adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

viscous scalar conservation law with nonlinear flux feedback and global attractors abstract in this paper we study the forced viscous scalar conservation law on 0 1 with the nonlinear flux feedback at the boundary global existence and uniqueness are established for l bounded initial conditions and forcing functions under an appropriate growth condition on the flux function and nonlinear dissipation at the boundary we show the existence of an absorbing set that absorbs the whole space l 0 1 and the existence of a compact global attractor in the l topology

a new class of truly consistent splitting schemes for incompressible flows a new class of splitting schemes for incompressible flows is introduced the new schemes are based on a weak form of the pressure poisson equation and at each time step only require to solve a set of helmholtz type equations for the velocity and a poisson equation in the weak form for the pressure just as pressure correction and velocity correction schemes however unlike pressure correction and velocity correction schemes the new splitting schemes are free of splitting errors and deliver full accuracy on the vorticity and the pressure

principal series of finite subgroups of su 3 we attempt to give a complete description of the exceptional finite subgroups 36 3 72 3 and 216 3 of su 3 with the aim to make them amenable to model building for fermion masses and mixing the information on these groups which we derive contains conjugacy classes proper normal subgroups irreducible representations character tables and tensor products of their three dimensional irreducible representations we show that for these three exceptional groups usage of their principal series i e ascending chains of normal subgroups greatly facilitates the computations and illuminates the relationship between the groups as a preparation and testing ground for the usage of principal series we study first the dihedral like groups 27 and 54 because both are members of the principal series of the three groups discussed in the paper

a splitting method for incompressible flows with variable density based on a pressure poisson equation a new fractional time stepping technique for solving incompressible flows with variable density is proposed the main feature of this method is that as opposed to other known algorithms the pressure is determined by just solving one poisson equation per time step which greatly reduces the computational cost the stability of the method is proved and the performance of the method is numerically illustrated

algebraic splitting methods for the steady incompressible navier stokes equations at moderate reynolds numbers abstract the unsteady incompressible navier stokes equations in primitive variables are often numerically solved by segregating the computation of velocity and pressure according to either functional analysis arguments following the pioneering work of a j chorin and r temam std split then discretize paradigm or linear algebra arguments based on the inexact block factorization of the discretized problem dts discretize then split paradigm the presence of the time derivative allows for the calibration of an appropriate approximation of the pseudo differential operator of the pressure problem and excellent results in terms of both accuracy and efficiency have been obtained as witnessed by the abundant literature the extension of the same segregated approach to the steady navier stokes equations is unclear unless a pseudo time advancing formulation is undertaken in this paper we present a methodology for a segregated computation of the primitive variables in a genuinely steady formulation so to avoid iterations to get to the steady limit the approach is largely inspired by the algebraic factorization of the unsteady problem dts approach yet we detail specific settings required by the absence of the velocity time derivative the basic idea relies on the introduction of some parameters in a modified picard linearization we discuss stability bounds and the convergence of the segregated method to the unsplit solution several numerical results on different test cases confirm the efficiency of the procedure

convergence analysis of a projection semi implicit coupling scheme for fluid structure interaction problems in this paper we provide a convergence analysis of a projection semi implicit scheme for the simulation of fluid structure systems involving an incompressible viscous fluid the error analysis is performed on a fully discretized linear coupled problem a finite element approximation and a semi implicit time stepping strategy are respectively used for space and time discretization the fluid is described by the stokes equations the structure by the classical linear elastodynamics equations linearized elasticity plate or shell models and all changes of geometry are neglected we derive an error estimate in finite time and we prove that the time discretization error for the coupling scheme is at least sqrt delta t finally some numerical experiments that confirm the theoretical analysis are presented

comments on the classification of the finite subgroups of su 3 many finite subgroups of su 3 are commonly used in particle physics the classification of the finite subgroups of su 3 began with the work of h f blichfeldt at the beginning of the 20th century in blichfeldt s work the two series c and d of finite subgroups of su 3 are defined while the group series 3n2 and 6n2 which are subseries of c and d respectively have been intensively studied there is not much knowledge about the group series c and d in this work we show that c and d have the structures and respectively furthermore we show that while the c groups can be interpreted as irreducible representations of 3n2 the d groups can in general not be interpreted as irreducible representations of 6n2

subgrid stabilized projection method for 2d unsteady flows at high reynolds numbers a subgrid stabilization technique is developed for solving the two dimensional incompressible navier stokes equations at high reynolds numbers the time marching algorithm is based on a well established fractional step pressure correction projection method the advection diffusion step is enriched by an implicit subgrid stabilizing term and by an explicit dissipative shock capturing term the former is calculated by means of a hierarchical finite element setting the latter is included to avoid gibbs phenomenon in the boundary layer convergence tests on prototypical two dimensional examples are reported and the method is used to simulate the viscous incompressible flows around the airfoil naca0012 at zero incidence and reynolds numbers ranging from 105 to 106

finite element matrices in congruent subdomains and their effective use for large scale computations the structure of finite element matrices in congruent subdomains is studied when a domain has a form of symmetries and or periodicities it is decomposed into a union of congruent subdomains each of which is an image of a reference subdomain by an affine transformation with an orthogonal matrix whose components consist of 1 0 and 1 stiffness matrices in subdomains are expressed by one in the reference subdomain with renumbering indices and changing signs corresponding to the orthogonal matrices the memory requirements for a finite element solver are reduced by the domain decomposition which is useful in large scale computations reducing rates of memory requirements to store matrices are reported with examples of domains both applicability and limitations of the algorithm are discussed with an application to the earth s mantle convection problem

a segregated implicit pressure projection method for incompressible flows in this paper a segregated implicit projection method is presented and investigated although high reynolds turbulent flow has been a motivating factor the present study is mainly restricted to the incompressible navier stokes equations the proposed method is analyzed for properties like stability accuracy and consistency aided by some test examples in addition two different flow cases are simulated to evaluate the ability and efficiency of the method compared with other results

error estimates of finite element methods for nonstationary thermal convection problems with temperature dependent coefficients general error estimates are proved for a class of finite element schemes for nonstationary thermal convection problems with temperature dependent coefficients these variable coefficients turn the diffusion and the buoyancy terms to be nonlinear which increases the nonlinearity of the problems an argument based on the energy method leads to optimal error estimates for the velocity and the temperature without any stability conditions error estimates are also provided for schemes modified by approximate coefficients which are used conveniently in practical computations

pressure stability in fractional step finite element methods for incompressible flows abstract the objective of this paper is to analyze the pressure stability of fractional step finite element methods for incompressible flows that use a pressure poisson equation for the classical first order projection method it is shown that there is a pressure control which depends on the time step size and therefore there is a lower bound for this time step for stability reasons the situation is much worse for a second order scheme in which part of the pressure gradient is kept in the momentum equation the pressure stability in this case is extremely weak to overcome these shortcomings a stabilized fractional step finite element method is also considered and its stability is analyzed some simple numerical examples are presented to support the theoretical results

algebraic fractional step schemes with spectral methods for the incompressible navier stokes equations the numerical investigation of a recent family of algebraic fractional step methods for the solution of the incompressible time dependent navier stokes equations is presented these methods are improved versions of the yosida method proposed in a quarteroni f saleri a veneziani factorization methods for the numerical approximation of navier stokes equations comput methods appl mech engrg 188 1 3 2000 505 526 a quarteroni f saleri a veneziani j math pures appl 9 78 5 1999 473 503 and one of them the yosida4 method is proposed in this paper for the first time they rely on an approximate lu block factorization of the matrix obtained after the discretization in time and space of the navier stokes system yielding a splitting in the velocity and pressure computation in this paper we analyze the numerical performances of these schemes when the space discretization is carried out with a spectral element method with the aim of investigating the impact of the splitting on the global accuracy of the computation

pressure correction algebraic splitting methods for the incompressible navier stokes equations in this paper we present a new family of methods for the effective numerical solution of the incompressible unsteady navier stokes equations these methods resort to an algebraic splitting of the discretized problem based on inexact lu block factorizations of the corresponding matrix following a quarteroni f saleri and a veneziani comput methods appl mech engrg 188 2000 pp 505 526 in particular we will start from inexact algebraic factorizations of algebraic chorin temam and yosida type and introduce a pressure correction step aimed at improving the time accuracy one of the schemes obtained in this way the algebraic chorin temam pressure correction method resembles a method previously introduced in the framework of differential projection schemes see l timmermans p minev and f v de vosse internat j numer methods fluids 22 1996 pp 673 688 a prohl projection and quasi compressibility methods for solving the incompressible navier stokes equations teubner stuttgart 1997 the stability and the dependence of splitting error on the time step of the new methods is investigated and tested on several numerical cases

domain decomposition and splitting methods for mortar mixed finite element approximations to parabolic equations we introduce in this article a new domain decomposition algorithm for parabolic problems that combines mortar mixed finite element methods for the space discretization with operator splitting schemes for the time discretization the main advantage of this method is to be fully parallel the algorithm is proven to be unconditionally stable and a convergence result in mathcal o t h 1 2 is presented

incompressible navier stokes solutions by a triangular spectral p element projection method the application of the fractional step projection method recently proposed by guermond and quartapelle to the numerical approximation of unsteady navier stokes solutions by means of a spectral p element method is considered in particular we illustrate the second order pressure correction technique and evaluate its accuracy properties in some test cases stability with respect to the compatibility condition between the approximation spaces for velocity and pressure is also addressed the high spectral accuracy in space and the second order accuracy in time are verified by two simple test cases with analytical solution a more interesting problem is solved showing the ability of the method to produce very accurate results also for problems in complex geometries

a finite element penalty projection method for incompressible flows the penalty projection method for the solution of navier stokes equations may be viewed as a projection scheme where an augmentation term is added in the first stage namely the solution of the momentum balance equation to constrain the divergence of the predicted velocity field after a presentation of the scheme in the time semi discrete formulation then in fully discrete form for a finite element discretization we assess its behaviour against a set of benchmark tests including in particular prescribed velocity and open boundary conditions the results demonstrate that the augmentation always produces beneficial effects as soon as the augmentation parameter takes a significant value the projection method splitting error is reduced pressure boundary layers are suppressed and the loss of spatial convergence of the incremental projection scheme in case of open boundary conditions does not occur anymore for high values of the augmentation parameter the results of coupled solvers are recovered consequently in contrast with standard penalty methods there is no need for a dependence of the augmentation parameter with the time step and this latter can be kept to reasonable values to avoid to degrade too severely the conditioning of the linear operator associated to the velocity prediction step

error analysis of projection methods for non inf sup stable mixed finite elements the transient stokes problem abstract a modified chorin teman euler non incremental projection method and a modified euler incremental projection method for non inf sup stable mixed finite elements are analyzed the analysis of the classical euler non incremental and euler incremental methods are obtained as a particular case we first prove that the modified euler non incremental scheme has an inherent stabilization that allows the use of non inf sup stable mixed finite elements without any kind of extra added stabilization we show that it is also true in the case of the classical chorin temam method for the second scheme we study a stabilization that allows the use of equal order pairs of finite elements the relation of the methods with the so called pressure stabilized petrov galerkin method pspg is established the influence of the chosen initial approximations in the computed approximations to the pressure is analyzed numerical tests confirm the theoretical results

a conforming finite element method for the time dependent navier stokes equations we study a spatial discretization of the stokes problem in a domain of mathbb r 2 or mathbb r 3 by a finite element method the unknowns being the velocity and the pressure optimal error

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

simple finite non abelian flavor groups the recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two and three dimensional irreducible representations this paper details the mathematics of the two finite simple groups with such representations the icosahedral group a5 a subgroup of so 3 and psl2 7 a subgroup of su 3

on the characterization of the su 3 subgroups of type c and d we investigate the two classes of finite subgroups of su 3 that are called type c and d in the book of miller blichfeldt and dickson we present two theorems which fully determine the form of the generators in a suitable basis after exploring further properties of these groups we are able to construct a complete list of infinite series in which these groups are arranged for type c there are infinitely many series whereas for type d there are only two explicit examples of these series are presented which illustrate the general results

pointwise control of burgers equation a numerical approach abstract we describe a methodology for numerically solving pointwise control problems for the viscous burger s equation in one space dimension the solution methods are based on a combination of finite difference and finite element techniques for the time and space discretizations with iterative algorithms such as quasi newton methods and gmres numerical experiments validate the methods

a pressure correction scheme for convection dominated incompressible flows with discontinuous velocity and continuous pressure in this work we present a pressure correction scheme for the incompressible navier stokes equations combining a discontinuous galerkin approximation for the velocity and a standard continuous galerkin approximation for the pressure the main interest of pressure correction algorithms is the reduced computational cost compared to monolithic strategies in this work we show how a proper discretization of the decoupled momentum equation can render this method suitable to simulate high reynolds regimes the proposed spatial velocity pressure approximation is lbb stable for equal polynomial orders and it allows adaptive p refinement for velocity and global p refinement for pressure the method is validated against a large set of classical two and three dimensional test cases covering a wide range of reynolds numbers in which it proves effective both in terms of accuracy and computational cost

on the approximation of the unsteady navier stokes equations by finite element projection methods this paper provides an analysis of a fractional step projection method to compute incompressible viscous flows by means of finite element approximations the analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method such a theoretical distinction leads to a finite element projection method with a poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm error estimates in finite time are given an extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

a mixed basis spectral projection method a new grid less no collocation spectral projection method is presented the unsteady navier stokes equations are approximated according to the variational framework of guermond and quartapelle which accommodates two vector spaces for the velocity fields obtained in the two half steps of the fractional step method but retains only one in the final solution algorithm two different bases built on legendre polynomials are used for the velocity and pressure to solve the corresponding helmholtz and poisson equations by direct spectral elliptic solvers interpolations pn and pn 2 are employed for velocity and pressure to satisfy the lbb stability requirement and a gauss legendre quadrature formula with 3 2n integration points is used to prevent aliasing error in the pseudospectral evaluation of the nonlinear terms a bdf second order time stepping is implemented to provide accurate numerical results about the stability of the singular driven cavity problem

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

the gauge uzawa finite element method part i the navier stokes equations the gauge uzawa fem is a new first order fully discrete projection method which combines advantages of both the gauge and uzawa methods within a variational framework a time step consists of a sequence of d 1 poisson problems d being the space dimension thereby avoiding both the incompressibility constraint as well as dealing with boundary tangential derivatives as in the gauge method this allows for a simple finite element discretization in space of any order in both two and three dimensions this first part introduces the method for the navier stokes equations of incompressible fluids and shows unconditional stability and error estimates for both velocity and pressure via a variational approach under realistic regularity assumptions several numerical experiments document performance of the gauge uzawa fem and compare it with other projection methods

on the finite subgroups of u 3 of order smaller than 512 we use the smallgroups library to find the finite subgroups of u 3 of order smaller than 512 which possess a faithful three dimensional irreducible representation from the resulting list of groups we extract those groups that cannot be written as direct products with cyclic groups these groups are the basic building blocks for models based on finite subgroups of u 3 all resulting finite subgroups of su 3 can be identified using the well known list of finite subgroups of su 3 derived by miller blichfeldt and dickson at the beginning of the 20th century furthermore we prove a theorem which allows us to construct infinite series of finite subgroups of u 3 from a special type of finite subgroups of u 3 this theorem is used to construct some new series of finite subgroups of u 3 the first members of these series can be found in the derived list of finite subgroups of u 3 of order smaller than 512 in the last part of this work we analyze some interesting finite subgroups of u 3 especially the group which is closely related to the important su 3 subgroup s4

error analysis of a fractional time stepping technique for incompressible flows with variable density in this paper we analyze the convergence properties of a new fractional time stepping technique for the solution of the variable density incompressible navier stokes equations the main feature of this method is that contrary to other existing algorithms the pressure is determined by just solving one poisson equation per time step first order error estimates are proved and stability of a formally second order variant of the method is established

generation of universal linear optics by any beam splitter universal quantum computers have proved difficult to build as one response researchers have proposed limited models of quantum computation which might be easier to realize three examples are the one clean qubit model of knill and laflamme 15 the commuting hamiltonians model of bremner jozsa and shepherd 3 and the boson sampling model of aaronson and arkhipov 1 none of these models are known or believed to be capable of universal quantum computation or depending on modeling details even universal classical computation but all of them can perform certain estimation or sampling tasks for which no polynomial time classical algorithm is known one obvious way to define a limited model of quantum computation is to restrict the set of allowed gates however almost every gate set is universal 17 and so are most natural gate sets for example controlled not together with any real one qubit gate that does not square to the identity is universal 21 as a result very few nontrivial examples of non universal gate sets are known all known non universal gate sets on o 1 qubits such as the clifford group 8 are efficiently classically simulable if the input and measurement outcomes both belong to an appropriately chosen qubit basis1 as a result it is tempting to conjecture that there does not exist such an intermediate gate set or more precisely that any gate set on o 1 qubits is either efficiently classical simulable with appropriate input and output states or else universal for quantum computing strikingly this dichotomy conjecture remains open even for the special case of 1and 2 qubit gates we regard proving or disproving the conjecture as an important open problem for quantum computing theory in this paper we prove a related conjecture in the quantum linear optics model in quantum optics the hilbert space is not built up as a tensor product of qubits instead it s built up as a direct sum of optical modes an optical gate is then just a unitary transformation that acts nontrivially ono 1 of the modes and as the identity on the rest whenever we have a k mode gate we assume that we can apply it to any subset of k modes in any order as often as desired the most common optical gates considered are beamsplitters which act on two modes and correspond to a 2 2 unitary matrix with determinant 1 2 and phaseshifters which act on one mode and simply apply a phase ei note that any unitary transformation acting on the one photon hilbert space automatically gets lifted by homomorphism to a unitary transformation acting on the hilbert space of n photons furthermore every element of the n photon linear optical group that is every n photon unitary transformation achievable using linear optics arises in this way see 1 sec iii for details of course if n 2 then there are also n photon unitaries that cannot be achieved linearoptically that is the n photon linear optical group is a proper subgroup of the full unitary group on the n photon hilbert space

numerical analysis and testing of a stable and convergent finite element scheme for approximate deconvolution turbulence models abstract this report presents a stable and convergent finite element scheme for the approximate deconvolution turbulence models adm the adm is a popular turbulence model intensely studied lately but the computation of its numerical solution raises issues in terms of efficiency and accuracy this report addresses this question the proposed scheme presented herein is based on a new interpretation of the adm model recently introduced by the author following this interpretation the solution of the adm is viewed as the average of a perturbed navier stokes system the scheme uses the crank nicolson time discretization and the finite element spatial discretization and is proved to be stable and convergent provided a moderate choice of the time step is made numerical tests to verify the convergence rates and performance on a benchmark problem are also provided and they prove the correctness of this approach to numerically solve the adm

error analysis of fully discrete velocity correction methods for incompressible flows a fully discrete version of the velocity correction method proposed by guermond and shen 2003 for the time dependent navier stokes equations is introduced and analyzed it is shown that when accounting for space discretization additional consistency terms which vanish when space is not discretized have to be added to establish stability and optimal convergence error estimates are derived for both the standard version and the rotational version of the method these error estimates are consistent with those by guermond and shen 2003 as far as time discretiztion is concerned and are optimal in space for finite elements satisfying the inf sup condition

on the penalty projection method for the navier stokes equations with the mac mesh we deal with the time dependent navier stokes equations nse with dirichlet boundary conditions on the whole domain or on a part of the domain and open boundary conditions on the other part it is shown numerically that combining the penalty projection method with spatial discretization by the marker and cell scheme mac yields reasonably good results for solving the above mentioned problem the scheme which has been introduced combines the backward difference formula of second order bdf2 namely gear s scheme for the temporal approximation the second order richardson extrapolation for the nonlinear term and the penalty projection to split the velocity and pressure unknowns similarly to the results obtained for other projection methods we estimate the errors for the velocity and pressure in adequate norms via the energy method

the flavor group δ 6n2 many non abelian finite subgroups of su 3 have been used to explain the flavor structure of the standard model in order to systematize and classify successful models a detailed knowledge of their mathematical structure is necessary in this paper we shall therefore look closely at the series of finite non abelian groups known as 6n2 its smallest members being s3 n 1 and s4 n 2 for arbitrary n we determine the conjugacy classes the irreducible representations the kronecker products as well as the clebsch gordan coefficients

finite flavour groups of fermions we present an overview of the theory of finite groups with regard to their application as flavour symmetries in particle physics in a general part we discuss useful theorems concerning group structure conjugacy classes representations and character tables in a specialized part we attempt to give a fairly comprehensive review of finite subgroups of so 3 and su 3 in which we apply and illustrate the general theory moreover we also provide a concise description of the symmetric and alternating groups and comment on the relationship between finite subgroups of u 3 and finite subgroups of su 3 although in this review we give a detailed description of a wide range of finite groups the main focus is on the methods which allow the exploration of their different aspects

a second order in time uniquely solvable unconditionally stable numerical scheme for cahn hilliard navier stokes equation we propose a novel second order in time numerical scheme for cahn hilliard navier stokes phase field model with matched density the scheme is based on second order convex splitting for the cahn hilliard equation and pressure projection for the navier stokes equation we show that the scheme is mass conservative satisfies a modified energy law and is therefore unconditionally stable moreover we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme thanks to the simple coupling of the scheme we design an efficient picard iteration procedure to further decouple the computation of cahn hilliard equation and navier stokes equation we implement the scheme by the mixed finite element method ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme

a coupled prediction scheme for solving the navier stokes and convection diffusion equations this paper presents a new algorithm for the numerical solution of the navier stokes equations coupled with the convection diffusion equation after establishing convergence of the semi discrete formulation at each time step we introduce a new iterative scheme based on a projection method called the coupled prediction scheme we show that even though the predicted temperature is advected by a velocity prediction which is not necessarily divergence free the theoretical time accuracy of the global scheme is conserved from a numerical point of view this new approach gives a faster and more efficient algorithm compared to the usual fixed point approaches

navier stokes spectral solver in a sphere the paper presents the first implementation of a primitive variable spectral method for calculating viscous flows inside a sphere a variational formulation of the navier stokes equations is adopted using a fractional step time discretization with the classical second order backward difference scheme combined with explicit extrapolation of the nonlinear term the resulting scalar and vector elliptic equations are solved by means of the direct spectral solvers developed recently by the authors the spectral matrices for radial operators are characterized by a minimal sparsity diagonal stiffness and tridiagonal mass matrix closed form expressions of their nonzero elements are provided here for the first time showing that the condition number of the relevant matrices grows as the second power of the truncation order a new spectral elliptic solver for the velocity unknown in spherical coordinates is also described that includes implicitly the coriolis force in a rotating frame but requires a minimal coupling between the modal velocity components in the fourier space the numerical tests confirm that the proposed method achieves spectral accuracy and ensures infinite differentiability to all orders of the numerical solution by construction these results indicate that the new primitive variable spectral solver is an effective alternative to the spectral method recently proposed by kida and nakayama where the velocity field is represented in terms of poloidal and toroidal functions

finite element solution of the unsteady navier stokes equations by a fractional step method abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous flows the method is based on a fractional step approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly this leads to a computational scheme of extremely simple algorithmic structure that is particularly attractive for cost effective solutions of large scale problems numerical results indicate the versatility and effectiveness of the proposed method

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

optimal first order error estimates of a fully segregated scheme for the navier stokes equations abstract a first order linear fully discrete scheme is studied for the incompressible time dependent navier stokes equations in three dimensional domains this scheme is based on an incremental pressure projection method and decouples each component of the velocity and the pressure solving in each time step a linear convection diffusion problem for each component of the velocity and a poisson neumann problem for the pressure using an inf sup stable and continuous finite elements approach of order o h in space unconditional optimal error estimates of order o k h are deduced for velocity and pressure without imposing constraints on the mesh size h and the time step k finally some numerical results are performed to validate the theoretical analysis and also to compare the studied scheme with other current first order segregated schemes

finite subgroups of su 3 we present a new class of finite subgroups of su 3 of the form zm s zn semidirect product we also apply the methods used to investigate semidirect products to the known su 3 subgroups 3n2 and 6n2 and give analytic formulae for representations characters and clebsch gordan coefficients

convergence analysis of a finite element projection lagrange galerkin method for the incompressible navier stokes equations this paper provides a convergence analysis of a fractional step method to compute incompressible viscous flows by means of finite element approximations in the proposed algorithm the convection the diffusion and the incompressibility are treated in three different substeps the convection is treated first by means of a lagrange galerkin technique whereas the diffusion and the incompressibility are treated separately in two subsequent substeps by means of a projection method it is shown that provided the time step delta t is of cal o h d 4 where h is the meshsize and d is the space dimension 2 leq d leq 3 the proposed method yields for finite time t an error of cal o h l 1 delta t in the l2 norm for the velocity and an error of cal o h l delta t in the h1 norm or the l2 norm for the pressure where l is the polynomial degree of the approximate velocity

a dissipative feedback control synthesis for systems arising in fluid dynamics a dissipative feedback control synthesis is constructed to regulate the systems arising in fluid dynamics the feedback law is obtained by utilizing nonlinear dynamic programming techniques the control law is designed for driving the system to a prescribed equilibrium state and enhancing the energy dissipation effects of the dynamical system two dimensional navier stokes equations and burgers equation are used for numerical experiments to illustrate the effects of the feedback synthesis and the theoretical results

error analysis of pressure correction schemes for the time dependent stokes equations with open boundary conditions the incompressible stokes equations with prescribed normal stress open boundary conditions on part of the boundary are considered it is shown that the standard pressure correction method is not suitable for approximating the stokes equations with open boundary conditions whereas the rotational pressure correction method yields reasonably good error estimates these results appear to be the first ever published for splitting schemes with open boundary conditions numerical results in agreement with the error estimates are presented

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

role of the lbb condition in weak spectral projection methods 405 this paper investigates the relevance of the ladyshenskaya babuska brezzi con dition in spectral projection methods we consider the stability and convergence properties for a first order nonincremental projection method and a second order incremental projection method both based on a spectral galerkin legendre spatial discretization we show that the convergence of both projection methods is controlled by the ability of the spectral framework to approximate correctly the steady stokes problem c 2001 elsevier science

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

a hybrid incremental projection method for thermal hydraulics applications a new second order accurate hybrid incremental projection method for time dependent incompressible viscous flow is introduced in this paper the hybrid finite element finite volume discretization circumvents the well known ladyzhenskaya babuska brezzi conditions for stability and does not require special treatment to filter pressure modes by either rhie chow interpolation or by using a petrov galerkin finite element formulation the use of a co velocity with a high resolution advection method and a linearly consistent edge based treatment of viscous diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows the high resolution advection method is shown to deliver second order spatial convergence on mixed element topology meshes and the implicit advective treatment significantly increases the stable time step size the algorithm is robust and extensible permitting the incorporation of features such as porous media flow rans and les turbulence models and semi fully implicit time stepping a series of verification and validation problems are used to illustrate the convergence properties of the algorithm the temporal stability properties are demonstrated on a range of problems with 2 c f l 100 the new flow solver is built using the hydra multiphysics toolkit the hydra toolkit is written in c and provides a rich suite of extensible and fully parallel components that permit rapid application development supports multiple discretization techniques provides i o interfaces dynamic run time load balancing and data migration and interfaces to scalable popular linear solvers e g in open source packages such as hypre petsc and trilinos a new second order hybrid finite element finite volume projection algorithm for transient viscous flow has been introduced the hybrid discretization prevents pressure modes without using rhie chow interpolation or a petrov galerkin formulation a monotonicity preserving advection method shown to deliver second order accuracy on mixed element topology meshes verification studies demonstrate hybrid projection solver accuracy and temporal stability for super cfl conditions

an adaptive pressure correction method without spurious velocities for diffuse interface models of incompressible flows in this article we propose to study two issues associated with the use of the incremental projection method for solving the incompressible navier stokes equation the first one is the combination of this time splitting algorithm with an adaptive local refinement method the second one is the reduction of spurious velocities due to the right hand side of the momentum balance we propose a new variant of the incremental projection method for solving the navier stokes equations with variable density and illustrate its behavior with the example of two phase flows simulations using a cahn hilliard navier stokes model

convergence analysis of the fem approximation of the first order projection method for incompressible flows with and without the inf sup condition in this paper we obtain convergence results for the fully discrete projection method for the numerical approximation of the incompressible navier stokes equations using a finite element approximation for the space discretization we consider two situations in the first one the analysis relies on the satisfaction of the inf sup condition for the velocity pressure finite element spaces after that we study a fully discrete fractional step method using a poisson equation for the pressure in this case the velocity pressure interpolations do not need to accomplish the inf sup condition and in fact we consider the case in which equal velocity pressure interpolation is used optimal convergence results in time and space have been obtained in both cases

on convergence of chorin s projection method to a leray hopf weak solution the projection method to solve the incompressible navier stokes equations was first studied by chorin math comput 1969 in the framework of a finite difference method and temam arch ration mech anal 1969 in the framework of a finite element method chorin showed convergence of approximation and its error estimates in problems with periodic boundary conditions assuming existence of a c 5 solution while temam demonstrated an abstract argument to obtain a leray hopf weak solution in problems on a bounded domain with the no slip boundary condition in the present paper the authors extend chorin s result with full details to obtain convergent finite difference approximation of a leray hopf weak solution to the incompressible navier stokes equations on an arbitrary bounded lipschitz domain of mathbb r 3 with the no slip boundary condition and an external force we prove unconditional solvability of our implicit scheme and strong l 2 convergence up to a subsequence under the scaling condition h 3 alpha le tau no upper bound is necessary where h tau are space time discretization parameters respectively and alpha in 0 2 is any fixed constant the results contain a compactness method based on a new interpolation inequality for step functions

some comments on finite subgroups of su 3 a recently published set of finite subgroups of su 3 is shown to contain some groups which are not subgroups of su 3 the others are subgroups of one of the dihedral like family of su 3 subgroups of order 3n2 some comments are made also on the structure of other finite subgroups previously listed

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel