on hearing the shape of a general multi connected vibrating membrane in r2 with piecewise smooth positive functions in the robin boundary conditions the asymptotic expansion of the trace of the heat kernel q t email protected j 1 exp email protected j as t 0 has been derived for a variety of domains where l j are the eigenvalues of the negative laplace email protected email protected i 1 email protected email protected x i 2in the x 1 x 2 plane the dependence of q t on the connectivity of domains and the boundary conditions are analyzed particular attention is given for a general multiply connected bounded domain in r 2 together with a finite number of piecewise robin boundary conditions where the coefficients in the boundary conditions are piecewise smooth positive functions some applications of an ideal gas enclosed in the general multiply connected domain are given

chebyshev pseudospectral solution of second order elliptic equations with finite element preconditioning abstract a new chebyshev pseudospectral algorithm for second order elliptic equations using finite element preconditioning is proposed and tested on various problems bilinear and biquadratic lagrange elements are considered as well as bicubic hermite elements the numerical results show that bilinear elements produce spectral accuracy with the minimum computational work l shaped regions are treated by a subdomain approach

a divergence free multidomain spectral solver of the navier stokes equations in geometries of high aspect ratio in order to solve with high accuracy the incompressible navier stokes equations in geometries of high aspect ratio one has developed a spectral multidomain algorithm well adapted to the parallel computing in cases of 2d problems a chebyshev collocation method and an extended influence matrix technique are used in each subdomain to solve the generalized stokes problem which results from the discretization in time the continuity conditions needed at the interfaces of each subdomain are computed by using again an influence matrix the setup of which ensures all the necessary compatibility conditions especially the incompressibility this work is also described for 3d problems with one homogeneous direction a study of accuracy versus the number of subdomains is presented as well as an example of an application concerned with rayleigh benard convection in a cavity of large aspect ratio

exact integration of the unsteady incompressible navier stokes equations gauge criteria and applications an exact first integral of the full unsteady incompressible navier stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with maxwell s theory subsequent to this gauge freedoms are explored showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns following which the inviscid limit case is discussed finally it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self adjoint form use of the new formulation is demonstrated for different gauge variants of the first integral as the starting point through the solution of a hierarchy of classical three dimensional flow problems two of which are tractable analytically the third being solved numerically in all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature concurrently the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface is established together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

simultaneous nulling for monopulse array with partially adaptive weights a new simple method is described for synthesizing low sidelobe sum and difference patterns with partially adaptive weights by partially adaptive we mean that only part of the weights are adapted for simultaneous nulling these adaptive weights are shared by the sum and difference channels leading to a significant reduction in the number of variable attenuators phase shifters used as compared to the fully adaptive implementation an objective function is derived that yields different configurations of the shared adaptive weights numerical examples are presented to ascertain the efficacy of the new method for both point and extended interference

regular article on a class of pade finite volume methods a class of pade finite volume methods providing an improved spectral resolution is presented and compared with well known methods the formulation is based on the sliding averages of the variables and allows the computation of derivatives of all orders using the fourier analysis these methods are examined with respect to i order of accuracy ii spectral resolution iii boundary conditions and iv stability

some recent trends and developments in finite element analysis for incompressible thermal flows a numerical procedure for solving the time dependent incompressible navier stokes and energy equations is presented the present method is based on a set of finite element equations of the primitive variable formulation and a time splitting procedure which has unique features in its formulation as well as in its evaluation from the viewpoint of efficiency and accuracy the applicability of the proposed formulation was verified by computations and comparison with known results

third order upwind finite element solutions of high reynolds number flows abstract a full upwind finite element scheme based on the petrov galerkin formulation is presented for accurate solutions of high reynolds number flows and then a simplified finite scheme with third order upwinding is developed in order to obtain a practical algorithm for numerical simulation because structures of the full upwind finite element scheme are very complicated numerical dissipation added in the proposed upwind scheme is represented by high order derivatives of flow velocities and pressure computational results for the subcritical and the supercritical reynolds number flows around a circular cylinder and for flows around twin circular cylinders are shown to illustrate the effectiveness and robustness of the simplified upwind finite element scheme

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

on the simulation of flows with violent free surface motion abstract a volume of fluid vof technique has been developed and coupled with an incompressible euler navier stokes solver operating on adaptive unstructured grids to simulate the interactions of extreme waves and three dimensional structures the present implementation follows the classic vof implementation for the liquid gas system considering only the liquid phase extrapolation algorithms to obtain velocities and pressure in the gas region near the free surface have been implemented the vof technique is validated against the classic dam break problem as well as series of 2d sloshing experiments and results from smoothed particle hydrodynamics sph calculations these and a series of other examples demonstrate that the present cfd method is capable of simulating violent free surface flows with strong nonlinear behavior

direct numerical simulation of flow past elliptic cylinders flow over elliptic cylinders can be considered prototypical of flow over a range of bluff bodies since the geometry allows one to study the effect of both thickness and angle of attack on the flow field therefore a careful study of this flow should provide valuable insight into the phenomenon of unsteady separation and the structure of bluff body wakes with this in mind a spectral collocation technique has been developed to simulate the full three dimensional incompressible flow over elliptic cylinders and unlike spectral element and spectral multidomain techniques here the flow is solved in a single domain the equations are discretized on a body fitted elliptic cylindrical grid and properties of the metric associated with this coordinate system are used to solve the governing equations in an efficient manner key issues including the inflow and outflow boundary conditions and time discretization are discussed in detail with the hope that this will facilitate future simulations of similar flows finally we present results of two and three dimensional simulations for a range of flow and geometric parameters the results are compared with available experimental data and it is found that important quantities like strouhal numbers and drag coefficients match well with established values

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

splitting method for the combined formulation of the fluid particle problem abstract in this paper a splitting method for the direct numerical simulation of solid liquid mixtures is presented where a symmetric pressure equation is newly proposed through numerical experiment it is found that the newly proposed splitting method works well with a matrix free formulation for some benchmark problems avoiding an erroneous pressure field which appears when using the conventional pressure equation of a splitting method when deriving a typical pressure equation of a splitting method the motion of a solid particle has to be approximated by the intermediate velocity instead of treating it as unknowns since it is necessary as a boundary condition therefore the motion of a solid particle is treated in such an explicit way that a particle moves by the known form drag pressure drag that is calculated from the pressure equation in the previous step from the numerical experiment it was shown that this method gives an erroneous pressure field even for a very small time step size as the particle velocity increases in this paper coupling the unknowns of particle velocities in the pressure equation is proposed where the resulting matrix is reduced to the symmetric one by applying the projector of the combined formulation it has been tested over some benchmark problems and gives reasonable pressure fields

14 velocity and 18 velocity multiple relaxation time lattice boltzmann models for three dimensional incompressible flows in this paper 14 velocity and 18 velocity multiple relaxation time mrt lattice boltzmann lb models are proposed for three dimensional incompressible flows these two models are constructed based on the incompressible lbgk model proposed by he et al 2004 and the mrt lb model proposed by d humieres et al 2002 which have advantages in the computational efficiency and stability respectively through the chapman enskog analysis the models can recover to three dimensional incompressible navier stokes equations in the low mach number limit to verify the present models the steady poiseuille flow unsteady pulsatile flow and lid driven cavity flow in three dimensions are simulated the simulation results agree well with the analytical solutions or the existing numerical results moreover it is found that the present models show higher accuracy than d humieres et al model and better stability than he et al model

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a velocity stream function method for three dimensional incompressible fluid flow abstract we describe a velocity stream function method for computing incompressible fluid flow extending earlier work in two to three dimensions we present a strictly divergence free finite element in primitive variables in 3d as the curl of a generalized hermite vector potential element with velocity degrees of freedom and show a method for its derivation this linear velocity element is defined on a reference cube with 8 nodes each node having 3 vector potential stream function and 3 velocity degrees of freedom the method and element are applied to the lid driven cavity problem and open duct flow in three dimensions

third order upwind finite element computation of the incompressible navier stokes equations part ii aerodynamic characteristics of a rectangular cylinder with an angle of attack abstract aerodynamic characteristics of rectangular cylinders at depth breadth ratios of 1 and 2 are investigated in detail by numerical simulation of the incompressible navier stokes equations using a third order upwind finite element scheme in the numerical computation a uniform flow is given at the inlet boundary in a computational region and the rectangular cylinders are inclined toward the approaching flow in the range of angles of attack from 0 up to 45 the present solutions for aerodynamic forces and moment by forces of the inclined rectangular cylinders are compared with other numerical results and experimental results

a pseudospectral matrix element method for calculation of double diffusive layers near corners abstract a numerical simulation of the time evolving layered structure in a fluid supporting both temperature and salinity gradients was conducted in an l shaped region where an initially stable salt stratified fluid was disturbed by heating the wall containing the corner protruding into the flow in order to resolve the interfacial gradient between each layer of the flow a recently developed pseudospectral element matrix method using the primitive variable formulation of the navier stokes equations was incorporated into a new implementation of the schwarz alternating procedure for navier stokes solutions which differs from the conventional technique this new procedure directly employs the continuity equation at the edge of overlapped domains as the boundary condition for the pressure rather than a dirichlet condition a novel feature of this method is that it allows the use of a previously developed eigenfunction expansion of the pressure operator to reduce the original complex two dimensional problem to a simple one dimensional problem the computational results show that not only are convective layers formed along the vertical wall above the corner but surprisingly the layer emanating from the corner region dominates the development of the upper and lower layers

hearing the shape of a general convex domain abstract the spectral function t j 1 exp t j where j j 1 are the eigenvalues of the laplace operator i 1 2 x i 2 in the x 1 x 2 plane is studied for a general convex domain together with an impedance condition on a part of its boundary and another impedance condition on the remaining part of that boundary

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

an inverse problem for a general annular bounded domain in r2 with mixed boundary conditions and its physical applications this paper deals with the very interesting problem about the influence of the boundary conditions on the distribution of the eigenvalues of the negative laplacian in r 2 the asymptotic expansion of the trace of the heat kernel q t u 1 exp t m n where m n n 1 are the eigenvalues of the negative laplacian d 2 k 1 2 x k 2 in the x 1 x 2 plane is studied for short time t of a general annular bounded domain w in r 2 together with its smooth inner boundary w 1 and its smooth outer boundary w 2 where a finite number of dirichlet neumann and robin boundary conditions on the piecewise smooth components c i i 1 m of w 1 and on the piecewise smooth components c i i m 1 n of w 2 such that w 1 i 1 m c i and w 2 i m 1 n c i are considered in this paper one may extract information on the geometry of w by analyzing the asymptotic expansions of q t for short time t some applications of q t for an ideal gas enclosed in w are given thermodynamic quantities of an ideal gas enclosed in w are examined we use an asymptotic expansion for high temperatures to obtain the partition function of an ideal gas showing the leading corrections to the internal energy due to a finite container we show that the ideal gas cannot feel the shape of its container although it can feel some geometrical properties of it

semi implicit discontinuous galerkin methods for the incompressible navier stokes equations on adaptive staggered cartesian grids in this paper a new high order semi implicit discontinuous galerkin method si dg is presented for the solution of the incompressible navier stokes equations on staggered space time adaptive cartesian grids amr in two and three space dimensions the pressure is written in the form of piecewise polynomials on the main grid which is dynamically adapted within a cell by cell amr framework according to the time dependent main grid different face based spatially staggered dual grids are defined for the piece wise polynomials of the respective velocity components although the resulting adaptive staggered grids are more complex than classical uniform cartesian meshes the numerical scheme can still be written in a rather compact form thanks to the use of a tensor product formulation for the definition of the nodal basis in the d dimensional space d 2 3 all the discrete operators can be efficiently written as a combination of linear one dimensional operators acting in the d space directions separately arbitrary high order of accuracy is achieved in space while a very simple semi implicit time discretization is obtained via an explicit discretization of the nonlinear convective terms and an implicit discretization of the pressure gradient in the momentum equation and of the divergence of the velocity field in the continuity equation the real advantages of the staggered grid arise in the solution of the schur complement associated with the saddle point problem of the discretized incompressible navier stokes equations i e after substituting the discrete momentum equations into the discrete continuity equation this leads to a linear system for only one unknown the scalar pressure indeed the resulting linear pressure system is shown to be symmetric and positive definite in order to avoid a quadratic stability condition for the parabolic terms given by the viscous stress tensor an implicit discretization is also used for the diffusive terms in the momentum equation a particular feature of our staggered dg approach is that the viscous stress tensor is discretized on the dual mesh this corresponds to the use of a lifting operator but on the staggered grid both linear systems for pressure and velocity are very efficiently solved by means of a classical matrix free conjugate gradient method for which fast convergence is observed moreover it should be noticed that all test cases shown in this paper have been performed without the use of any preconditioner due to the explicit discretization of the nonlinear convective terms the final algorithm is stable within the classical cfl type time step restriction for explicit dg methods based on the fluid velocity moreover by using a suitable local time stepping technique based on the ader dg framework each element can use its optimal local time step also within the amr context the new space time adaptive staggered dg scheme has been thoroughly verified for polynomial degrees up to n 9 for a large set of non trivial test problems in two and three space dimensions for which analytical numerical or experimental reference solutions exist the high order of accuracy of the scheme is shown by means of a numerical convergence table obtained by comparing the numerical solution against a smooth analytical solution to the knowledge of the authors this is the first staggered semi implicit dg scheme for the incompressible navier stokes equations on space time adaptive meshes in two and three space dimensions

chebyshev 3 d spectral and 2 d pseudospectral solvers for the helmholtz equation two chebyshev solvers are presented for the linear helmholtz equation the first algorithm is a 3 d direct spectral solver based on a diagonalization technique whilst the second performs an iterative pseudospectral 2 d calculation with finite difference preconditioning both techniques handle general nonhomogeneous boundary conditions computing times and accuracies of the two methods are compared

simple method for pattern nulling by phase perturbation a method of sidelobe hulling which involves perturbing the array illumination phase only is presented the general nonlinear problem is linearized by assuming the perturbations to be small and an analytic solution is derived illustrative examples of sinc and chebyshev patterns with imposed nulls are given

simultaneous nulling in sum and difference patterns by amplitude control a method is discussed of suppressing jammers simultaneously in the sum and the difference patterns of a linear antenna array by either using complex weights or controlling the current amplitudes only with special emphasis on the latter method for a given array size the total number of jammers that can be nulled is doubled if complex weights are used instead of real weights however the amplitude only technique has many attractions it is shown that because the resulting current amplitude distribution has a double symmetry the number of attenuators required for simultaneous nulling can be as low as a quarter of the total number of elements in the array this means a much faster computing speed as well as a considerable saving in hardware the method also allows the main beam of the antenna to be scanned by using phase shifters while nulls are placed in directions of known jammers in both the sum and difference patterns by using attenuators as a result the maximization of the signal to jammer ratio can be achieved with relative ease because the stronger a jammer is the easier it is to locate it and hence to suppress it

on hearing the shape of rectilinear regions from complete knowledge of the eigenvalues of the negative laplacian on a bounded domain one may extract information on the geometry and the boundary conditions by analyzing the asymptotic expansion of a spectral function explicit calculations are performed for an equilateral triangular domain with dirichlet or neumann boundary conditions yielding in particular the corner angle terms in three dimensions some applications to eigenvalue problems for an equilateral triangular prism are dealt with including the solid vertex terms

an inverse problem of the wave equation for a general doubly connected region in r2 with a finite number of piecewise smooth robin boundary conditions the spectral distribution m t w 1 exp ite w 1 2 where e w w 1 are the eigenvalues of the negative laplacian d k 1 2 x k 2in the x 1 x 2 plane is studied for a variety of domains where 0

finite element analysis of oscillatory flow with heat transfer inside a square cavity in this work a semi implicit projection type finite element method is applied to solve the incompressible oscillatory cavity flow with heat transfer the two dimensional time dependent navier stokes and energy equations are numerically integrated by a time split galerkin finite element method using direct matrix solvers the time accuracy of the method was tested by calculating the transient buoyancy driven flow in a square cavity with differentially heated vertical walls the oscillatory cavity flow is then studied considering the effects of heat transfer reynolds number and oscillatory stokes number to measure the stability of the scheme for such a high singularity phenomenon the proposed scheme is found to be stable and convergent for high rayleigh numbers and will be applicable to general problems involving flow and heat transfer especially in three dimensions

chebyshev expansion methods for the solution of the extended graetz problem abstract the extended graetz problem a classical problem described by an equation with anon self adjoint second order elliptic differential operator is solved by two numerical methods based on chebyshev expansions a chebyshev finite difference method and a chebyshev finite element method the latter relies entirely on chebyshev expansions global in the bounded radial coordinate direction and local in the unbounded axial direction and proves to be more accurate than the chebyshev finite difference method in resolving singularities both methods can be applied to general type boundary value problems involving second order elliptic operators have accuracy comparable to high order finite difference schemes and are operation cost efficient

three dimensional fluid flow calculations using a flux spline method this paper reports the application of a flux spline method to three dimensi onal fluid flow problems the performance of the method is compared to that of a first order differencing scheme the numerical results are compared with a reference solution available in the literature the flux spline scheme is shown to be significantly more accurate than the first order schemes for a prescribed accuracy the flux spline scheme requires a much smaller number of grid points

semi implicit and explicit finite element schemes for coupled fluid thermal problems a comparative investigation based on a series of numerical tests of two purely explicit and one semi implicit finite element methods used for incompressible flow computation is presented the segregated approach is followed and the equations of motion are considered sequentially the fundamental concepts and characteristics of the formulations and the solution methodology used are described in technical detail various modifications to chorin s projection algorithm are investigated particularly with respect to their effects on stability and accuracy the stability of the semi implicit method is shown to be less restrictive when compared to the explicit methods as the reynolds number increases at large time steps the artificial viscosity is also reduced and higher accuracy is obtained the performance of the methods discussed in this paper is illustrated by the numerical solutions obtained for the cavity flow and flow past a rearward facing step problems at high reynolds numbers and free convection flow problem at high rayleigh numbers it is shown that the semi implicit method needs fewer iterations than the explicit methods and the accuracy of the present methods is guaranteed by comparison with the existing methods

on the adoption of velocity variable and grid system for fluid flow computation in curvilinear coordinates abstract the issues of adopting the velocity components as dependent velocity variables including the cartesian and culvilinear ones for the navier stokes flow computations are investigated the viewpoint advocated is that a numerical algorithm should preferably honor both the physical conservation law in differential form and the geometric conservation law in discrete form it is demonstrated that with the curvilinear velocity vectors the curvatures of the grid lines introduce extra source terms into the governing equations with the cartesian velocity vector on the other hand the governing equations in curvilinear coordinates can retain the full conservation law form and honor the physical conservation laws the nonlinear combinations of the metric terms also cause the algorithms based on curvilinear velocity components to be more difficult to satisfy the geometric conservation law and hence more sensitive to grid skewness effect for the combined utilization of the cartesian velocity vector and the staggered grid arrangement the implications of spurious pressure oscillation arising from the 90 turning are discussed it is demonstrated that these spurious oscillations can possibly appear only under a very specific circumstance namely the meshes in the region with 90 turning must be parallel to the cartesian coordinates and of uniform spacing along coordinates otherwise no spurious oscillations can appear several flow solutions for domain with 90 and 360 turnings are presented to demonstrate that satisfactory results can be obtained by using the cartesian velocity components and the staggered grid arrangement

analysis of flow in the spiral casing using a streamline upwind petrov galerkin method numerical simulation of complex three dimensional flow through the spiral casing has been accomplished using a finite element method an explicit eulerian velocity correction scheme has been deployed to solve the reynolds average navier stokes equations the simulation has been performed to describe the flow in high reynolds number 106 regime for spatial discretization a streamline upwind petrov galerkin technique has been used the velocity field and the pressure distribution inside the spiral casing corroborate the results available in literature the flow structure reveals the fact that very strong secondary flow is evolved on the cross stream planes copyright 1999 john wiley sons ltd

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

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

an inverse eigenvalue problem for a general convex domain the underlying problem is to deduce the precise shape of a membrane from the complete knowledge of the eigenvalues i for the lapace operator a cf a ax in the x1x2 plane let d g r be a simply connected bounded domain with a smooth boundary ad let us suppose that the a are the eigenvalues of the impedance problem au k o in d

three dimensional analysis of flow in the spiral casing of a reaction turbine using a differently weighted petrov galerkin method abstract a weighted residual based finite element method has been used to predict the flow structure and the head loss in the spiral casing of a reaction turbine an explicit eulerian velocity correction scheme has been employed to solve the complete reynolds averaged navier stokes equations a differently weighted petrov galerkin dwpg method has been used for spatial discretization the simulation has been performed for high reynolds numbers the head loss in the spiral casing has been calculated for re 5 105 and re 106 the velocity field and the pressure distribution inside the spiral casing corroborate the trends available in literature the velocity field reveals the existence of a free vortex character of the global flow field a strong secondary flow is evolved on the cross stream plane due to the centrifugal forces which act at right angles to the main flow

numerical modeling of viscoelastic flows using equal low order finite elements a mixed finite element scheme abbreviated as i ps devss cnbs scheme for modeling viscoelastic flow problems is presented the finite incremental calculus fic pressure stabilization process and the discrete elastic viscous stress splitting method devss are introduced into the general framework of the iterative version of the fractional step algorithm with the use of the crank nicolson based splitting inconsistent streamline upwinding method su is employed to spatially discretize the constitutive equation of viscoelastic fluids equal low order finite elements which violate the lbb compatibility conditions are successfully used in the proposed scheme in addition the oldroyd b and the ptt models have been integrated into the proposed scheme to solve the 4 1 sudden contraction flow problem the numerical results demonstrate prominent stability and accuracy of both pressure and stress distributions over the flow domains provided by the proposed scheme within the weissenberg number range studied in the present work as compared with the reference solutions reported in the literatures

improving the speed and accuracy of projection type incompressible flow solvers abstract superseding so called first generation incompressible flow solvers of the projection type based on taylor galerkin advection second order pressure damping and element based data structures the current second generation solvers based on high order upwind advection fourth order pressure damping and edge based data structures have now been in use for half a decade and have proven remarkably robust and efficient for many large scale problems in order to achieve higher accuracy and speed these solvers have recently been enhanced in a variety of ways a substepping for advection b implicit treatment of advective terms via sgs and gmres lu sgs iterative solvers c fully implicit time accurate advancement of pressure and velocities and d linelet preconditioning for the pressure poisson equation the combined effect of these third generation improvements leads to speedups of the order of o 1 5 1 10 with similar or even better temporal accuracy as demonstrated on a variety of academic and industrial problems

an inverse eigenvalue problem of the wave equation for a multi connected region in r2 together with three different types of boundary conditions the trace of the wave kernel m t email protected w 1exp ite 1 2 w where e w w 1 are the eigenvalues of the negative laplacian email protected email protected 2 k 1 email protected x k 2 in the x 1 x 2 plane is studied for a variety of bounded domains where

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

integral conditions for the pressure in the computation of incompressible viscous flows abstract the problem of finding the correct conditions for the pressure in the time discretized navier stokes equations when the incompressibility constraint is replaced by a poisson equation for the pressure is critically examined it is shown that the pressure conditions required in a nonfractional step scheme to formulate the problem as a system of split second order equations are of an integral character and similar to the previously discovered integral conditions for the vorticity the novel integral conditions for the pressure are used to derive a finite element method which is very similar to that developed by glowinski and pironneau and is the finite element counterpart of the influence matrix method of kleiser and schumann

an ale based iterative cbs algorithm for non isothermal non newtonian flow with adaptive coupled finite element and meshfree method this paper presents a generalized scheme of the fractional step algorithm using characteristic based split cbs in ale framework for the numerical simulation of incompressible non isothermal non newtonian fluid flows and applies it combined with the adaptive coupled finite element and meshfree method for spatial discretizations to the polymer injection molding process based on the idea to discretize the material time derivative instead of the spatial time derivative the characteristic galerkin method is derived in a more general way and is used to discretize the non newtonian momentum and the energy conservation equations an iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain numerical experiments with the power law fluid model demonstrate and validate the performance and the capability of the proposed scheme

meshfree iterative stabilized taylor galerkin and characteristic based split cbs algorithms for incompressible n s equations abstract this paper presents two stabilized schemes of the fractional step algorithm using characteristic based split and taylor galerkin like based split respectively in the meshfree context an iterative procedure which makes the convective term satisfy the momentum conservation equation in an implicit sense is introduced into the two schemes to allow much larger time step sizes a modified version of finite increment calculus process for incompressibility stabilization is developed to avoid the calculation of high order spatial derivatives numerical experiments demonstrate the capability and stability of the proposed schemes of the meshfree based fractional step method in the simulation of incompressible flows

the wave equation approach to an inverse problem for a general multi connected domain in r2 with mixed boundary conditions the spectral function email protected t email protected j 1 exp email protected j 1 2 where m j j 1 are the eigenvalues of the negative laplacian email protected email protected u 1 email protected x u 2 in r 2 is studied for small t for a variety of domains where

finite element simulation of combined buoyancy and thermocapillary driven convection in open cavities thermocapillary induced and buoyancy driven convective flows that commonly occur in crystal growth are numerically simulated using galerkin finite element method the physical domain comprises of a open cavity with aspect ratio one and differentially heated vertical walls the top gas melt interface is free to deform subject to 90 contact angle boundary conditions at the two vertical walls the unsteady two dimensional navier stokes equations are discretized in time using chorin type splitting scheme and pressure is determined from the poisson s equation the free surface is taken to be resting on vertical spines and its evolution in time is determined from the kinematic free surface equation the governing equations for heat and momentum are solved in the arbitrary lagrangian eulerian frame of reference to handle the moving boundary the influence of grashof number marangoni number bond number ohnesorge number and prandtl number on the flow field and heat transfer is investigated

vorticity conditioning in the computation of two dimensional viscous flows abstract the problem of evaluating the boundary values of the vorticity in the calculation of two dimensional viscous flows is considered it is shown that the splitting of the fourth order equation for the stream function into two second order problems implies specific integral conditions which fix the abstract projection of the vorticity field with respect to the linear manifold of the harmonic functions these conditions are a direct consequence of the boundary conditions on the velocity and ensure satisfaction of physically essential conservation laws for the vorticity the discrete analogue of the projection conditions produces as many algebraic equations as the number of boundary points and requires the solution of an equal number of dirichlet problems in the particular case of stationary linearized equations stokes equations a direct i e noniterative method of solution is obtained steady and unsteady computational schemes relying on the projection conditions on the vorticity are introduced and extensive numerical results of finite difference calculations of the driven cavity model problem are reported and discussed

semi implicit taylor galerkin finite element methods for incompressible viscous flows abstract semi implicit taylor galerkin finite element methods are developed for solution of incompressible flows with heat transfer in the methods the primitive variables are split into two parts and the equations for the one part are solved using a semi implicit taylor galerkin method while the equations for the second part are dealt with by an implicit method the methods are tested and analysed by numerical calculations of several problems

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

development of bem for convective viscous flow problems abstract three kinds of boundary element approaches for an unsteady flow problem of incompressible viscous fluid are presented the first approach which is the so called boundary domaintype is based on the use of fundamental solution for the only linear differential operator and the newton raphson iterative procedure the second one is based on the time splitting technique of the governing equations in which the fundamental equations are split into the convection equation and the stokes equations the third one is based on the well known fractional step fs method which is one of the time splitting techniques in order to show the applicability and effectiveness of our approaches numerical results of the driven cavity flow example are demonstrated through a comparison with other numerical results

a fractional four step finite element formulation of the unsteady incompressible navier stokes equations using supg and linear equal order element methods a numerical algorithm using equal order linear finite element and fractional four step methods is presented for the analyses of incompressible fluid flow and heat transfer problems the supg streamline upwind petrov galerkin method is used for the weighted formulation of the navier stokes equations with the fractional four step method the memory and cost requirements of computations are significantly reduced because the pressure is split from the momentum equation the pressure equation is derived from the mass conservation without any approximation procedure such as adopted in the previously developed simple algorithm based finite element method therefore the present numerical algorithm gives more accurate results than it does furthermore the newly proposed pressure equation successfully treats the outflow boundary condition the present algorithm has been applied to the well known bench mark problems and proves to be efficient and accurate

spectral multigrid methods for elliptic equations ii a detailed description of spectral multigrid methods is provided this includes the interpolation and coarse grid operators for both periodic and dirichlet problems the spectral methods for periodic problems use fourier series and those for dirichlet problems are based upon chebyshev polynomials an improved preconditioning for dirichlet problems is given numerical examples and practical advice are included

third order upwind finite element computation of the incompressible navier stokes equations part i computation of flow around rectangular cylinders abstract aerodynamic behaviours of two dimensional unsteady flows around rectangular cylinders are numerically investigated by third order upwind finite element computation of the incompressible navier stokes equations a turbulence model such as the two equation model is not incorporated in the computational scheme so that the rectangular cylinders at depth breadth ratios from 0 7 to 4 to be considered are located in a uniform flow it is found that the numerical results of flows around the rectangular cylinders obtained by using the third order upwind finite element scheme are in good agreement with other computational and experimental results

a semi explicit parallel solver for viscous incompressible flows abstract an incompressible viscous flow solver is parallelized using a database management program gpar developed for parallel domain decomposition the approach presented involves subdivision of the flow domain into sub domains called solution blocks and distribution of the solution blocks to network of computers the equations for each block are solved in block solvers while the information exchange between neighboring blocks is achieved via interface solvers the data structure for communication between block and interface solvers are provided by gpar the incompressible flow solver is based on the fractional step method in which the momentum equations are solved explicitly while the pressure equation is solved implicitly results are presented illustrating the performance of the algorithms with increasing number of blocks and processors

effective vorticity velocity formulations for three dimensional incompressible viscous flows the vorticity velocity formulation for incompressible viscous flows is studied the main concern is effective numerical solution of the kinematic cauchy riemann equations for velocity especially when the divergence free condition of vorticity is violated due to numerical error the mathematical formulation of a differential and an integral approaches are revisited a novel projection of vorticity onto the divergence free space and its application to the two approaches are studied as an illustration of the differential approach the 3d lid driven cavity problem is solved the projection scheme is justified through numerical tests by comparing it to a new fully divergence free scheme numerical tests indicate that keeping vorticity divergence free is important for obtaining correct and accurate solutions the theory and methods apply to other divergence free fields of physical interest as well such as that in electro magnetic dynamics

shepard s interpolation for solution adaptive methods in numerical simulations of fluid dynamics problems solution adaptive methods have proven to be very powerful the implementation of the modified shepard s interpolation to the structured grids used in cfd is suggested and described in this paper which takes advantage of the logical grid structure this technique which is demonstrated to be robust efficient smoother and a more accurate alternative to linear interpolation is used in the remapping step during the solution adaption procedure applications to the solutions of the incompressible navier stokes equations both 2d and 3d are included

supg stabilized finite element resolution of the navier stokes equations applications to water treatment engineering in this paper an analysis of the viscous incompressible flow has been carried out from the very definition of the governing equations up to the resolution of some practical problems passing through the comprehensive study of the stabilized finite element techniques used in their resolution as a consequence of this analysis a code based upon a realistic interpretation of the forces has been written which allows for the modelling of the open channel flow with optimum results in the resolution of some benchmark and real flow problems related with the wastewater industry

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

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