit root f crystal has rank one in particular this settles the first nontrivial case the rank one unit root f crystal coming from the family of higher dimensional kloosterman sums our method further allows us to understand reasonably well about analytic variation of an arithmetic family of such rank one unit root zeta functions motivated by the gouv ea mazur conjecture about dimension variation of classical and p adic modular forms we shall introduce another this work was partially supported by nsf the author wishes to thank p deligne and n katz for valuable discussions at one stage of this work during 1993 and 1994 the author would also like to thank s sperber for his careful reading of the manuscript and for his many detailed comments which led to a significant improvement of the exposition

improvements of the weil bound for artin schreier curves for the artin schreier curve y q y f x defined over a finite field mathbb f q of q elements the celebrated weil bound for the number of mathbb f q r rational points can be sharp especially in super singular cases and when r is divisible in this paper we show how the weil bound can be significantly improved using ideas from moment l functions and katz s work on l adic monodromy calculations roughly speaking we show that in favorable cases which happens quite often one can remove an extra sqrt q factor in the error term

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

rationality of trace and norm l functions for a given l adic sheaf f on a commutative algebraic group g over a finite field k and an integer r 1 we define the rth local norm l function of f at a point t g k and prove its rationality this function gives information on the sum of the local frobenius traces of f over the points of g kr where kr is the extension of degree r of k with norm t for g the 1 dimensional affine line or the torus these sums can in turn be used to estimate the number of rational points on curves or the absolute value of exponential sums which are invariant under a large group of translations or homotheties

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

higher rank case of dwork s conjecture journal of the american mathematical society volume 00 number 0 xxxx xxxx pages 000 000 s 0894 0347 xx 0000 0 arxiv math 0005309v1 math nt 9 may 2000 higher rank case of dwork s conjecture daqing wan dedicated to the memory of bernard dwork 1 introduction in this series of two papers we prove the p adic meromorphic continuation of the pure slope l functions arising from the slope decomposition of an overconvergent f crystal as conjectured by dwork 6 more precisely we prove a suitable extension of dwork s conjecture in our more general setting of modules see section 2 for precise definitions of the various notions used in this introduction our main result is the following theorem theorem 1 1 let x be a smooth affine variety defined over a finite field f q of characteristic p 0 let m be a finite rank overconvergent module over x f q then for each rational number s the pure slope s l function l s t attached to is p adic meromorphic everywhere the proof of this theorem will be completed in two papers in the present higher rank paper we introduce a reduction approach which reduces theorem 1 1 to the special case when the slope s s 0 part of has rank one and the base space x is the simplest affine space a n this part is essentially algebraic it depends on monsky s trace formula grothendieck s specialization theorem the hodge newton decomposition and katz s isogeny theorem in our next paper 23 we will handle the rank one case over the affine space a n the rank one case is very much analytic in nature and forces us to work in a more difficult infinite rank setting generalizing and improving the limiting approach introduced in 19 dwork s conjecture grew out of his attempt to understand the p adic analytic variation of the pure pieces of the zeta function of a variety when the variety moves through an algebraic family to give an important geometric example let us con sider the case that f y x is a smooth and proper morphism over f q with a smooth and proper lifting to characteristic zero berthelot s result 1 says that the relative crystalline cohomology r i f crys z p modulo torsion is an overconvergent f crystal m i over x applying theorem 1 1 we conclude that the pure l functions arising from these geometric overconvergent f crystals m i are p adic meromorphic in particular this implies the existence of an exact p adic formula for geometric p adic character sums and a suitable p adic equi distribution theorem for the roots of zeta functions for more detailed arithmetic motivations and further open prob lems see the expository papers 20 21 1991 mathematics subject classification primary 11g40 11s40 secondary 11m41 14g15 key words and phrases l functions p adic meromorphic continuation modules this work was partially supported by nsf c american mathematical society

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

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

input disturbance predictive control of shallow water flows abstract the purpose of this paper is to describe the predictive control of flood flows over the surface of reservoirs in a mountainous area with a complicated terrain shape it is expected that damage to villages around the reservoir can be reduced if the water elevation of water discharge is controlled using an artificially constructed aqueduct the control method uses the first order adjoint equation and the numerical technique used is the finite element method in order to control water elevation prediction of input discharge is necessary and optimal discharges can accordingly be determined predictive control of water flows is carried out in this study the adjoint equation method is applied to obtain the optimal control a performance function is used as the index of the optimal control which is defined by the sum of the square of the computed water elevation at the target points as a minimization technique the weighted gradient method is applied the gradient of the extended performance function with respect to the control of water discharge is obtained by solving the first order adjoint equation the predictive control method employed in this paper is a technique to make prediction of the input disturbance and compute the optimal control value at a certain time duration the shallow water equation based on the water discharge and elevation is used as the governing equation as the spatial discretization the finite element method based on the linear function interpolation is employed as the temporal discretization the two step explicit scheme is applied after verification based on the predictive control of the water elevation in simple rectangular channel and sinusoidal water elevation model the present method is applied to flood control of the ikari reservoir located in the tochigi prefecture in japan

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

freudenthal triple systems by root system methods abstract for certain lie algebras g we can use a grading g g 2 g 1 g 0 g 1 g 2 and define a quartic form and a skew symmetric bilinear form on g 1 thereby constructing a freudenthal triple system the structure of the freudenthal triple system is examined using root system methods available in the lie algebra context in the cases g e 8 where g 1 is the minuscule representation of e 7 and g d 4 we determine the groups stabilizing the quartic form and both the quartic and bilinear forms

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

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

rank one case of dwork s conjecture journal of the american mathematical society volume 00 number 0 xxxx xxxx pages 000 000 s 0894 0347 xx 0000 0 arxiv math 0005308v1 math nt 9 may 2000 rank one case of dwork s conjecture daqing wan 1 introduction in the higher rank paper 17 we reduced dwork s conjecture from higher rank case over any smooth affine variety x to the rank one case over the simplest affine space a n in the present paper we finish our proof by proving the rank one case of dwork s conjecture over the affine space a n which is called the key lemma in 17 the key lemma had already been proved in 16 in the special case when the frobenius lifting is the simplest q th power map x x q thus the aim of the present paper is to treat the general frobenius lifting case our method here is an improvement of the limiting method in 16 it allows us to move one step further and obtain some explicit information about the zeros and poles of the unit root l function as in 16 to handle the rank one case we are forced to work in the more difficult infinite rank setting see section 2 for precise definitions of the various basic infinite rank notions let f q denote the finite field of characteristic p 0 our main result of this paper is the following theorem theorem 1 1 let be a nuclear overconvergent module over the affine n space a n f q ordinary at the slope zero side let unit be the unit root slope zero part of assume that unit has rank one let be another nuclear overconvergent module over a n f q then for each integer k the l function l k unit t is p adic meromorphic furthermore the family l k t of l functions unit parametrized by integers k in each residue class modulo q 1 is a strong family of meromorphic functions with respect to the p adic topology of k a finite rank module is automatically nuclear thus theorem 1 1 includes the key lemma of 17 over a n as a special case the basic ideas of the present paper are the same as the limiting approach in 16 the details are however quite different in the simplest q th power frobenius lifting case one has the fundamental dwork trace formula available which is completely explicit for uniform estimates this makes it easy to extend the dwork trace formula to infinite rank setting it also makes it possible to see the various analytic subtleties involved in a concrete case as a result we were able to prove analytically optimal results in 16 for a general frobenius lifting even over the simplest affine n space a n as we shall work in this paper one has to use the much more difficult monsky trace formula which is a generalization of dwork s trace formula thus the first task of this paper is to extend the monsky trace formula to infinite rank setting and to make it sufficiently 1991 mathematics subject classification primary 11g40 11s40 secondary 11m41 14g15 key words and phrases l functions fredholm determinants p adic meromorphic continua tion nuclear modules and banach modules this work was partially supported by nsf c american mathematical society

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

generators and irreducible polynomials over finite fields weil s character sum estimate is used to study the problem of constructing generators for the multiplicative group of a finite field an application to the distribution of irreducible polynomials is given which confirms an asymptotic version of a conjecture of hansen mullen

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

freudenthal triple systems in arbitrary characteristic abstract let q v k be the form of degree 4 and h the alternating bilinear form that together give rise to a freudenthal triple system when the characteristic of k is different from 2 and 3 we give a form of degree 4 on a central cover of v over an arbitrary field in arbitrary characteristic and determine the group of similitudes of this group coincides with the intersection of the group of similitudes of q and the isometry group of h when the characteristic is different from 2 and 3 and has the expected structure of a suitable levi subgroup in general we extend known results about the stabilizers of elements of v and orbits of the group of similitudes and show in particular the existence of an exotic set of orbits when char k 2 and k is not perfect

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

structurable algebras and groups of type e6 and e7 abstract it is well known that every group of type f 4 is the automorphism group of an exceptional jordan algebra and that up to isogeny all groups of type 1 e 6 with trivial tits algebras arise as the isometry groups of norm forms of such jordan algebras we describe a similar relationship between groups of type e 6 and groups of type e 7 and use it to give explicit descriptions of the homogeneous projective varieties associated to groups of type e 7 with trivial tits algebras

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

on the stability of thek1 functor for chevalley groups of type e7 abstract this paper is devoted to the study of the surjective stability of the k 1 functor for chevalley groups of type e 7 this is a particular case of the stability problem for chevalley groups which was posed by h bass in this paper surjective stability of the k 1 functor is proved under natural conditions on the dimension of the maximal spectrum of a ring and independently under a special condition which is meaningful from the point of view of equations defining a chevalley group

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

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

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 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