accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

a faffa mlfma algorithm for electromagnetic scattering based on the multilevel fast multipole algorithm mlfma an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation where the fast far field approximation faffa is combined with mlfma the translation between groups in mlfma is expensive because spherical hankel functions and legendre polynomials are involved and the translator is defined on an eward sphere with many k spl circ directions when two groups are in the far field region however the translation can be greatly simplified by faffa where only a single k spl circ direction is involved in the translator the condition for using faffa and the way to efficiently incorporate faffa with mlfma are discussed complexity analysis illustrates that the computational cost in faffa mlfma can be asymptotically cut by half compared to the conventional mlfma numerical results are given to verify the efficiency of the algorithm

seed size strongly affects cascades on random networks the average avalanche size in the watts model of threshold dynamics on random networks of arbitrary degree distribution is determined analytically existence criteria for global cascades are shown to depend sensitively on the size of the initial seed disturbance the dependence of cascade size upon the mean degree z of the network is known to exhibit several transitions these are typically continuous at low z and discontinuous at high z here it is demonstrated that the low z transition may in fact be discontinuous in certain parameter regimes connections between these results and the zero temperature random field ising model on random graphs are discussed

a new consistent splitting scheme for incompressible navier stokes flows a least squares spectral element implementation this paper presents a new consistent splitting scheme for the numerical solution of incompressible navier stokes flows allowing to consistently decouple the computation of velocity and pressure the scheme is not a pressure correction or velocity correction scheme and does not display the splitting error in pressure associated with these fractional step methods the linearized momentum equations are first solved based on an explicit treatment of the pressure resulting in an advection diffusion problem for each velocity component a least squares projection is used to numerically solve the advection diffusion problem next a div curl problem is solved to make the velocity field solenoidal this step is also handled by a least squares projection finally a pressure poisson problem is solved to obtain the pressure field induced by the solenoidal velocity field this is done by solving the weak poisson problem by a galerkin projection or alternatively by solving the strong poisson problem by a least squares projection at each stage we only see coefficient matrices with a symmetric positive definite structure and use matrix free preconditioned conjugate gradient methods to numerically solve for the velocity and pressure fields high order c 0 spectral basis are used to span the finite element spaces a verification benchmark shows optimal algebraic convergence rates in time for the velocity pressure and vorticity the scheme is further verified by simulating the two dimensional unsteady flow past a circular cylinder up to moderately high reynolds numbers

on the influence of different stabilisation methods for the incompressible navier stokes equations two different stabilisation methods for the incompressible navier stokes equations are investigated both methods are based on a special interpolation scheme for the velocity components but with different effects and behaviour they introduce varying errors in the continuity equation but also the derivation of terms contributing to the special interpolation have a great influence on the quality of the results by means of various examples the two stabilisation methods and their contributing parts are compared

ptd analysis of impedance structures based on an approximate dyadic diffraction coefficient equivalent currents ecs are derived for computing the scattering by a finite length impedance wedge of arbitrary angle the derived equivalent currents are implemented in a standard general purpose physical theory of diffraction ptd code and results are presented demonstrating the accuracy of the formulation for a number of impedance and dielectrically coated structures these include typical shapes such as plates finite length cones and cylinders which have been partially or fully coated the ptd implementation requires a dyadic physical optics diffraction coefficient which is presented in the appendix

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

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

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

numerical analysis of quasioptical multireflector antennas in 2 d with the method of discrete singularities e wave case numerical method for modeling the e polarized wave scattering by electrically large quasioptical two dimensional 2 d reflectors is presented reflectors are assumed zero thickness and perfectly electrically conducting efficient numerical solution is obtained from the coupled singular integral equations discretized using new quadrature formulas of interpolation type it has controlled accuracy and deals with small size matrices to simulate a small horn feeding the incident field is taken as a beam generated by a complex source point csp current presented numerical results validate empirical rule of 10 db edge illumination needed to provide the best electromagnetic performance of reflector

a new higher order finite volume method based on moving least squares for the resolution of the incompressible navier stokes equations on unstructured grids in this work a new higher order 2 accurate finite volume method for the resolution of the incompressible navier stokes equations on unstructured grids is presented the formulation is based on the use of moving least squares mls approximants third and fourth order accurate discretizations of the convective and viscous fluxes are obtained on collocated meshes in addition mls is employed to design a new momentum interpolation method that allows interpolations better than linear on any kind of mesh the accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems on unstructured grids

a diagonalized multilevel fast multipole method with spherical harmonics expansion of the k space integrals diagonalization of the fast multipole method fmm for the helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves the resulting k space integral over the ewald sphere is numerically evaluated storing the k space quadrature samples of the method of moments mom basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems in this paper it is proposed to expand the k space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules aggregations plane wave translations and disaggregations in the realized multilevel fast multipole method mlfmm are carried out using the k space samples of a numerical quadrature rule however the incoming plane waves on the finest mlfmm level are expanded in spherical harmonics again thus due to the orthonormality of spherical harmonics the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients overall the resulting mlfmm can save a considerable amount of memory without compromising accuracy and numerical speed

a domain decomposition method for electromagnetic radiation and scattering analysis of multi target problems a domain decomposition method is presented for analyzing electromagnetic problems involving multiple separable scatterers the method first decomposes the original problem into several disjoint subregions in each subregion the domain decomposition method is further applied by decomposing the region into smaller possibly repeated subdomains the domain decomposition method is general enough for arbitrary geometries but is also capable of exploiting repetitions this renders geometrically complicated and electrically large subregion problems tractable the subregions communicate through the near field green s function to overcome the vast computational costs required in exchanging information between electrically large subregions the adaptive cross approximation algorithm is adopted to expedite the process the method is applied to study radiation characteristics of a reflector antenna system and an antenna array in the presence of a frequency selective surface to demonstrate the utility of the present approach

a second order accurate projection method for the incompressible navier stokes equations on non graded adaptive grids we present an unconditionally stable second order accurate projection method for the incompressible navier stokes equations on non graded adaptive cartesian grids we employ quadtree and octree data structures as an efficient means to represent the grid we use the supra convergent poisson solver of c h min f gibou h ceniceros a supra convergent finite difference scheme for the variable coefficient poisson equation on fully adaptive grids cam report 05 29 j comput phys in press a second order accurate semi lagrangian method to update the momentum equation an unconditionally stable backward difference scheme to treat the diffusion term and a new method that guarantees the stability of the projection step on highly non graded grids we sample all the variables at the grid nodes producing a scheme that is straightforward to implement we propose two and three dimensional examples to demonstrate second order accuracy for the velocity field and the divergence free condition in the l1 and l norms

pair approximation for the q voter model with independence on complex networks we investigate the q voter model with stochastic noise arising from independence on complex networks using the pair approximation we provide a comprehensive mathematical description of its behavior and derive a formula for the critical point the analytical results are validated by carrying out monte carlo experiments the pair approximation prediction exhibits substantial agreement with simulations especially for networks with weak clustering and large average degree nonetheless for the average degree close to q some discrepancies originate it is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise up till now the analytical results have been obtained only for a complete graph we show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network

configuring random graph models with fixed degree sequences random graph null models have found widespread application in diverse research communities analyzing network datasets including social information and economic networks as well as food webs pr

high order accurate solution of the incompressible navier stokes equations high order methods are of great interest in the study of turbulent flows in complex geometries by means of direct simulation with this goal in mind the incompressible navier stokes equations are discretized in space by a compact fourth order finite difference method on a staggered grid the equations are integrated in time by a second order semi implicit method stable boundary conditions are implemented and the grid is allowed to be curvilinear in two space dimensions the method is extended to three dimensions by a fourier expansion in every time step a system of linear equations is solved for the velocity and the pressure by an outer and an inner iteration with preconditioning the convergence properties of the iterative method are analyzed the order of accuracy of the method is demonstrated in numerical experiments the method is used to compute the flow in a channel the driven cavity and a constricted channel

implicit solution of the incompressible navier stokes equations on a non staggered grid abstract this paper presents an implicit procedure for the solution of the incompressible navier stokes equations in primitive variables the time dependent momentum equations are solved implicitly for the velocity field using the approximate factorization technique the continuity equation is satisfied at each time step through the solution of a poisson type equation for the static pressure a consistent finite difference scheme which satisfies the compatibility condition using a non staggered grid is used in the finite difference approximation of the static pressure poisson equation the results of the numerical computations in a driven cavity which are presented for the history of the residues at several reynolds numbers using different computational parameters demonstrate the excellent convergence characteristics of the solution procedure a stability analysis is conducted for the non iterative phase and numerical results are presented for a given set of compational parameters numerical results obtained for the steady state static pressure in the driven cavity are presented for the first time at re 1000 using a non staggered grid and the steady state velocity vorticity and pressure contours at re 100 400 and 1000 are compared with the computational results of other investigators additional results using a curvilinear grid are also presented for the flow in a cascade of circular airfoils at re 1000

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

imex extensions of linear multistep methods with general monotonicity and boundedness properties for solving hyperbolic systems with stiff sources or relaxation terms time stepping methods should combine favorable monotonicity properties for shocks and steep solution gradients with good stability properties for stiff terms in this paper we consider implicit explicit imex multistep methods suitable methods will be constructed based on explicit methods with general monotonicity and boundedness properties for hyperbolic equations numerical comparisons are made with several implicit explicit runge kutta methods

dynamical influence processes on networks general theory and applications to social contagion we study binary state dynamics on a network where each node acts in response to the average state of its neighborhood by allowing varying amounts of stochasticity in both the network and node responses we find different outcomes in random and deterministic versions of the model in the limit of a large dense network however we show that these dynamics coincide we construct a general mean field theory for random networks and show this predicts that the dynamics on the network is a smoothed version of the average response function dynamics thus the behavior of the system can range from steady state to chaotic depending on the response functions network connectivity and update synchronicity as a specific example we model the competing tendencies of imitation and nonconformity by incorporating an off threshold into standard threshold models of social contagion in this way we attempt to capture important aspects of fashions and societal trends we compare our theory to extensive simulations of this limited imitation contagion model on poisson random graphs finding agreement between the mean field theory and stochastic simulations

the unreasonable effectiveness of tree based theory for networks with clustering we demonstrate that a tree based theory for various dynamical processes operating on static undirected networks yields extremely accurate results for several networks with high levels of clustering we find that such a theory works well as long as the mean intervertex distance l is sufficiently small that is as long as it is close to the value of l in a random network with negligible clustering and the same degree degree correlations we support this hypothesis numerically using both real world networks from various domains and several classes of synthetic clustered networks we present analytical calculations that further support our claim that tree based theories can be accurate for clustered networks provided that the networks are sufficiently small worlds

efficient analysis of aperture antennas on generally shaped convex multilayered surfaces using a hybrid sd utd method a novel hybrid method is described for analyzing convex multilayered conformal array antennas the hybrid method is based on the spectral domain approach in combination with the ray based uniform theory of diffraction utd method the analysis is divided in two parts first the spectral domain approach is accelerated by using an asymptotic extraction technique where the extracted term of the green s function is calculated using utd it is shown that this new approach results in significant acceleration of the existing spectral domain algorithm without losing accuracy the modified spectral domain method is then used in the second part where generally shaped convex multilayered surfaces are analyzed by using sets of canonically shaped surfaces spheres and or circular cylinders their radii are obtained using the utd formulation which contains important information such as distance and curvature of the generally shaped surface along each geodesic the results obtained using the new algorithm are compared to the available results calculated and measured for different conformal antennas showing very good agreement

boundary conditions for a divergence free velocity pressure formulation of the navier stokes equations new sets of boundary conditions for the velocity pressure formulation of the incompressible navier stokes equations are derived the boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution moreover the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure numerical experiments support the theoretical conclusions

stability of pressure boundary conditions for stokes and navier stokes equations abstract the stability of a finite difference discretization of the time dependent incompressible navier stokes equations in velocity pressure formulation is studied in paticular we compare the stability for different pressure boundary conditions in a semiimplicit time integration scheme where only the viscous term is treated implicitly the stability is studied in three different ways by a normal mode analysis by numerical computation of the amplification factors and by direct numerical simulation of the governing equations all three approaches identify the same pressure boundary condition as the best alternative this condition implicitly enforces the normal derivative of the divergence to be zero on the boundary by coupling the normal derivative of the pressure to the normal component of the curl of the vorticity using this boundary condition we demonstrate that the time step is determined only by the convective term

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

bidirectional analytic ray tracing for fast computation of composite scattering from electric large target over a randomly rough surface the bidirectional analytic ray tracing bart method is developed to rapidly calculate composite scattering from three dimensional 3d electrically large complex targets above a randomly rough surface ray tracing is carried out both along the incident forward direction and converse direction of scattering backward recording different orders of ray illumination on each facet or edge of the target and surface once a pair of forward and backward rays meet on a facet edge a scattering term is constructed using the diffused scattering diffraction of this facet edge and all reflections occurred on the tracing paths the rough surface is modeled with ldquorough facetsrdquo including coherent scattering and diffused incoherent scattering which can be directly calculated according to the iem integral equation method of a randomly rough surface analytic tracing of polygon ray tubes is developed to precisely calculate the illumination and shadowing of facets which exempt large patches of the target from any finer meshing it significantly reduces the complexity relevant to the target electric size higher orders of scattering and in particular interactions between the target and rough surface are then taken into account the accuracy and performance of bart is validated and evaluated by comparing with exact computational electromagnetic methods for electrically small targets numerical examples of angularly composite scattering from a three dimensional electrically large e g a ship like target over a randomly rough surface are presented and discussed

finite volume methods for two dimensional incompressible flows with complex boundaries abstract the paper discusses possible ways of developing accurate and efficient finite volume methods for complex incompressible flows the issues of boundary fitted grid generation choice of coupled or uncoupled procedures cartesian or grid aligned velocity components staggered or non staggered variable arrangement discretization methods solution algorithms and convergence acceleration by multigrid methods are addressed an example of a finite volume method for general two dimensional flows is described in some detail and applications of this method to a variety of flows are presented

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

kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow the collocated mesh scheme is often favored over the staggered mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates the collocated mesh scheme does not conserve kinetic energy however and few careful checks of the impact of these errors have been made in this work analysis is used to identify two sources of kinetic energy conservation error in the collocated mesh scheme 1 errors arising from the interpolations used to estimate the velocity on the cell faces and 2 errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes it is shown that the interpolation error can be eliminated through the use of first order accurate centered interpolation operators with mesh independent weights the pressure error appears to be intrinsic to the scheme and it is shown to scale as o t2 x2 the effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the cartesian mesh is stretched in only one direction the inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error the standard second order centered interpolation is shown to lead to severe numerical oscillations while the kinetic energy conserving first order centered interpolation produces solutions that are almost as smooth as those obtained with a third order upwind interpolation when compared in channel flow simulations however the first order centered interpolation is shown to be far superior to the third order upwind interpolation the latter being adversely affected by numerical dissipation only slight differences were noted when comparing channel flow simulations using first order and second order centered interpolations these results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly constructed non dissipative centered interpolations

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

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

driven cavity flows by efficient numerical techniques abstract efficient and reliable numerical techniques of high order accuracy are presented for solving problems of steady viscous incompressible flow in the plane and are used to obtain accurate solutions for the driven cavity a solution is obtained at reynolds number 10 000 on a 180 180 grid the numerical methods combine an efficient linear system solver an adaptive newton like method for nonlinear systems and a continuation procedure for following a branch of solutions over a range of reynolds numbers

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

a higher order formulation of the mimetic finite difference method a new mimetic finite difference method for the diffusion problem is developed by using a linear interpolation for the numerical fluxes this approach provides a higher order accurate approximation to the flux of the exact solution in analogy with the original formulation a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability the scalar solution field is approximated by a piecewise constant function a computationally efficient postprocessing technique is also proposed to get a piecewise quadratic polynomial approximation to the exact scalar variable finally optimal convergence rates and accuracy improvement with respect to the lower order formulation are shown by numerical examples

a hybrid febi mlfmm utd method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects numerical solutions of electromagnetic scattering and radiation problems including arbitrarily shaped objects are obtained by solving integral equations with the method of moments mom fast and efficient solution of the integral equation with low computation and memory complexity is provided by the multilevel fast multipole method mlfmm the presence of electrically large conducting objects leads to hybrid mom techniques with high frequency methods for ray based high frequency methods no discretization of the electrically large objects is needed resulting into a more efficient numerical treatment of the problem however in order to retain low computation and memory complexity the high frequency fields must be taken into account in the matrix vector product computations in the various levels of the mlfmm in this contribution a ray based hybridization of the mlfmm with the uniform geometrical theory of diffraction utd is proposed within a hybrid finite element boundary integral febi technique using the combined field integral equation cfie resulting into a hybrid febi mlfmm utd method the hybridization is performed at the translation procedure on the various levels of the mlfmm using a far field approximation of the appropriate translation operator to obtain the high frequency incident fields at the critical points of the utd the formulation of this new hybrid technique is presented and numerical results are shown

numerical solutions for the pressure poisson equation with neumann boundary conditions using a non staggered grid 1 abstract numerical solutions are obtained for the pressure poisson equation with neumann boundary conditions using a non staggered grid the existence of a solution for this equation requires the satisfaction of a compatibility condition which relates the source of the poisson equation and the neumann boundary conditions this compatibility condition is not automatically satisfied on non staggered grids failure to satisfy the compatibility condition leads to non convergent iterative solutions consistent finite difference approximations for the pressure equation with neumann boundary conditions are developed to satisfy the compatibility condition on non staggered grids the method is applied to calculate the pressure coefficient in a driven cavity when given the velocity field the velocity is computed from the stream function vorticity formulation of the navier stokes equations

a mimetic discretization of the stokes problem with selected edge bubbles a new mimetic finite difference method for the stokes problem is proposed and analyzed the mimetic discretization methodology can be understood as a generalization of the finite element method to meshes with general polygons polyhedrons in this paper the mimetic generalization of the unstable p 1 p 0 and the conditionally stable q1 p0 finite element is shown to be fully stable when applied to a large range of polygonal meshes moreover we show how to stabilize the remaining cases by adding a small number of bubble functions to selected mesh edges a simple strategy for selecting such edges is proposed and verified with numerical experiments

hipsters on networks how a minority group of individuals can lead to an antiestablishment majority the spread of opinions memes diseases and alternative facts in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread one feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network in this paper we explore how antiestablishment nodes e g hipsters influence the spreading dynamics of two competing products we consider a model in which spreading follows a deterministic rule for updating node states which indicate which product has been adopted in which an adjustable probability p hip of the nodes in a network are hipsters who choose to adopt the product that they believe is the less popular of the two the remaining nodes are conformists who choose which product to adopt by considering which products their immediate neighbors have adopted we simulate our model on both synthetic and real networks and we show that the hipsters have a major effect on the final fraction of people who adopt each product even when only one of the two products exists at the beginning of the simulations a small fraction of hipsters in a network can still cause the other product to eventually become the more popular one to account for this behavior we construct an approximation for the steady state adoption fractions of the products on k regular trees in the limit of few hipsters additionally our simulations demonstrate that a time delay in the knowledge of the product distribution in a population as compared to immediate knowledge of product adoption among nearest neighbors can have a large effect on the final distribution of product adoptions using a local tree approximation we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters in all networks we find that either of the two products can become the more popular one at steady state depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution our simple model and analysis may help shed light on the road to success for antiestablishment choices in elections as such success and qualitative differences in final outcomes between competing products political candidates and so on can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals

cascade dynamics of complex propagation abstract random links between otherwise distant nodes can greatly facilitate the propagation of disease or information provided contagion can be transmitted by a single active node however we show that when the propagation requires simultaneous exposure to multiple sources of activation called complex propagation the effect of random links can be just the opposite it can make the propagation more difficult to achieve we numerically calculate critical points for a threshold model using several classes of complex networks including an empirical social network we also provide an estimation of the critical values in terms of vulnerable nodes

limitations of discrete time approaches to continuous time contagion dynamics continuous time markov process models of contagions are widely studied not least because of their utility in predicting the evolution of real world contagions and in formulating control measures it is often the case however that discrete time approaches are employed to analyze such models or to simulate them numerically in such cases time is discretized into uniform steps and transition rates between states are replaced by transition probabilities in this paper we illustrate potential limitations to this approach we show how discretizing time leads to a restriction on the values of the model parameters that can accurately be studied we examine numerical simulation schemes employed in the literature showing how synchronous type updating schemes can bias discrete time formalisms when compared against continuous time formalisms event based simulations such as the gillespie algorithm are proposed as optimal simulation schemes both in terms of replicating the continuous time process and computational speed finally we show how discretizing time can affect the value of the epidemic threshold for large values of the infection rate and the recovery rate even if the ratio between the former and the latter is small

the noisy voter model under the influence of contrarians abstract the influence of contrarians on the noisy voter model is studied at the mean field level the noisy voter model is a variant of the voter model where agents can adopt two opinions optimistic or pessimistic and can change them by means of an imitation herding and an intrinsic noise mechanisms an ensemble of noisy voters undergoes a finite size phase transition upon increasing the relative importance of the noise to the herding form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states by the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents anti herding we first consider the case of only contrarians and show that the only possible steady state is the unimodal one more generally when voters and contrarians are present we show that the bimodal unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four and their characteristic rates are small enough for the number of contrarians bigger or equal to four the voters and the contrarians can be seen only in the unimodal phase moreover if the number of voters and contrarians as well as the noise and herding rates are of the same order then the probability functions of the steady state are very well approximated by the gaussian distribution

factorization methods for the numerical approximation of navier stokes equations we investigate a general approach for the numerical approximation of incompressible navier stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve the splitting is obtained through an algebraic approximate factorization of the matrix arising from space and time discretization of the original equations several schemes based on approximate factorization are investigated for some of these methods a formal analogy with well known time advancing schemes such as the projection chorin temam s can be pointed out features and limits of this analogy that was earlier introduced in b perot j comp phys 108 1993 51 8 are addressed other new methods can also be formulated starting from this approach in particular we introduce the so called yosida method which can be investigated in the framework of quasi compressibility schemes numerical results illustrating the different performances of the different methods addressed are presented for a couple of test cases

a unified method for computing incompressible and compressible flows in boundary fitted coordinates a unified method for computing incompressible and compressible flows with mach uniform accuracy and efficiency is described the method is equally applicable to stationary and nonstationary flows a pressure based discretisation on a staggered grid in general boundary fitted coordinates is used for the euler equations extension to navier stokes is straightforward dimensionless variables that remain finite for all mach numbers are used mach number independent accuracy and efficiency is shown by numerical experiments

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

a co located incompressible navier stokes solver with exact mass momentum and kinetic energy conservation in the inviscid limit the incompressible navier stokes equations conserve mass momentum and kinetic energy in the inviscid limit therefore numerical methods should attempt to mimic these conservation properties as well there exists many well established methods with exact conservation properties based on staggered grids but existing methods based on co located grids introduce numerical dissipation in order to yield smooth pressure fields in the present work a novel method that utilizes null space vectors to yield a smooth pressure field is presented the method exactly preserves mass momentum and kinetic energy on co located grids

additive semi implicit runge kutta methods for computing high speed nonequilibrium reactive flows this paper is concerned with time stepping numerical methods for computing stiff semi discrete systems of ordinary differential equations for transient hypersonic flows with thermo chemical nonequilibrium the stiffness of the equations is mainly caused by the viscous flux terms across the boundary layers and by the source terms modeling finite rate thermo chemical processes implicit methods are needed to treat the stiff terms while more efficient explicit methods can still be used for the nonstiff terms in the equations this paper studies three different semi implicit runge kutta methods for additively split differential equations in the form ofu f u g u wherefis treated by explicit runge kutta methods andgis simultaneously treated by three implicit runge kutta methods a diagonally implicit runge kutta method and two linearized implicit runge kutta methods the coefficients of up to third order accurate additive semi implicit runge kutta methods have been derived such that the methods are both high order accurate and strongly a stable for the implicit terms the results of two numerical tests on the stability and accuracy properties of these methods are also presented in the paper

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

a fourth order accurate finite volume compact method for the incompressible navier stokes solutions abstract this paper presents a finite volume fourth order accurate compact scheme for discretization of the incompressible navier stokes equations in primitive variable formulation the numerical method of integrating the navier stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes the pressure velocity coupling is achieved via the coupled solution of the resulting system of equations the solution of the coupled set of equations is performed with an implicit newton krylov matrix free method for stationary problems for simulation of unsteady flows a standard fourth order runge kutta method was used for temporal discretization and the velocity pressure coupling was ensured at each stage also using the matrix free method several incompressible viscous steady and unsteady flow problems have been computed to assess the robustness and accuracy of the proposed method

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

finite difference schemes for incompressible flow based on local pressure boundary conditions in this paper we discuss the derivation and use of local pressure boundary conditions for finite difference schemes for the unsteady incompressible navier stokes equations in the velocity pressure formulation their use is especially well suited for the computation of moderate to large reynolds number flows we explore the similarities between the implementation and use of local pressure boundary conditions and local vorticity boundary conditions in the design of numerical schemes for incompressible flow in 2d in their respective formulations when these local numerical boundary conditions are coupled with a fully explicit convectively stable time stepping procedure the resulting methods are simple to implement and highly efficient unlike the vorticity formulation the use of the local pressure boundary condition approach is readily applicable to 3d flows the simplicity of the local pressure boundary condition approach and its easy adaptation to more general flow settings make the resulting scheme an attractive alternative to the more popular methods for solving the navier stokes equations in the velocity pressure formulation we present numerical results of a second order finite difference scheme on a nonstaggered grid using local pressure boundary conditions stability and accuracy of the scheme applied to stokes flow is demonstrated using normal mode analysis also described is the extension of the method to variable density flows

higher order mimetic methods for unstructured meshes a higher order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer mimetic discretization methods create discrete versions of the partial differential operators such and the gradient and divergence that are exact in some sense and therefore mimic the important mathematical properties of their continuous counterparts the proposed numerical method is an interesting mixture of both finite volume and finite element ideas while the ideas presented can be applied to arbitrarily high order accuracy we focus in this work on the details of creating a third order accurate method the proposed method is shown to be exact for piecewise quadratic solutions and shows third order convergence on arbitrary triangular tetrahedral meshes the numerical accuracy of the method is confirmed on both two dimensional and three dimensional unstructured meshes the computational cost required for a desired accuracy is analyzed against lower order mimetic methods

phase transitions in the q voter model with two types of stochastic driving we study a nonlinear q voter model with stochastic driving on a complete graph we investigate two types of stochasticity that using the language of social sciences can be interpreted as different kinds of nonconformity from a social point of view it is very important to distinguish between two types nonconformity so called anticonformity and independence a majority of work has suggested that these social differences may be completely irrelevant in terms of microscopic modeling that uses tools of statistical physics and that both types of nonconformity play the role of so called social temperature in this paper we clarify the concept of social temperature and show that different types of noise may lead to qualitatively different emergent properties in particular we show that in the model with anticonformity the critical value of noise increases with parameter q whereas in the model with independence the critical value of noise decreases with q moreover in the model with anticonformity the phase transition is continuous for any value of q whereas in the model with independence the transition is continuous for q 5 and discontinuous for q 5

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

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

a domain decomposition finite difference time domain fdtd method for scattering problem from very large rough surfaces a domain decomposition finite difference time domain dd fdtd method is proposed to solve the problem of electromagnetic scattering from very large rough surfaces the entire computational domain is decomposed into multiple subdomains each subdomain is simulated by using the conventional fdtd method to obtain the scattered fields on a huygens surface and the total fields on the rough surface the latter is used to compute the scattered field on the huygens surface in adjacent subdomains by invoking the reciprocity theorem simulation results are compared with those in the literatures to validate this method the normalized radar cross sections nrcss from very large surfaces of 66 lambda times 66 lambda are also presented to demonstrate the efficacy of this method

new hybrid runge kutta methods for unsteady reactive flow simulation in the numerical simulation of transient reacting flow standard explicit calculation is prohibitively expensive because of the small time steps needed to address the stiffness of a governing differential system to circumvent this new hybrid implicit explicit methods proposed treat the stiffness whereas the underlying time step control is governed by the courant stability criterion because the coefficients of both explicit and implicit operations are entirely determined by solving the necessary conditions of accuracy and l stability without any extra assumptions the methods are more generalized than other similar methods in the literature two families of semi implicit runge kutta schemes are developed for split differential equations in the form of u f t u g t u where f is treated explicitly and g is simultaneously treated implicitly like the rest of all the developed schemes a low storage family of semi implicit schemes is also derived to be globally high order accurate and l stable for implicit calculations in a companion paper yoh j j and zhong x new hybrid runge kutta methods for unsteady reactive flow simulation applications aiaa journal v ol 42 no 8 2004 pp 1601 1611 the new schemes are tested to solve a wide range of applications in high speed flow physics involving combustion

a cell centered adaptive projection method for the incompressible navier stokes equations in three dimensions we present a method for computing incompressible viscous flows in three dimensions using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time we use an l0 stable second order semi implicit scheme to evaluate the viscous terms results are presented to demonstrate the accuracy and effectiveness of this approach

a discrete calculus analysis of the keller box scheme and a generalization of the method to arbitrary meshes abstract the keller box scheme is a face based method for solving partial differential equations that has numerous attractive mathematical and physical properties it is shown that these attractive properties collectively follow from the fact that the scheme discretizes partial derivatives exactly and only makes approximations in the algebraic constitutive relations appearing in the pde the exact discrete calculus associated with the keller box scheme is shown to be fundamentally different from all other mimetic physics capturing numerical methods this suggests that a unique exact discrete calculus does not exist it also suggests that existing analysis techniques based on concepts in algebraic topology in particular the discrete de rham complex are unnecessarily narrowly focused since they do not capture the keller box scheme the discrete calculus analysis allows a generalization of the keller box scheme to non simplectic meshes to be constructed analysis and tests of the method on the unsteady advection diffusion equations are presented

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

finite difference method for incompressible navier stokes equations in arbitrary orthogonal curvilinear coordinates a finite difference method for solving three dimensional time dependent incompressible navier stokes equations in arbitrary curvilinear orthogonal coordinates is presented the method is oriented on turbulent flow simulations and consists of a second order central difference approximation in space and a third order semi implicit runge kutta scheme for time advancement spatial discretization retains some important properties of the navier stokes equations including energy conservation by the nonlinear and pressure gradient terms numerical tests cover cartesian cylindrical polar spherical cylindrical elliptic and cylindrical bipolar coordinate systems both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method

velocity correction projection methods for incompressible flows we introduce and study a new class of projection methods namely the velocity correction methods in standard form and in rotational form for solving the unsteady incompressible navier stokes equations we show that the rotational form provides improved error estimates in terms of the h1 norm for the velocity and of the l2 norm for the pressure we also show that the class of fractional step methods introduced in s a orsag m israeli and m deville j sci comput 1 1986 pp 75 111 and k e karniadakis m israeli and s a orsag j comput phys 97 1991 pp 414 443 can be interpreted as the rotational form of our velocity correction methods thus to the best of our knowledge our results provide the first rigorous proof of stability and convergence of the methods in those papers we also emphasize that contrary to those of the above groups our formulations are set in the standard l2 setting and consequently they can be easily implemented by means of any variational approximation techniques in particular the finite element methods

hybrid sup 2 combining the three dimensional hybrid finite element boundary integral technique for planar multilayered media with the uniform geometrical theory of diffraction the fully three dimensional 3 d hybrid finite element fe boundary integral bi technique is extended by further hybridization with the uniform geometrical theory of diffraction utd resulting in a so called hybrid sup 2 fe bi utd approach the formulation is capable of modeling arbitrarily shaped strongly inhomogeneous objects together with electrically large obstacles of relatively simple shape within the common environment of a planar multilayered medium the arbitrarily shaped inhomogeneous objects are discretized by finite elements whereas the electrically large obstacles are described by the utd and both of these models are included into an integral equation derived from the equivalence principle for planar multilayered media thus full electromagnetic coupling is realized between all parts of the formulation the integral equation is implemented using mixed potentials with appropriate green s functions derived from sommerfeld integral representations for planar multilayered media the utd contributions are accounted for by corresponding modifications of the green s functions and the fe technique is coupled to the integral equation via introduction of equivalent surface current densities in the bounding surfaces of the discretized objects after presenting the formulation of this novel fully 3 d hybrid sup 2 technique the implemented computer code is validated against conventional hybrid fe bi computations and a wireless base station antenna is analyzed in several situations of complex real world microcell environments

anticonformity or independence insights from statistical physics the aim of this paper is to examine how different types of social influence introduced on the microscopic individual level manifest on the macroscopic level i e in the society the inspiration for this task came mainly from two sources social psychology that recognize two different types of nonconformity anticonformity and independence and the observation related to the agent based modeling that was verbalized in 2002 by macy and willer that there was a little effort to provide analysis of how results differ depending on the model designs to achieve the goal we propose a generalized model of opinion dynamics that as a special cases reduces to the linear voter model sznajd model q voter model and the majority rule we use the model to examine the differences that appear at the macroscopic level under the influence of two types of nonconformity introduced on the microscopic level we answer the question if the observed differences are universal or model dependent

an accurate compact treatment of pressure for colocated variables we propose a new scheme for the pressure treatment in computations of incompressible flow using a colocated grid arrangement to avoid oscillations associated with the sparse non compact stencil we introduce a compact fourth order equivalent of this stencil and study its advantages over the classical second order averaging procedure

a 2d compact fourth order projection decomposition method a 2d fourth order compact direct scheme projection decomposition method for solving incompressible viscous flows in multi connected rectangular domains is devised in each subdomain the governing navier stokes equations are discretized by using fourth order compact schemes in space and second order scheme in time the coupling between subdomains is based on a direct non overlapping multidomain method it allows to solve each helmholtz poisson problem resulting of a projection method in complex geometries the major difficulty of the poisson neumann problem solvability is addressed and correctly treated the present numerical method is checked through some classical numerical experiments first the second order accuracy in time and the fourth order accuracy in space are shown by matching with the analytical solution of the taylor problem the method is also tested by simulating the flow in a 2d lid driven cavity the utility of the compact scheme projection decomposition method approach is further illustrated by two other benchmark problems viz the flow over a backward facing step and the laminar flow past a square prism the present results are in good agreement with the experimental data and other numerical solutions available in the literature

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