rigidity for anosov actions of higher rank lattices this is the simplest example of a large class of analytic standard actions of lattices in semisimple lie groups on locally homogeneous spaces a basic problem is to understand the differentiable actions near to such a standard action in terms of their geometry and dynamics cf 13 50 51 a cr action so if x x x of a group f on a compact manifold x is said to be anosov if there exists at least one element yh e f such that p yh is an anosov diffeomorphism of x we begin in this paper to study the anosov differentiable actions of lattices including many standard algebraic examples and especially to study their stability properties our main theme is that either the cr rigidity or the cr deformation rigidity of an anosov action for 1 r cr or even for the real analytic case can be shown just by studying the behavior of the periodic orbits for the action there are two notions of structural stability that appear in this paper rigidity and deformation rigidity a cl perturbation of a cr action so is simply another cr action spl such that for a finite set of generators 81 ad of f the cr diffeomorphisms p 8i and pl 8i are cl close for all i an action so is said to be cr rigid or topologically rigid if r 0 if every sufficiently small c perturbation of so is cr conjugate to so for 0 r oo or r w in the case of real analytic actions a cl deformation of an action so is a continuous path of cr actions pt defined for some 0 t e with spo sd an action sd is said to be cr deform

global rigidity of higher rank abelian anosov algebraic actions we show that all c infty anosov mathbb z r actions on tori and nilmanifolds without rank one factor actions are up to c infty conjugacy actions by automorphisms

semi crossed products of c algebras abstract given a c algebra u and endomorphim there is an associated nonselfadjoint operator algebra z x u called the semi crossed product of u with if is an automorphim z x u can be identified with a subalgebra of the c crossed product z x u if u is commutative and is an automorphim satisfying certain conditions z x u is an operator algebra of the type studied by arveson and josephson suppose s is a locally compact hausdorff space s s is a continuous and proper map and is the endomorphim of u c0 s given by necessary and sufficient conditions on the map are given to insure that the semi crossed product z x c0 s is i semiprime ii semisimple ii strongly semisimple

on local rigidity of partially hyperbolic affine ℤ k actions the following dichotomy for affine z k actions on the torus t d k d is an element of n is shown to hold i the linear part of the action has no rank one factors and then the affine action is

operator algebras and the conjugacy of transformations abstract a family of algebras is associated with each continuous map on a compact hausdorff space these algebras are called conjugacy algebras it is shown that two continuous maps are conjugate if and only if some conjugacy algebra of one is isomorphic to some conjugacy for the other numerous examples of conjugacy algebras are provided

a conservative treatment of zonal boundaries for euler equation calculations finite difference calculations require the generation of a grid for the region of interest a zonal approach wherein the given region is subdivided into zones and the grid for each zone is generated independently makes the grid generation process for complicated topologies and for regions requiring selective grid refinement a fairly simple task this approach results in new boundaries within the given region that is zonal boundaries at the interfaces of the various zones the zonal boundary scheme the integration scheme used to update the points on the zonal boundary for the euler equations must be conservative accurate stable and applicable to general curvilinear coordinate systems a zonal boundary scheme with these desirable properties is developed in this study the scheme is designed for explicit first order accurate integration schemes but can be modified to accommodate second order accurate explicit and implicit integration schemes results for inviscid flow including supersonic flow over a cylinder blast wave diffraction by a ramp and one dimensional shock tube flow are obtained on zonal grids the conservative nature of the zonal boundary scheme permits the smooth transition of the discontinuities associated with these flows from one zone to another the calculations also demonstrate the continuity of contour lines across zonal boundaries that can be achieved with the present zonal scheme

a general non iterative riemann solver for godunov s method abstract godunov s method is characterized by the use of a riemann problem solution to resolve discontinuities at the interface between cells the major drawback of this method is the difficulty and the high cost of solving the nonlinear riemann problem exactly especially for materials with complex equations of state this paper describes a simplified and noniterative approximate riemann solver which is characterized by only two material dependent parameters for a given material these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks these parameters are conveniently obtained from a linear fit to the experimental data for the shock hugoniot in various materials the approximate riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

a shift transformation for fully conservative methods turbulence simulation on complex unstructured grids abstract operator transformations are presented that allow matrix operators for collocated variables to be transformed into matrix operators for staggered variables while preserving symmetries these shift transformations permit conservative skew symmetric convective operators and symmetric positive definite diffusive operators to be obtained for staggered variables using collocated operators shift transformations are not limited to uniform or structured meshes and this formulation leads to a generalization of the works of perot j comput phys 159 2000 58 and verstappen and veldman j comput phys 187 2003 343 a set of shift operators have been developed for and applied to a time adaptive cartesian mesh method with a fractional step algorithm the resulting numerical scheme conserves mass to machine error and conserves momentum and energy to second order in time a mass conserving interpolation is used for the variables during mesh adaptation the interpolation conserves momentum and energy to second order in space turbulent channel flow simulations were conducted at re 180 using direct numerical simulation dns the dns results from the adaptive method compare favourably with spectral dns results despite the use of a formally second order accurate scheme

nest representations and dynamical systems abstract a nest representation is a generalized irreducible representation of a banach algebra on hubert space for a free discrete dynamical system every ideal in the semicrossed product algebra is equal to an intersection of kernels of nest representations a proper subset of all such kernels is a topological space homeomorphic to the space of all discrete finite arcs in the dynamical system with the subarc topology for certain continuous dynamical systems the corresponding set of kernels is isomorphic to the topological space of continuous finite arcs a banach algebra isomorphism of semicrossed products implies orbit order conjugacy of the underlying dynamical systems nest algebras and a non free action are also considered

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

a dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations in this work we have derived an optimized upwind compact difference scheme for achieving excellent spatial resolution the derived numerical scheme adds numerical diffusion which is strictly restricted to a high wavenumber region in order to control numerical instabilities as well as to achieve de aliasing ability more importantly the derived numerical scheme has excellent dispersion relation preserving drp property the applicability of the proposed scheme in simulating real flow problems has been demonstrated by solving flow inside a lid driven cavity a transitional flow past ag24 aerofoil and a two dimensional decaying turbulence flow

freestream capturing for moving coordinates in three dimensions a detailed formula is developed that can be used in both finite volume fv and finite difference fd methods for constructing freestream capturing metrics in space and time it is shown that considering an fv cell on the fd grid the freestream capturing metrics in space and time can be constructed from the fd formulation the approach is costly but guarantees the global conservation for an arbitrary motion of the grid

semisimple triangular af algebras abstract we give several necessary and sufficient conditions for a triangular af algebra to be semisimple in particular a triangular af algebra which can be written using the standard embedding infinitely often is semisimple we also give a semisimple triangular af algebra which does not have a presentation of this form if two triangular af algebras have the same peters poon wagner diagonal invariant then either both are semisimple or both are not however we give two algebras with the same diagonal invariant where one has the jacobson radical equal to the strong radical and the other does not semisimplicity can be characterized in terms of power s fundamental relation we give generalizations of these results to triangular subalgebras of groupoid c algebras it is shown that there is a unique maximal bimodule over the diagonal which does not intersect the radical using this we show that the wedderburn principal theorem does not hold for all triangular af algebras a necessary condition for the theorem to hold is that the above mentioned unique bimodule is a subalgebra

a relaxation approach to patched grid calculations with the euler equations abstract a conservative zonal boundary condition that was used with explicit integration schemes is extended to implicit upwind relaxation schemes in particular to the osher scheme the rate of convergence was found to increase considerably with the use of the implicit relaxationzonal scheme when compared to the explicit scheme the relaxation zonal scheme has also been used in a time accurate mode results demonstrating the time accuracy of the scheme and the feasibility of performing calculations in cases where some parts of the given system move relative to others e g rotor stator configurations are presented

local rigidity of partially hyperbolic actions i kam method and mathbb z k actions on the torus we show c local rigidity for k k 2 higher rank partially hyperbolic actions by toral automorphisms using a generalization of the kam kolmogorov arnold moser iterative scheme we also prove the existence of irreducible genuinely partially hyperbolic higher rank actions on any torus t n for any even n 6

the sensitivity and accuracy of fourth order finite difference schemes on nonuniform grids in one dimension abstract we construct local fourth order finite difference approximations of first and second derivatives on nonuniform grids in one dimension the approximations are required to satisfy symmetry relationships that come from the analogous higher dimensional fundamental operators the divergence the gradient and the laplacian for example we require that the discrete divergence and gradient be negative adjoint of each other div grad and the discrete laplacian is defined as lap divgrad the adjointness requirement on the divergence and gradient guarantees that the laplacian is a symmetric negative operator the discrete approximations we derive are fourth order on smooth grids but the approach can be extended to create approximations of arbitrarily high order we analyze the loss of accuracy in the approximations when the grid is not smooth and include a numerical example demonstrating the effectiveness of the higher order methods on nonuniform grids

navier stokes simulations of slender axisymmetric shapes in supersonic turbulent flow computational fluid dynamics is used to study flows about slender axisymmetric bodies at very high speeds numerical experiments are conducted to simulate a broad range of flight conditions mach number is varied from 1 5 to 8 and reynolds number is varied from 1 x 106 m to 2 x 108 m the primary objective is to develop and validate a computational methodology for the accurate simulation of a wide variety of flow structures accurate results are obtained for detached bow shocks recompression shocks corner point expansions base flow recirculations and turbulent boundary layers accuracy is assessed through comparison with theory and experimental data computed surface pressure shock structure base flow structure and velocity profiles are within measurement accuracy throughout the range of conditions tested the methodology is both practical and general general in its applicability and practical in its performance to achieve high accuracy modifications to previously reported techniques are implemented in the scheme these modifications improve computed results in the vicinity of symmetry lines and in the base flow region including the turbulent wake

a space time conservation element and solution element method for solving the two and three dimensional unsteady euler equations using quadrilateral and hexahedral meshes in this paper we report a version of the space time conservation element and solution element ce se method in which the 2d and 3d unsteady euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes respectively in the present method mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for at each mesh point the value of a flow variable is obtained by imposing a flux conservation condition on the other hand the spatial derivatives are evaluated using a finite difference weighted average procedure note that the present extension retains many key advantages of the original ce se method which uses triangular and tetrahedral meshes respectively for its 2d and 3d applications these advantages include efficient parallel computing ease of implementing nonreflecting boundary conditions high fidelity resolution of shocks and waves and a genuinely multidimensional formulation without the need to use a dimensional splitting approach in particular because riemann solvers the cornerstones of the godunov type upwind schemes are not needed to capture shocks the computational logic of the present method is considerably simpler to demonstrate the capability of the present method numerical results are presented for several benchmark problems including oblique shock reflection supersonic flow over a wedge and a 3d detonation flow

smooth linearization of commuting circle diffeomorphisms we show that a finite number of commuting diffeomorphisms with simultane ously diophantine rotation numbers are smoothly conjugated to rotations this solves a problem raised by moser

high order finite volume schemes for the advection diffusion equation a high order finite volume method based on piecewise interpolant polynomials is proposed to discretize spatially the one dimensional and two dimensional advection diffusion equation evolution equations for the mean values of each control volume are integrated in time by a classical fourth order runge kutta since our work focuses on the behaviour of the spatial discretization the time step is chosen small enough to neglect the time integration error two dimensional interpolants are built by means of one dimensional interpolants it is shown that when the degree of the one dimensional interpolant q is odd the proper selection of a fixed stencil gives rise to centred schemes of order q 1 in order not to lose precision due to the change of stencil near boundaries the degree of the interpolants close to boundaries is raised to q 1 four test cases with small values of diffusion are integrated with high order methods it is shown that the spatial discretization of the advection diffusion equation with periodic boundary conditions leads to normal discretization matrices and asymptotic stability must be assured to bound the spatial discretization error once the asymptotic stability is assured by means of the spectra of the discretization matrix the spatial error is of the order of the truncation error however it is shown that the discretization of the advection diffusion equation with arbitrary boundary conditions gives rise to non normal matrices if asymptotic stability is assured the spatial order of steady solutions is of the order of the truncation error but for transient processes the order of the spatial error is determined by both the truncation error and the norm of the exponential matrix of the spatial discretization the use of the pseudospectra of the discretization matrix is proposed as a valuable tool to analyse the transient error of the numerical solution copyright 2001 john wiley sons ltd

a q1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh abstract in this paper we study a q 1 finite volume element scheme for anisotropic diffusion problems on general convex quadrilateral mesh it is known that the coercivity is the basement for some other theoretical results stability h 1 and l 2 error estimates etc and the existing results were mainly obtained on h 1 parallelogram meshes with scalar diffusion coefficients for the cases of full diffusion tensors and arbitrary convex quadrilateral meshes we obtain a necessary and sufficient condition for the positive definiteness of the cell matrix related to the cell bilinear form based on this result a sufficient condition is suggested to guarantee the coercivity of the scheme more interesting is that this sufficient condition covers the traditional h 1 parallelogram mesh assumption and has an explicit expression by which one can easily judge on any diffusion tensor and any mesh with arbitrary mesh size h 0 moreover an h 1 error estimate is obtained without the h 1 parallelogram assumption and some numerical results are also provided to validate the theoretical results

voronoi cell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids we introduce a new numerical grid based method on unstructured grids in the three dimensional real space to investigate the electronic structure of polyatomic molecules the voronoi cell finite difference vfd method realizes a discrete laplacian operator based on voronoi cells and their natural neighbors featuring high adaptivity and simplicity to resolve multicenter coulomb singularity in all electron calculations of polyatomic molecules this method utilizes highly adaptive molecular grids which consist of spherical atomic grids it provides accurate and efficient solutions for the schrodinger equation and the poisson equation with the all electron coulomb potentials regardless of the coordinate system and the molecular symmetry for numerical examples we assess accuracy of the vfd method for electronic structures of one electron polyatomic systems and apply the method to the density functional theory for many electron polyatomic molecules

conservation properties of unstructured staggered mesh schemes classic cartesian staggered mesh schemes have a number of attractive properties they do not display spurious pressure modes and they have been shown to locally conserve mass momentum kinetic energy and circulation to machine precision recently a number of generalizations of the staggered mesh approach have been proposed for unstructured triangular or tetrahedral meshes these unstructured staggered mesh methods have been created to retain the attractive pressure aspects and mass conservation properties of the classic cartesian mesh method this work addresses the momentum kinetic energy and circulation conservation properties of unstructured staggered mesh methods it is shown that with certain choices of the velocity interpolation unstructured staggered mesh discretizations of the divergence form of the navier stokes equations can conserve kinetic energy and momentum both locally and globally in addition it is shown that unstructured staggered mesh discretizations of the rotational form of the navier stokes equations can conserve kinetic energy and circulation both locally and globally the analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation these novel conserving unstructured staggered mesh schemes have not been previously analyzed it is shown that they are first order accurate on nonuniform two dimensional unstructured meshes and second order accurate on uniform unstructured meshes numerical confirmation of the conservation properties and the order of accuracy of these unstructured staggered mesh methods is presented

high order finite volume approximations of differential operators on nonuniform grids abstract when computing numerical solutions to partial differential equations difference operators that mimic the crucial properties of the differential operators are usually more accurate than those that do not properties such as symmetry conservation stability and the duality relationships and identities between the gradient curl and divergence operators are all important using the finite volume method we have derived local accurate reliable and efficient difference methods t divergence gradient and curl operators are defined using a discrete versions of the divergence theorem and stokes theorem these methods are especially powerful on coarse nonuniform grids and in calculations where the mesh moves to track interfaces or shocks numerical examples comparing local second and fourth order finite volume approximations to conservation laws on very rough grids are used to demonstrate the advantages of the higher order methods

a contribution to the numerical prediction of unsteady flows methods based on flux differe nce splitting are investigated with reference to the prediction of unsteady compressible flows they combine the feature of taking into account the wake like nature of these flows and the capability of correctly capturing shock waves two recently proposed approaches and a third one suggested here are compared for one dimensional flow with particular reference to the means of operating the splitting they are extended to the cases of variable area ducts and a general transformation of the independent variables firstand second order accurate schemes are presented and procedures for the computation at the boundaries are shown finally numerical experiments are reported and discussed

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

crossed products of operator algebras applications of takai duality abstract let g be a partially ordered abelian group with haar measure let a g be a dynamical system and let a be the associated semicrossed product using takai duality we establish a stable isomorphism a s a k g ad g where k g denotes the compact operators in the csl algebra alg l g and denotes the right regular representation of g we also show that there exists a complete lattice isomorphism between the invariant ideals of a and the ad invariant ideals of a k g using takai duality we also continue our study of the radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra we also show that the permanence of semisimplicity fails for crossed products by r a final section of the paper is devoted to the study of radically tight dynamical systems i e dynamical systems a g for which the identity rad a g rad a g persists a broad class of such dynamical systems is identified

damped euler equation method to compute transonic flow around wing body combinations inviscid transonic flows containing either strong shock waves or complex vortex structure call for the euler equations as a realistic model presented here is a computational procedure for solving the euler equations for transonic flow around a wing and fuselage upon an o o mesh generated by transfinite interpolation an explicit time marching finite volume procedure solves the flow equations and features a nonreflecting far field boundary condition an internal mechanism for temporal damping and use of the local time step all of which improve the convergence of the computation converged after several hundred iterations results computed on the cyber 203 vector processor are compared with experimental data and potential flow computations the euler equation model is found to predict the existence of a tip vortex created by inviscid flow separation in the downstream region of the tip of the m6 wing where the radius of curvature approaches zero ast year a workshop 1 was held in order to assess the currently used computational procedures one against the other in several carefully specified two dimensional transonic flow problems while reasonable agreement among the results given by the various full potential and euler equation methods was obtained in the subcritical cases a disparity between the results of these two models was found to grow with cases of increasing shock strength for the naca 0012 airfoil and conditions m 0 80 and a 1 25 deg for example the lift coefficients cl given by all the euler methods ranged between 0 30 and 0 38 whereas the range of cl for the potential method was 0 28 1 1 this discrepancy has led to a reconsideration of the validity of the potential model when strong shocks are present in the flow not only locally in terms of the isentropic shock jumps but also and perhaps even more importantly with regard to the correct modeling of vortex phenomena throughout the entire flowfield in the potential representation the vorticity that is bound to the airfoil is accounted for by a jump in the potential across a line originating at the trailing edge and lying a priori along some chosen coordinate direction downstream the so called kutta condition the euler equations in contrast admit vorticity in the solution and the equivalent to the kutta condition evidently does not need to be enforced explicitly this situation is currently under study by researchers using a variety of numerical methods in three dimensions the flow past a finite wing is even more complex and less is known vortices for example are shed continuously from the wing tips and the entire trailing edge whether a kutta condition or its equivalent is necessary in this case has not been in vestigated but because vorticity is so crucial to the realism achieved by inviscid flow models interest has been aroused in questions like this and in numerical methods that solve the euler equations a number of methods 2 4 exist to solve the euler equations for three dimensional flow but they have been developed exclusively for and applied only to internal flows apparently the solution of the euler equations for

geometric interpretations and spatial symmetry property of metrics in the conservative form for high order finite difference schemes on moving and deforming grids the role of a geometric conservation law gcl on a finite difference scheme is revisited for conservation laws and the conservative forms of coordinate transformation metrics are introduced in general dimensions the sufficient condition of a linear high order finite difference scheme is arranged in detail for which the discretized conservative coordinate transformation metrics and jacobian satisfy the gcl identities on three dimensional moving and deforming grids subsequently the geometric interpretation of the metrics and jacobian discretized by a linear high order finite difference scheme is discussed and only the symmetric conservative forms of the discretized metrics and jacobian are shown to have the appropriate geometric structures the symmetric and asymmetric conservative forms of the metrics and jacobian are examined by the computation of an inviscid compressible fluid on highly skewed stationary and deforming grids using sixth order compact and fourth order explicit central difference schemes respectively the resolution of the isentropic vortex and the robustness of the computation are improved by employing symmetric conservative forms on the coordinate transformation metrics and jacobian that have an appropriate geometry background an integrated conservation of conservative quantities is also attained on the deforming grid when symmetric conservative forms are adopted to the time metrics and jacobian

the ideal structure of certain nonselfadjoint operator algebras soit x un systeme dynamique localement compact et z x co x la sous algebre close en norme du produit croise zx co x engendre par les puissances non negatives de dans le cas homeomorphisme on determine la structure ideale de ces algebres dans le cas ou agit librement

isomorphisms between topological conjugacy algebras a family of algebras which we call topological conjugacy algebras is associated with each proper continuous map on a locally compact hausdorff space assume that i xi xi is a continuous proper map on a locally compact hausdorff space xi for i 1 2 we show that the dynamical systems x1 1 and x2 2 are conjugate if and only if some topological conjugacy algebra of x1 1 is isomorphic as an algebra to some topological conjugacy algebra of x2 2 this implies as a corollary the complete classification of the semicrossed products c0 x z which was previously considered by arveson and josephson 3 peters 19 hadwin and hoover 8 and power 21 we also obtain a complete classification of all semicrossed products of the form a d z where a d denotes the disc algebra and d d a continuous map which is analytic on the interior in this case a surprising dichotomy appears in the classification scheme which depends on the fixed point set of we also classify more general semicrossed products of uniform algebras

the jacobson radical for analytic crossed products we characterise the jacobson radical of an analytic crossed product c0 x z answering a question first raised by arveson and josephson in 1969 in fact we characterise the jacobson radical of analytic crossed products c0 x zd this consists of all elements whose fourier coefficients vanish on the recurrent points of the dynamical system and the first one is zero the multidimensional version requires a variation of the notion of recurrence taking into account the various degrees of freedom

local rigidity of affine actions of higher rank groups and lattices let j be a semisimple lie group with all simple factors of real rank at least two let r j be a lattice we prove a very general local rigidity result about actions of j or r this shows that almost all so called standard actions are locally rigid as a special case we see that any action of by toral automorphisms is locally rigid more generally given a manifold m on which acts isometrically and a torus t n on which it acts by automorphisms we show that the diagonal action on t n m is locally rigid this paper is the culmination of a series of papers and depends heavily on our work in two recent articles the reader willing to accept the main results of those papers as black boxes should be able to read the present paper without referring to them

pseudo unsteady difference schemes for discontinuous solutions of steady state one dimensional fluid dynamics problems abstract this paper presents two unsteady difference schemes for one dimensional steady state shock solutions starting from the pseudo unsteady equations the so called explicit upwind scheme is actually an explicit forward time centered space difference scheme with an appropriate artificial viscosity term which depends on the directions of the characteristics this scheme considered as an iterative scheme has good convergence properties and leads to steady state numerical shocks each with at most one point of transition regardless of the position of the shock with respect to the mesh the mesh can be refined locally and computation continued locally to make the profile of the shock sharper to increase the rate of convergence the corresponding implicit scheme is presented results of numerical tests for a shock tube and a convergent divergent nozzle are given

truncation error analysis of the finite volume method for a model steady convective equation abstract a fundamental error relation inherent in the gauss divergence theorem provided the basis for studying the truncation error of the finite volume method with cell center formulation for a model steady convective equation the consistency of the classical first and second order upwind schemes are proved to be seriously dependent on the grid distribution if the simple nature of the finite volume method is retained it is found that a consistent scheme for convective terms can not avoid the dissipation due to grid nonuniformity the geometrical interpretation of the diffusive terms such as vzo are undertaken classical finite volume methods which average an undefined 0 from its neighbouring nodes are shown to introduce false fluxes whenever grid nonuniformity is present a simple modification is proposed to cancel the false fluxes two test cases for the laplace equation illustrate the applicability of the proposed scheme however even with this modified scheme the consistency problem of the diffusion term is found to be seriously dependent on the grid uniformity

the development of a free surface capturing approach for multidimensional free surface flows in closed containers a new surface capturing method is developed for numerically simulating viscous free surface flows in partially filled containers the method is based on the idea that the flow of two immiscible fluids within a closed container is governed by the equations of motion for an incompressible viscous nonhomogeneous variable density fluid by computing the flow fields in both the liquid and gas regions in a consistent manner the free surface can be captured as a discontinuity in the density field thereby eliminating the need for special free surface tracking procedures the numerical algorithm is developed using a conservative implicit finite volume discretization of the equations of motion the algorithm incorporates the artificial compressibility method in conjunction with a dual time stepping strategy to maintain a divergence free velocity field a slope limited high order muscl scheme is adopted for approximating the inviscid flux terms while the viscous fluxes are centrally differenced the capabilities of the surface capturing method are demonstrated by calculating solutions to several two and three dimensional problems

efficient computation of volume in flow predictions an efficient method for calculating cell volumes for time dependent three dimensional flow predictions by finite volume calculations is presented eight arbitrary corner points are considered and the shape face is divided into two planar triangles the volume is then dependent on the orientation of the partitioning in the case of a hexahedron it is noted that any open surface with a boundary that is a closed curve possesses a surface vector independent of the surface shape expressions are defined for the surface vector which is independent of the partitioning surface diagonal used to quantify the volume using a decomposition of the cell volume involving two corners with each the vertex of three diagonals and six corners which are vertices of one diagonal gives portions which are tetrahedra the resultant mesh is can be used for time dependent finite volume calculations one requires less computer time than previous methods

a new consistent spatial differencing scheme for the transonic full potential equation a new spatial differencing scheme for the transonic full potential equation in conservative form has been developed three consistency conditions for the full potential equations are derived and are satisifed by the new scheme this scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two or three space dimensions solutions obtained with this new differencing scheme away from freestream regions exhibit greatly improved accuracy especially for nonsmooth or singular meshes the computing times associated with the new scheme are approximately the same as the less accurate old scheme when computations are performed on the same mesh

generalized coordinate forms of governing fluid equations and associated geometrically induced errors the governing equations of fluid flow may be cast into various forms upon application of a generalized coordinate mapping these forms are the nonconservation law form nclf and strong weak and chain rule conservation law forms sclf wclf crclf respectively this paper describes the geometrically induced errors resulting from the failure to satisfy a certain consistency condition for each of these four forms and also demonstrates the ability of the crclf to produce exactly the same numerical solution as the wclf provided a condition is met on where to evaluate the transformation metrics it is also demonstrated that considerably fewer arithmetic operations are required to advance the solution from n to n 1 when the crclf is used in com parison to both the sclf and wclf he effort devoted to the field of computational fluid dynamics is progressing at an ever increasing rate at certain points in time during this natural evolution of numerical methods schemes and ideas it is sometimes in structive to pause to reflect upon past work in an attempt to gain the proper perspective it is important that this reflection reaches all of the way to the fundamental rules and practices used to develop numerical techniques some of these practices are often taken for granted much too soon after their in troduction into the literature only through a global view of this past effort can subtle mutually experienced problem areas and possible causes be identified the present work deals with the numerical solution to the transformed fluid flow equations i e euler equations etc using the finite difference approach the transformed equations are obtained through application of a generalized mapping from physical coordinates to computational coordinates at the time of application of the mapping to the original equations and prior to choosing the numerical in tegration scheme the analyst must decide in which form the equations should be written the choices are the non conservation law form nclf strong conservation law form sclf weak conservation law form wclf and chain rule conservation law form crclf this decision is one of the fundamental practices alluded to in the previous paragraph the present work illustrates how such a fundamental decision can strongly influence both the amount of analysis required to develop a consistent algorithm and the number of arithmetic operations required to execute the algorithm in addition it is shown that large solution errors and in some cases instabilities can result from failure to implement the results of such an analysis

nonnegativity monotonicity or convexity preserving cubic and quintic hermite interpolation the hermite polynomials are simple effective interpolants of discrete data these interpolants can preserve local positivity monotonicity and convexity of the data if we restrict their derivatives to satisfy constraints at the data points this paper de scribes the conditions that must be satisfied for cubic and quintic hermite interpolants to preserve these properties when they exist in the discrete data we construct algorithms to ensure that these constraints are satisfied and give numerical examples to illustrate the effectiveness of the algorithms on locally smooth and rough data 1 introduction piecewise polynomial interpolants especially those based on hermite polynomials polynomials determined by their values and values of one or more derivatives at both ends of an interval have a number of desirable properties they are easy to compute once the derivative values are chosen if the derivative values are chosen locally e g by finite difference methods then the interpolant at a given point will depend only on the given data at nearby mesh points if the derivatives are computed by spline methods then the interpolant will have an extra degree of continuity at the mesh points in either case the interpolant is linear in the given function values and has excellent convergence properties as the mesh spacing decreases these methods however do not necessarily preserve the shape of the given data when the data arise from a physical experiment it may be vital that the interpolant preserve nonnegativity f x 0 nonpositivity f x 0 or f x 0 or concavity f x 0 in this and other cases geometric considerations such as preventing spurious behavior near rapid changes in the data may be more important than the asymptotic accuracy of the interpolation method one can construct a shape preserving interpolant by constraining the derivatives for the hermite polynomials to meet conditions which imply the desired properties 4 5 8 11 15 20 by adding new mesh points

an efficient solution method for incompressible n s equations using non orthogonal collocated grid an efficient strategy for the solution of n s equations using collocated non orthogonal grids is presented the governing equations have been discretized in the physical plane itself without co ordinate transformation thereby retaining the lucidity of the basic finite volume method the non orthogonal terms and quick type corrections for the convective terms in the momentum equations are treated explicitly while the other terms are taken in implicit form in the pressure correction equation the non orthogonal terms have been dropped altogether the discretized equations have been solved by the preconditioned conjugate gradient square method the specific combination of above steps has resulted in better convergence properties as compared to those of existing algorithms even for highly skewed grids the scheme has been validated against benchmark solutions such as lid driven flow in square and skewed cavities and experi mental results of flow over a single cylinder its applicability has also been illustrated for flow through a bank of staggered cylinders with anti symmetric inlet and outlet boundary conditions copyright 1999 john wiley sons ltd

ideals in some continuous nonselfadjoint crossed product algebras abstract let y t be a locally compact dynamical system where the t denotes a continuous one parameter semigroup of maps on y when each t is a homeomorphism a nonselfadjoint crossed product algebra is defined as the subalgebra of the c crossed product c 0 y r supported on t 0 when each t is only continuous the crossed product c 0 y r can still be defined the ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete free action on a smaller space x a generalization of effros hahn is given whereby one may find a meet irreducible ideal over any arc closure in y the meet irreducible ideals form a topological space in the hull kernel topology and there is a one to one correspondence between closed sets in this space and closed ideals in the algebra a subset of this space is homeomorphic to the space of finite arcs in the subarc topology the irrational flow algebra is considered as a special case