an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part i theory and implementation a robust artificial compressibility scheme has been developed for modelling laminar steady state and transient incompressible flows over a wide range of reynolds and rayleigh numbers artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations a locally generalized preconditioner is introduced designed to be robust and offer good convergence rates free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme memory efficiency is achieved through a multistage pseudo time explicit time marching solution procedure a node centred dual cell edge based finite volume discretization technique suitable for unstructured grids is used due to its computational efficiency and high resolution spatial accuracy in the interest of computational efficiency and ease of implementation stabilization is achieved via a scalar valued artificial dissipation scheme temporal accuracy is facilitated by employing a second order accurate dual time stepping method in this part of the paper the theory and implementation details are discussed in part 11 the scheme will be applied to a number of example problems to solve flows over a wide range of reynolds and rayleigh numbers

explicit and semi implicit cbs procedures for incompressible viscous flows this paper presents a numerical comparison of two different numerical procedures based on the characteristic based split cbs algorithm for the solution of incompressible flows the first procedure is based on the original semi implicit version of the cbs introduced in the early days of the scheme development the second was proposed more recently in order to have a fully explicit version of the scheme and is based on the introduction of an artificial compressibility type of formulation the interest in fully explicit schemes has increased because of the easy and efficient parallelization the main differences between the two versions of the schemes are highlighted in this work and a numerical comparison is presented on the basis of several benchmark solutions both steady and unsteady flows are considered with the explicit version of the scheme a dual time stepping procedure is needed to recover unsteady solutions copyright 2006 john wiley sons ltd

rank tests and a one sample logrank test for comparing observed survival data to a standard population for cox s proportional hazards model test procedures are described for the comparison of randomly right censored observed and expected standard population survival data it is observed that the class of linear rank tests proposed by prentice 1978 biometrika 65 167 179 may be employed to test regression hypotheses in this one sample setting in order to compare globally the observed and expected survival data the one sample limit of mantel s logrank test is formally derived the statistic derived is identical to one proposed from a diflerent viewpoint by breslow 1975 intemational statistical review 43 45 58 throughout it is assumed that the standard population survival function is a continuous function of time and that the survival or censoring time for each study sample individual is exact and is not grouped into categories

sample size calculation for the one sample log rank test an improved method of sample size calculation for the one sample log rank test is provided the one sample log rank test may be the method of choice if the survival curve of a single treatment group is to be compared with that of a historic control such settings arise for example in clinical phase ii trials if the response to a new treatment is measured by a survival endpoint present sample size formulas for the one sample log rank test are based on the number of events to be observed that is in order to achieve approximately a desired power for allocated significance level and effect the trial is stopped as soon as a certain critical number of events are reached we propose a new stopping criterion to be followed both approaches are shown to be asymptotically equivalent for small sample size though a simulation study indicates that the new criterion might be preferred when planning a corresponding trial in our simulations the trial is usually underpowered and the aspired significance level is not exploited if the traditional stopping criterion based on the number of events is used whereas a trial based on the new stopping criterion maintains power with the type i error rate still controlled

an implicit explicit solution method for electro osmotic flow through three dimensional micro channels this paper presents a comprehensive finite element modelling approach to electro osmotic flows on unstructured meshes the non linear equation governing the electric potential is solved using an iterative algorithm the employed algorithm is based on a preconditioned gmres scheme the linear laplace equation governing the external electric potential is solved using a standard pre conditioned conjugate gradient solver the coupled fluid dynamics equations are solved using a fractional step based fully explicit artificial compressibility scheme this combination of an implicit approach to the electric potential equations and an explicit discretization to the navier stokes equations is one of the best ways of solving the coupled equations in a memory efficient manner the local time stepping approach used in the solution of the fluid flow equations accelerates the solution to a steady state faster than by using a global time stepping approach the fully explicit form and the fractional stages of the fluid dynamics equations make the system memory efficient and free of pressure instability in addition to these advantages the proposed method is suitable for use on both structured and unstructured meshes with a highly non uniform distribution of element sizes the accuracy of the proposed procedure is demonstrated by solving a basic micro channel flow problem and comparing the results against an analytical solution the comparisons show excellent agreement between the numerical and analytical data in addition to the benchmark solution we have also presented results for flow through a fully three dimensional rectangular channel to further demonstrate the application of the presented method copyright 2007 john wiley sons ltd

immersed smoothed finite element method for two dimensional fluid structure interaction problems summary a novel method called immersed smoothed fem using three node triangular element is proposed for two dimensional fluid structure interaction fsi problems with largely deformable nonlinear solids placed within incompressible viscous fluid the fluid flows are solved using the semi implicit characteristic based split method smoothed fems are employed to calculate the transient responses of solids based on explicit time integration the fictitious fluid with two assumptions is introduced to achieve the continuous form of the fsi conditions the discrete formulations to calculate the fsi forces are obtained in terms of the characteristic based split scheme and the algorithm based on a set of fictitious fluid mesh is proposed for evaluating the fsi force exerted on the solid the accuracy stability and convergence properties of immersed smoothed fem are verified by numerical examples investigations on the mesh size ratio indicate that the stability is fairly independent of the wide range of the mesh size ratio no additional volume correction is required to satisfy the incompressible constraints copyright 2012 john wiley sons ltd

the cyclicity of the elliptic segment loops of the reversible quadratic hamiltonian systems under quadratic perturbations abstract denote by q h and q r the hamiltonian class and reversible class of quadratic integrable systems there are several topological types for systems belong to q h q r one of them is the case that the corresponding system has two heteroclinic loops sharing one saddle connection which is a line segment and the other part of the loops is an ellipse in this paper we prove that the maximal number of limit cycles which bifurcate from the loops with respect to quadratic perturbations in a conic neighborhood of the direction transversal to reversible systems called in reversible direction is two we also give the corresponding bifurcation diagram

a dual time method for two dimensional unsteady incompressible flow calculations a method for computing unsteady incompressible viscous flows on moving or deforming meshes is described it uses a well established time marching finite volume flow solver developed for steady compressible flows past rigid bodies time marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic such methods can be extended to steady incompressible flows using an artificial compressibility scheme a time accurate scheme for unsteady incompressible flows is achieved by using an implicit real time discretization and a dual time approach which uses a technique similar to the artificial compressibility scheme results are presented for test cases on both fixed and deforming meshes experimental numerical and theoretical data have been included for comparison where available and reasonable agreement has been achieved 1998 john wiley sons ltd

adaptive designs for the one sample log rank test summary traditional designs in phase iia cancer trials are single arm designs with a binary outcome for example tumor response in some settings however a time to event endpoint might appear more appropriate particularly in the presence of loss to follow up then the one sample log rank test might be the method of choice it allows to compare the survival curve of the patients under treatment to a prespecified reference survival curve the reference curve usually represents the expected survival under standard of the care in this work convergence of the one sample log rank statistic to brownian motion is proven using rebolledo s martingale central limit theorem while accounting for staggered entry times of the patients on this basis a confirmatory adaptive one sample log rank test is proposed where provision is made for data dependent sample size reassessment the focus is to apply the inverse normal method this is done in two different directions the first strategy exploits the independent increments property of the one sample log rank statistic the second strategy is based on the patient wise separation principle it is shown by simulation that the proposed adaptive test might help to rescue an underpowered trial and at the same time lowers the average sample number asn under the null hypothesis as compared to a single stage fixed sample design

the infinitesimal 16th hilbert problem in the quadratic case let h x y be a real cubic polynomial with four distinct critical values in a complex domain and let x h h y frac partial partial x h x frac partial partial y be the corresponding hamiltonian vector field we show that there is a neighborhood of x h in the space of all quadratic plane vector fields such that any x has at most two limit cycles

boundary cloud method a combined scattered point boundary integral approach for boundary only analysis abstract a boundary cloud method bcm for boundary only analysis of partial differential equations is presented in this paper for solving potential equations in two dimensions 2 d the bcm combines a weighted least squares approach for construction of interpolation functions with a boundary integral formulation for the governing equations given a set of scattered points on the surface of an arbitrary object hermite type interpolation functions are constructed by developing a weighted least squares approach we also introduce truncated hermite type interpolation functions the boundary integrals are evaluated by using a cell structure we propose various schemes for evaluating the singular nearly singular and nonsingular integrals we also propose a true meshless approach for boundary only analysis of potential equations numerical results comparing the classical boundary element method and the bcm are presented for several 2 d potential problems

an efficient artificial compressibility ac scheme based on the characteristic based split cbs method for incompressible flows in this paper an artificial compressibility scheme using the finite element method is introduced 2002 zienkiewicz silver medal and prize winning paper the multi purpose cbs scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems it is important to note that the scheme developed here includes split and velocity correction the proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes unlike many other artificial compressibility schemes the proposed one works on a variety of grids and gives results for a wide range of reynold s numbers the paper presents some bench mark two and three dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme copyright 2003 john wiley sons ltd

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

a matrix free implicit incompressible fractional step algorithm for fluid structure interaction applications in this paper we detail a fast fully coupled partitioned fluid structure interaction fsi scheme for the incompressible fluid new fractional step algorithms are proposed which make possible the fully implicit but matrix free parallel solution of the entire coupled fluid solid system these algorithms include artificial compressibility pressure poisson solution in conjunction with upwind velocity stabilisation as well as simplified pressure stabilisation for improved computational efficiency a dual timestepping approach is proposed where a jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix free preconditioned gmres methodology this enables efficient sub iteration level coupling between the fluid and solid domains parallelisation is effected for distributed memory systems the accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature the new schemes are shown to be efficient and robust with the developed preconditioned gmres solver furnishing speed ups ranging between 50 and 80

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

petrov galerkin solutions of the incompressible navier stokes equations in primitive variables with adaptive remeshing the solution of the incompressible navier stokes equations in primitive variables is addressed in this paper a petrov galerkin formulation which automatically introduces streamline upwinding and allows equal order interpolation for all flow variables is presented the solution algorithm is segregated involving a series of updatings of the velocity and pressure fields error estimation and adaptive remeshing strategies for both steady and unsteady problems are demonstrated in some representative numerical examples

perturbation from an asymmetric cubic hamiltonian this paper concerns with the number of limit cycles from an asymmetric hamiltonian of degree three under cubic perturbation eleven limit cycles are found and three different distributions are given by using the methods of bifurcation theory and qualitative analysis two of which are new

numerical comparison of cbs and sgs as stabilization techniques for the incompressible navier stokes equations in this work we present numerical comparisons of some stabilization methods for the incompressible navier stokes the first is the characteristic based split cbs it combines the characteristic galerkin method to deal with convection dominated flows with a classical splitting technique which in some cases allows us to use equal velocity pressure interpolations the other two approaches are particular cases of the subgrid scale sgs method the first obtained after an algebraic approximation of the subgrid scales is very similar to the popular galerkin least squares gls method whereas in the second the subscales are assumed to be orthogonal to the finite element space it is shown that all these formulations display similar stabilization mechanisms provided the stabilization parameter of the sgs methods is identified with the time step of the cbs approach this paper provides the numerical experiments for the comparison of formulations made by codina and zienkiewicz in a previous article copyright 2006 john wiley sons ltd

the distribution of limit cycles in quadratic systems with four finite singularities abstract in this paper we prove that if a quadratic system with four finite singularities contains a weak singularity then there exists at most one limit cycle not surrounding this singularity we also show that if the limit cycles of quadratic systems with four finite singularities are distributed over two nests then each nest contains exactly one limit cycle

discrete sequential boundaries for clinical trials summary pocock 1977 o brien fleming 1979 and slud wei 1982 have proposed different methods to construct discrete sequential boundaries for clinical trials these methods require that the total number of decision times be specified in advance in the present paper we propose a more flexible way to construct discrete sequential boundaries the method is based on the choice of a function a t which characterizes the rate at which the error level ac is spent the boundary at a decision time is determined by a t and by past and current decision times but does not depend on the future decision times or the total number of decision times

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part ii application in part i of this paper a preconditioned artificial compressibility scheme was developed for modelling laminar steady state and transient incompressible flows for a wide range of reynolds and rayleigh numbers in this part several examples of laminar incompressible problems are solved and discussed the influence of various ac parameters on robustness and convergence rates are assessed for a complex category of problems it is shown that the scheme developed in part i is an accurate robust and easy to use method for solving incompressible laminar flow problems over a wide range of flow regimes copyright 2002 john wiley sons ltd

unsteady two dimensional flows in complex geometries comparative bifurcation studies with global eigenfunction expansions we present a bifurcation study of the incompressible navier stokes equations in a model complex geometry a spatially periodic array of cylinders in a channel the dynamics of the flow include a hopf bifurcation from steady to oscillatory flow at an approximate reynolds number r of 350 and the appearance of a second frequency at approximately r simeq 890 the multiple frequency dynamics include a substantial increase in spatial and temporal scales with reynolds number as compared with the simple limit cycle oscillation present close to r 350 numerical bifurcation studies of the dynamics are performed using three forms of global eigenfunction expansions the first basis set is derived through principal factor analysis karhunen loeve expansion of snapshots from accurate direct spectral element numerical solutions of the navier stokes equations the second set is obtained from the eigenfunctions of the stokes operator for this geometry finally eigenfunctions are derived from a singular stokes operator i e the stokes operator modified to include a variable coefficient which vanishes at the domain boundaries truncated systems of sim 100 odes are obtained through projection of the navier stokes equations onto the basis sets and a comparative study of the resulting dynamical models is performed

error estimation for reduced order models of dynamical systems the use of reduced order models to describe a dynamical system is pervasive in science and engineering often these models are used without an estimate of their error or range of validity in this paper we consider dynamical systems and reduced models built using proper orthogonal decomposition we show how to compute estimates and bounds for these errors by a combination of small sample statistical condition estimation and error estimation using the adjoint method most important the proposed approach allows the assessment of regions of validity for reduced models i e ranges of perturbations in the original system over which the reduced model is still appropriate numerical examples validate our approach the error norm estimates approximate well the forward error while the derived bounds are within an order of magnitude

finite cloud method a true meshless technique based on a fixed reproducing kernel approximation we introduce fixed moving and multiple fixed kernel techniques for the construction of interpolation functions over a scattered set of points we show that for a particular choice of nodal volumes the fixed moving and multiple fixed kernel approaches are identical to the fixed moving and multiple fixed least squares approaches a finite cloud method which combines collocation with a fixed kernel technique for the construction of interpolation functions is presented as a true meshless technique for the numerical solution of partial differential equations numerical results are presented for several one and two dimensional problems including examples from elasticity heat conduction thermoelasticity stokes flow and piezoelectricity copyright 2001 john wiley sons ltd

computation of natural convection in two dimensional cavities with chebyshev polynomials abstract a semi implicit spectral method for the computation of buoyancy induced two dimensional flow of a viscous incompressible fluid is presented the incompressible navier stokes equations expressed in terms of the primitive variables velocity and pressure and an additional equation for the temperature are considered all the variables are expanded in double truncated series of chebyshev polynomials the pressure distribution at the boundary of the computational domain is determined by means of an influence matrix technique in order to satisfy the incompressibility condition everywhere in the field the algorithm is applied to the classical problem of natural convection of a boussinesq fluid within a differentially heated vertical square cavity results show that for a prandtl number of 0 71 corresponding to air and up to rayleigh numbers of 106 very accurate solutions are obtained with a spatial resolution of 33 polynomials in each direction new interesting phenomena are shown for higher values of the rayleigh number

transient analysis of electro osmotic transport by a reduced order modelling approach transient behaviour of electro osmotic transport in typical electrokinetic channels is studied in this paper the time needed for the electro osmotic flow to reach steady state exhibits multiple time scales depending on whether the flow is governed by either a viscous force electrokinetic force or by a combination of both when an intersection is present in the electrokinetic channel such as in a cross or a t channel the flow in the main channel and in the intersection gets to steady state at different times a weighted karhunen loeve kl decomposition method is proposed in this paper to generate the global basis function for reduced order simulation the key idea in a weighted kl approach is that instead of minimizing a least squares measure of error between the linear subspace spanned by the basis functions and the observation space we minimize the weighted error between the two spaces the global basis functions in a weighted kl approach can be generated by computing the singular value decomposition svd of the matrix containing the weighted snapshots we show that the weighted kl decomposition based reduced order model is computationally more efficient and can capture the multiple time scales encountered in electro osmotic transport much more effectively compared to the classical kl decomposition based reduced order model copyright 2003 john wiley sons ltd

preconditioned methods for solving the incompressible low speed compressible equations abstract acceleration methods are presented for solving the steady state incompressible equations these systems are preconditioned by introducing artificial time derivatives which allow for a faster convergence to the steady state we also consider the compressible equations in conservation form with slow flow two arbitrary functions and are introduced in the general preconditioning an analysis of this system is presented and an optimal value for is determined given a constant it is further sown that the resultant incompressible equations form a symmetric hyperbolic system and so are well posed several generalizations to the compressible equations are presented which extend previous results

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

numerical solution of the incompressible navier stokes equations with coriolis forces based on the discretization of the total time derivative in this paper we present a numerical formulation to solve the incompressible navier stokes equations written in a rotating frame of reference the method is based on a finite difference discretization in time and a finite element discretization in space when the viscosity is very small numerical oscillations may appear due both to the high reynolds number and to the presence of the coriolis forces to overcome these oscillations a special discretization in time is proposed the idea is to discretize the total time derivative in an inertial basis rather than only the partial time derivative in the rotating reference system after this is done a further high order approximation is introduced leading to a problem posed in the rotating frame of reference and in spatial coordinates in contrast with the straightforward discretization of the original equations some additional terms appear that enhance the stability of the numerical scheme in the absence of coriolis forces the method is a generalization of the characteristic galerkin technique for convection dominated flows

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

comparison of pressure based and artificial compressibility methods for solving 3d steady incompressible viscous flows pressure based and artificial compressibility methods for calculating three dimensional steady incompressible viscous flows are compared in this work each method is applied to the prediction of three dimensional laminar flows in strongly curved ducts of square and circular cross sections numerical predictions from each method are compared with available experimental data and previously reported predictions using a multigrid numerical method the accuracy grid independence convergence behavior and computational efficiency of each method are critically examined hence some of the merits and demerits of each method are revealed in this study

group sequential designs for monitoring survival probabilities in the present paper we derive the asymptotic joint distribution of the nelson aalen estimators for the cumulative hazard function or the kaplan meier estimators for the survival function calculated at different possibly random calendar time points of a survival study this result is used to develop group sequential designs for clinical trials in which patients are enrolled over an extended period and the survival probability at a given failure time point is the parameter of primary interest the proposed designs allow monitoring the survival probability or probabilities at interim looks so that the study can be terminated when there is sufficient evidence for a positive or negative result a detailed illustration is provided with a problem from the national wilms tumor study group which motivated this research

preconditioning applied to variable and constant density flows a time derivative preconditioning of the navier stokes equations suitable for both variable and constant density fluids is developed the ideas of low mach number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density based time marching schemes for solving flows of incompressible and variable density fluids at all speeds the preconditioning is coupled with a dual time stepping scheme implemented within an explicit multistage algorithm for solving time accurate flows the resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured solution adaptive mesh topologies this method is shown to provide accurate steady state solutions for transonic and low speed flow of variable density fluids the time accurate solution of unsteady incompressible flow is also demonstrated