a multiplicity result for a nonlinear fractional schrodinger equation in rn without the ambrosetti rabinowitz condition abstract in this paper we study the existence and the multiplicity of positive solutions for the following class of fractional schrodinger equations 2 s s u v x u f u in r n where 0 is a parameter s 0 1 n 2 s v r n r is a continuous positive potential and f r r is a c 1 superlinear nonlinearity which does not satisfy the ambrosetti rabinowitz condition the main result is established by using minimax methods and ljusternik schnirelmann theory of critical points

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

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

improvements on open and traction boundary conditions for navier stokes time splitting methods we present in this paper a numerical scheme for incompressible navier stokes equations with open and traction boundary conditions in the framework of pressure correction methods a new way to enforce this type of boundary condition is proposed and provides higher pressure and velocity convergence rates in space and time than found in the present state of the art we illustrate this result by computing some numerical and physical tests in particular we establish reference solutions of a laminar flow in a geometry where a bifurcation takes place and of the unsteady flow around a square cylinder

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

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

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

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

a conservative level set method for two phase flow ii in this paper we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in j comput phys 210 2005 225 246 we formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method a finite element discretization is presented as well as an adaptive mesh control procedure numerical experiments relevant for problems in petroleum engineering and material science are presented for these problems the surface tension is strong and conservation of mass is important problems in both two and three dimensions with uniform as well as non uniform grids are studied from these calculations convergence and conservation is studied good conservation and convergence are observed

finite element approximation of the nonstationary navier stokes problem part iii smoothing property and higher order error estimates for spatial discretization this paper continues our error analysis of finite element galerkin approximation of the nonstationary navier stokes equations optimal order error estimates both local and global are derived for higher order finite elements under appropriate assumptions about the smoothness and stability of the solution these assumptions take into account the loss of regularity at t 0 that one generally has to expect in the absence of higher order nonlocal compatibility conditions for the data of the problem

signed digit representations of minimal hamming weight the authors give an online algorithm for computing a canonical signed digit representation of minimal hamming weight for any integer n using combinatorial techniques the probability distributions pr k sub r h where k sub r is taken to be a random variable on the uniform probability space of k digit integers is computed also using a markov chain analysis it is shown that e k sub r approximately r 1 k r 1 as k to infinity

a conservative finite volume second order accurate projection method on hybrid unstructured grids this paper describes a finite volume discretization method to compute steady two dimensional incompressible viscous recirculating flows using hybrid unstructured meshes composed of triangles and quadrilaterals however the proposed formulation is not restricted to these topologies the new method includes a second order least squares scheme for convection discretization and a fractional step projection method based on a staggered grid arrangement for pressure velocity coupling numerical results are reported to demonstrate the robustness second order accuracy and flexibility of the proposed method to the authors knowledge this paper represents the first general unstructured grid finite volume method to achieve full second order accuracy for the steady incompressible 2d version of navier stokes equations

a comment on an efficient common multiplicand multiplication method to the montgomery algorithm for speeding up exponentiation in 2009 wu proposed a fast modular exponentiation algorithm and claimed that the proposed algorithm on average saved about 38 9 and 26 68 of single precision multiplications as compared to dusse kaliski s montgomery algorithm and ha moon s montgomery algorithm respectively however in this comment we demonstrate that wu s algorithm on average reduces the number of single precision multiplications by at most 22 43 and 6 91 when respectively compared with dusse kaliski s version and ha moon s version that is the computational efficiency of wu s algorithm is obviously overestimated

efficient unstructured mesh generation by means of delaunay triangulation and bowyer watson algorithm this work is devoted to the description of an efficient unstructured mesh generation method entirely based on the delaunay triangulation the distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously this result is achieved by taking advantage of the sequential way in which the bowyer watson algorithm computes the delaunay triangulation two methods are proposed which have great geometrical flexibility in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes the methods are computationally efficient and are applicable both in two and three dimensions

closed form expression for the average weight of signed digit representations in radix r number system the minimal weight signed digit sd representation has minimal number of nonzero signed digits which belong to the set spl plusmn 1 spl plusmn 2 spl plusmn r 1 in this article we derive closed form expressions for the average number of nonzero digits in the minimal weight sd representation and for the average length of the canonical sd representation a special case of the minimal weight sd form of a positive integer whose radix r form is of length n n spl ges 1

a new family of projection schemes for the incompressible navier stokes equations with control of high frequency damping abstract a simple spatially discrete model problem consisting of mass points and dash pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible navier stokes equations in particular the temporal accuracy the stability and the numerical damping are investigated the present study suggests that it is not possible to formulate a second order accurate projection pressure correction scheme which possesses any high frequency damping motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised method respectively and offer control over high frequency damping both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible navier stokes equations comprehensive numerical studies of the flow in a lid driven cavity and the flow around a cylinder are presented the observations made are in agreement with the conclusions drawn from the model problem

algorithm of asynchronous binary signed digit recoding on fast multiexponentiation multiexponentiation for the 2 dimension one especially is a very important but time consuming operation in many elgamal like public key cryptosystems an efficient multiexponentiation method is firstly proposed by shamir in elgamal s paper shamir s method requires 1 75n modular multiplications in average where n is the bit length of the exponents using minimal weight binary signed digit bsd representations in shamir s method can reduce the number of multiplications to 1 556n due to there are many minimal weight bsd representations for an integer dimitrov et al proposed a new 2 dimension multiexponentiation algorithm to recode the canonical binary signed digit representations the average number of the number 1 556n is reduced to 1 534n after the publish of the dimitrov jullien miller algorithm there are many research on receding bsd representation of a pair of integers the most interesting one is the joint sparse form the number of multiplication can be reduced to 1 500n in joint sparse form when the exponent length is near infinite in this paper we propose a new asynchronous recoding algorithm to reduce the factor to 1 509n for comparison to all the previous algorithm the property of asynchronous receding is especially suitable for multi dimension multiexponentiation

weakly compressible high order i stable central difference schemes for incompressible viscous flows abstract in this paper we propose a weakly compressible model for numerical simulation of the incompressible viscous flows this model asymptotically approximates the incompressible navier stokes equations when the mach number tends to zero the main advantage of this model is that its numerical discretization avoids any poisson solver thus is very attractive for problems with complicated geometries this model is discretized by high order center differences in space and the so called i stable method for time the linear stability region of an i stable method contains part of the imaginary axis when solving a system of convection diffusion equations with a small viscosity the i stable method allows a very large cell reynolds number thus is particularly suitable for the simulation of fluid flows with large reynolds numbers numerical experiments illustrate the efficiency and robustness of this approach

minimal weight digit set conversions we consider the problem of recoding a number to minimize the number of nonzero digits in its representation that is to minimize the weight of the representation a general sliding window scheme is described that extends minimal binary sliding window conversion to arbitrary radix and to encompass signed digit sets this new conversion expresses a number of known recoding techniques as special cases proof that this scheme achieves minimal weight for a given digit set is provided and results concerning the theoretical average and worst case weight are derived

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

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

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

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

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

convergence analysis of a class of massively parallel direction splitting algorithms for the navier stokes equations in simple domains we provide a convergence analysis for a new fractional timestepping technique for the incompressible navier stokes equations based on direction splitting this new technique is of linear complexity unconditionally stable and convergent and suitable for massive parallelization

a conservative level set method for contact line dynamics a new model for simulating contact line dynamics is proposed we apply the idea of driving contact line movement by enforcing the equilibrium contact angle at the boundary to the conservative level set method for incompressible two phase flow e olsson g kreiss a conservative level set method for two phase flow j comput phys 210 2005 225 246 a modified reinitialization procedure provides a diffusive mechanism for contact line movement and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface we are able to capture contact line movement without loosing the conservation numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct

generalized signed digit number systems a unifying framework for redundant number representations signed digit sd number representation systems have been defined for any radix r or 3 with digit values ranging over the set alpha 1 0 1 alpha where alpha is an arbitrary integer in the range 1 2r

steady viscous flow in a triangular cavity steady recirculating viscous flow inside an equilateral triangular cavity is generated by translating one side the navier stokes equations are solved numerically using finite differences on a transformed geometry alternative numerical approaches and associated numerical difficulties are also discussed the results show a primary eddy and a series of secondary eddies at the stagnant corner for high reynolds numbers the interior of the primary eddy has constant vorticity but its value cannot be predicted by the mean squared law

optimal left to right binary signed digit recoding this paper describes new methods for producing optimal binary signed digit representations this can be useful in the fast computation of exponentiations contrary to existing algorithms the digits are scanned from left to right i e from the most significant position to the least significant position this may lead to better performances in both hardware and software

complexity and fast algorithms for multiexponentiations in this paper we propose new algorithms for multiple modular exponentiation operations the major aim of these algorithms is to speed up the performance of some cryptographic protocols based on multiexponentiation our new algorithms are based on binary like complex arithmetic introduced by k pekmestzi 1989 and generalized in this paper

nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a fourier finite element technique and an interior penalty method the maxwell equations in the mhd limit in heterogeneous axisymmetric domains composed of conducting and non conducting regions are solved by using a mixed fourier lagrange finite element technique finite elements are used in the meridian plane and fourier modes are used in the azimuthal direction parallelization is made with respect to the fourier modes continuity conditions across interfaces are enforced using an interior penalty technique the performance of the method is illustrated on kinematic and full dynamo configurations

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

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

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 efficient common multiplicand multiplication method to the montgomery algorithm for speeding up exponentiation the modular exponentiation is a common operation for scrambling secret data and is used by several public key cryptosystems such as the rsa scheme and dss digital signature scheme however the calculations involved in modular exponentiation are time consuming especially when performed in software in this paper we propose an efficient cmm msd montgomery algorithm by utilizing the montgomery modular reduction method common multiplicand multiplication cmm method and minimal signed digit msd recoding technique for fast modular exponentiation by using the technique of recording the common signed digit representations in the grouped substrings of exponent our algorithm can improve the efficiency of both the original cmm exponentiation algorithm and the montgomery multiplication algorithm the fast modular exponentiation algorithm developed in this paper can be easily implemented in general signed digit computing machine and is therefore well suited for parallel implementation to fast evaluating modular exponentiation moreover by using the proposed cmm msd montgomery algorithm on average the total number of single precision multiplications can be reduced by about 38 9 and 26 68 as compared with dusse kaliski s montgomery algorithm and ha moon s montgomery algorithm respectively

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

implicit formulation of material point method for analysis of incompressible materials abstract material point method mpm is a particle based numerical technique with application to solid mechanics problems involving large deformations recently mpm has been successfully applied in many engineering applications including solid and solid fluid interaction problems due to its capability to model complex history dependent material behaviours however the conventional explicit mpm approach exhibits numerical limitations in incompressible or near incompressible material behaviour problems we study an implicit treatment of the pressure in mpm algorithm to simulate material incompressibility avoiding artificial pressure oscillations and significantly small time steps present in the explicit mpm approach applying chorin s projection method to the velocity pressure coupled equations an elliptic equation is solved for the pressure which is then used to solve the divergence free velocity field the results of dam break problem show no spurious pressure oscillations and large time steps compared to the traditional explicit mpm the ability of the present implicit mpm formulation to model incompressible materials will be an additional advantage in simulating materials with complex constitutive equations which exhibit a time dependent memory

a w nnaf method for the efficient computation of scalar multiplication in elliptic curve cryptography based on the non adjacent form naf expression here we present a new method to express a large positive integer k with the base of any positive integer w other than 2 we call this method the w nnaf method as the expression is near to the naf one and with base w this expression leads to the minimal hamming weight of all the base w expressions based on the proposed expression and some existing methods an algorithm is developed to compute kp efficiently

fast modular multi exponentiation using modified complex arithmetic abstract modular multi exponentiation i 1 n m i e i mod n is a very important but time consuming operation in many modern cryptosystems in this paper a fast modular multi exponentiation is proposed utilizing the binary like complex arithmetic method complement representation method and canonical signed digit recoding technique by performing complements and canonical signed digit recoding technique the hamming weight number of 1 s in the binary representation or number of non zero digits in the binary signed digit representations of the exponents can be reduced based on these techniques an algorithm with efficient modular multi exponentiation is proposed for modular multi exponentiation in average case the proposed algorithm can reduce the number of modular multiplications mms from 1 503k to 1 306k where k is the bit length of the exponent we can therefore efficiently speed up the overall performance of the modular multi exponentiation for cryptographic applications

a low complexity lut based squaring algorithm the computation of large modular multi exponentiation is a time consuming arithmetic operation used in cryptography the standard squaring algorithm is well known and the guajardo paar algorithm fixes the improper carry handling bug produced by the standard squaring algorithm but produces error indexing bug in this paper a novel squaring algorithm is proposed which stores base products in the look up table before the squaring computation and base size comparison method the proposed algorithm can not only evaluate squaring efficiently but also avoid bugs produced in other proposed algorithms the guajardo paar algorithm and the yang heih laih algorithm the performance of the proposed algorithm is 1 615 times faster than the standard squaring algorithm and much faster than other algorithms

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

the spatial operator in the incompressible navier stokes oseen and stokes equations abstract we investigate the spatial operator in the incompressible navier stokes oseen and stokes equations and show how to avoid singularities associated with null spaces by choosing specific boundary conditions the theoretical results are derived for a general form of energy stable boundary conditions and applied to a few commonly used ones the analysis is done on a system that simultaneously covers the nonlinear incompressible navier stokes the oseen and the stokes equations when the spectrum of the spatial operator is investigated we restrict the analysis to the oseen and stokes equations the continuous analysis carries over to the discrete setting by using the summation by parts framework

finite element approximation of the nonstationary navier stokes problem part ii stability of solutions and error estimates uniform in time in this paper assumptions about the stability of a solution are introduced in the numerical analysis of the nonstationary navier stokes problem for the purpose of extending local a priori error estimates and local a posteriori error estimates globally in time