a fourth order compact scheme for heat transfer problem in porous media in this paper we have extended the recently proposed fourth order compact scheme by pandit et al 2007 which was used earlier only for the convection diffusion equations without considering reaction and nonhomogeneous source terms and designed to compute flow in a two sided lid driven differentially heated square cavity filled with a fluid saturated porous medium the governing navier stokes n s equations in streamfunction vorticity form of brinkman extended darcy model including the energy transport equation are all solved as a coupled system of equations for the five field variables consisting of streamfunction vorticity two velocities and temperature moreover local entropy generation distributions are determined based on the obtained dimensionless velocity and temperature values the derivative source term present in vorticity equation has been treated as fourth order compact using pade scheme the details for the derivation of difference relations at boundaries to generate accurate and stable solutions are also given we have computed the results for three different cases depending on the direction of moving walls to assess the numerical accuracy of our proposed scheme one pertinent test problem with known exact solution is used the higher order compact scheme adopted in the present study yields consistent performance for variation of key parameters e g richardson number r i darcy number d a grashof number g r and fixed prandtl number p r 0 7 the present results are compared with numerical results available in the literature and excellent match is observed in all the cases establishing the efficiency and accuracy of the extended combined formulations of our fourth order compact scheme and pade schemes

minimal kernels of weakly complete spaces abstract let x be a weakly complete space i e x a complex space endowed with a c k smooth k 0 plurisubharmonic exhaustion function we give the notion of minimal kernel 1 1 x of x by the following property x 1 if no continuous plurisubharmonic exhaustion function is strictly plurisubharmonic near x the study of the geometric properties of the minimal kernels is the aim of present paper after stating that the minimal kernel 1 of a weakly complete space can be defined by a single plurisubharmonic exhaustion function called minimal using the characterization in terms of bremermann envelopes we prove the following crucial result if x is a weakly complete manifold and a minimal function for x the nonempty level sets c 1 1 c have the local maximum property in the last section we discuss the special case of weakly complete surfaces we prove that if dim c x 2 and c is a regular value of a minimal function then the nonempty level sets c 1 1 c are compact spaces foliated by holomorphic curves

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

discrete signal matching using coarse to fine wavelet basis functions in this paper we propose a matching algorithm to estimate accurate and dense displacements between two signals the displacements are characterized by a coarse to fine wavelet representation which is a linear combination of hierarchical basis functions developed by cai and wang siam numer anal 33 3 1996 937 the coarser scale basis function has larger support while the finer scale basis function has smaller support during the iterative minimization process the basis functions are utilized as large to small windows in selecting global to local regions for signal matching the estimated wavelet coefficients are then used to reconstruct the signal in a coarse to fine manner two sets of synthetic examples one with small displacement and the other with large displacements have been employed to illustrate the advantages of the wavelet based method this method has been applied to estimate the dense disparity between stereo images in several real examples and the results demonstrate its effectiveness

local maximum property and q plurisubharmonic functions in uniform algebras abstract there is proven a formula expressing higher order shilov boundaries of the tensor products of uniform algebras in terms of boundaries of the factor algebras main step cartesian product of k and l maximum sets is a k l 1 maximum set definition locally closed x cn is a k maximum set if polynomials have local maximum property on intersections of x with n k dimensional complex planes other properties and characterizations of k maximum sets are given e g x cn is a k maximum set iff each k plurisubharmonic function has local maximum property on x

adaptive mesh finite volume calculation of 2d lid cavity corner vortices abstract an anisotropic refinement criterion suitable for finite volume methods is presented and navier stokes solutions are reported for the lid driven cavity flow configuration at re 1000 with adaptive anisotropic meshes h refinement the a posteriori error estimation criterion is based on the assessment of the goodness of fit of the least squares regression used to perform the variables profile reconstruction and it is capable of detecting both large scale and small scale flow phenomena the criterion allowed to capture in detail the large scale flow structure and also the sequence of creeping flow small sharp corner s 1 eddies up to the fourth corner vortex in addition to the primary cavity vortex the smallest corner vortex detected is o 10 16 smaller in velocity magnitude compared with the cavity primary recirculation flow

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

moffatt eddies in the driven cavity a quantification study by an hoc approach abstract in this paper we establish moffatt likeness of the corner vortices in the lid driven square cavity for stokes flow and flow for moderate reynolds numbers in the pre asymptotic regime the flow is computed by using an efficient transient navier stokes n s solver on compact non uniform space grids the quantification of the corner vortices in succession as moffatt vortices follows from them following a fixed geometric ratio in sizes and intensities in the process we also provide more detailed benchmarking results for the corner vortices in the cavity flow the accuracy of the scale resolution of the vortices has been verified by a novel approach to grid independence analysis this approach utilizes the concept of adverse pressure gradients as a tool to validate that the separation zones in the neighborhood of the corners are consistent with the vortices obtained from our computed solution of the n s equations

a locally adaptive window for signal matching this article presents a signal matching algorithm that can select an appropriate window size adaptively so as to obtain both precise and stable estimation of correspondences matching two signals by calculating the sum of squared differences ssd over a certain window is a basic technique in computer vision given the signals and a window there are two factors that determine the difficulty of obtaining precise matching the first is the variation of the signal within the window which must be large enough relative to noise that the ssd values exhibit a clear and sharp minimum at the correct disparity the second factor is the variation of disparity within the window which must be small enough that signals of corresponding positions are duly compared these two factors present conflicting requirements to the size of the matching window since a larger window tends to increase the signal variation but at the same time tends to include points of different disparity a window size must be adaptively selected depending on local variations of signal and disparity in order to compute a most certain estimate of disparity at each point there has been little work on a systematic method for automatic window size selection the major difficulty is that while the signal variation is measurable from the input the disparity variation is not since disparities are what we wish to calculate we introduce here a statistical model of disparity variation within a window and employ it to establish a link between the window size and the uncertainty of the computed disparity this allows us to choose the window size that minimizes uncertainty in the disparity computed at each point this article presents a theory for the model and the resultant algorithm together with analytical and experimental results that demonstrate their effectiveness

weak solutions for the levi equation and envelope of holomorphy we consider the dirichlet problem for the levi equation in c2 and we prove an existence theorem of weak solutions i e in the sense of viscosity as an application we obtain the existence of the envelope of holomorphy for certain compact 2 manifolds

pseudoconvex classes of functions iii characterization of dual pseudoconvex classes on complex homogeneous spaces invariant classes of functions on complex homogeneous spaces with properties similar to those of the class of plurisubharmonic functions are studied the main tool is a regularization method for these classes and the main theorem characterizes dual classes of functions where duality is defined in terms of the local maximum property these results are crucial in proving a duality theorem for complex interpolation of normed spaces which is given elsewhere

adaptive multiresolution collocation methods for initial boundary value problems of nonlinear pdes we have designed a cubic spline wavelet like decomposition for the sobolev space h 0 2 i where i is a bounded interval based on a special point value vanishing property of the wavelet basis functions a fast discrete wavelet transform dwt is constructed this dwt will map discrete samples of a function to its wavelet expansion coefficients in at most 7n log n operations using this transform we propose a collocation method for the initial boundary value problem of nonlinear partial differential equations pdes then we test the efficiency of the dwt and apply the collocation method to solve linear and nonlinear pdes

resolution locale du bar partial avec regularite gevrey au bord d un domainer convexeavec regularite gevrey au bord d un domainer convexe

pseudoconvex domains with smooth boundary in projective spaces given a pseudoconvex domain u with mathscr c 1 boundary in mathbb p n n geqslant 3 we show that if h 2n 2 mathrm dr u ne 0 then there is a strictly psh function in a neighborhood of partial u we also solve the overline partial equation in x mathbb p n setminus u for data in mathscr c infty 0 1 x we discuss levi flat domains in surfaces if z is a real algebraic hypersurface in mathbb p 2 resp a real analytic hypersurface with a point of strict pseudoconvexity then there is a strictly psh function in a neighborhood of z

complex interpolation of normed and quasinormed spaces in several dimensions i a variety of complex interpolation methods for families of normed or quasi normed spaces parametrized by points of domains in complex homo geneous spaces parametrized by points of domains in complex homogeneous spaces is developed results on existence continuity uniqueness reiteration and duality for interpolation are proved as well as on interpolation of oper ators a minimum principle for plurisubharmonic functions is obtained and used as a tool for the duality theorem

a divergence free condition compensated method for incompressible navier stokes equations the present study aims to develop a new formulation to effectively calculate the incompressible navier stokes solutions in non staggered grids the distinguished feature of the proposed method which avoids directly solving the divergence free equation is to add a rigorously derived source term to the momentum equation to ensure satisfaction of the fluid incompressibility for the sake of numerical accuracy dispersion relation preserving upwind scheme developed within the two dimensional context was employed to approximate the convection terms the validity of the proposed mass preserving navier stokes method is justified by solving two benchmark problems at high reynolds and rayleigh numbers based on the simulated navier stokes solutions the proposed formulation is shown to outperform the conventional segregated method in terms of the reduction of cpu time 2007 elsevier b v all rights reserved

a robust higher order compact scheme for solving general second order partial differential equation with derivative source terms on nonuniform curvilinear meshes abstract a fourth order compact finite difference scheme is proposed for solving general second order steady partial differential equation pde in two dimension 2d on geometries having nonuniform curvilinear grids in this work the main efforts are focused not only on nonorthogonal curvilinear grids but also on the presence of mixed derivative term and nonhomogeneous derivative source terms in the governing equation this is in turn suitable for solving fluid flow and heat transfer problems governed by navier stokes n s equations on geometries having nonuniform and nonorthogonal curvilinear grids the newly proposed scheme has been applied to solve general second order partial differential equation having analytical solution and some pertinent fluid flow problems namely viscous flows in a lid driven cavity such as trapezoidal cavity using nonorthogonal grid square cavity using distorted grid complicated enclosures using curvilinear grid and mixed convection flow in a bottom wavy wall cavity it is seen to efficiently capture steady state solutions of the n s equations with dirichlet as well as neumann boundary conditions detailed comparison data produced by the proposed scheme for all the test cases are provided and compared with existing analytical as well as established numerical results available in the literature excellent comparison is obtained in all the cases

domains with a continuous exhaustion in weakly complete surfaces in previous works tomassini and the authors studied and classified complex surfaces admitting a real analytic plurisubharmonic exhaustion function let x be such a surface and d subseteq x a domain admitting a continuous plurisubharmonic exhaustion function what can be said about the geometry of d if the exhaustion of d is assumed to be smooth the second author already answered this question however the continuous case is more difficult and requires different methods in the present paper we address such question by studying the local maximum sets contained in d and their interplay with the complex geometric structure of x we conclude that if d is not a modification of a stein space then it shares the same geometric features of x

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

an element by element bicgstab iterative method for three dimensional steady navier stokes equations construction of a stabilized galerkin upwind finite element model for steady and incompressible navier stokes equations in three dimensions is the main theme of this study in the time independent context the weighted residuals statement is kept biased in favor of the upstream flow direction by adding an artificial damping term of physical plausibility to the galerkin framework this upwind approach has significant advantage of seeking solutions free from cross stream diffusion error finite element solutions have been found by mixed formulation implemented in quadratic cubic elements which are characterized as possessing the so called lbb ladyzhenskaya babuska brezzi condition an element by element bicgstab solution solver is intended to alleviate difficulties regarding the asymmetry and indefiniteness arising from the use of a mixed formulation for incompressible fluid flows the developed three dimensional finite element code is first rectified by solving a problem amenable to analytic solution a well known lid driven cavity flow problem in a cubical cavity is also studied

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

the mini mixed finite element for the stokes problem an experimental investigation abstract o h 3 2 superconvergence in pressure and velocity has been experimentally investigated for the two dimensional stokes problem discretized with the mini mixed finite element even though the classic mixed finite element theory for the mini element guarantees linear convergence for the total error recent theoretical results indicate that superconvergence of order o h 3 2 in pressure and of the linear part of the computed velocity to the piecewise linear nodal interpolation of the exact velocity is in fact possible with structured three directional triangular meshes the numerical experiments presented here suggest a more general validity of o h 3 2 superconvergence possibly to automatically generated and unstructured triangulations in addition the approximating properties of the complete computed velocity have been compared with the approximating properties of the piecewise linear part of the computed velocity finding that the former is generally closer to the exact velocity whereas the latter conserves mass better

image registration using wavelet based motion model an image registration algorithm is developed to estimate dense motion vectors between two images using the coarse to fine wavelet based motion model this motion model is described by a linear combination of hierarchical basis functions proposed by cai and wang siam numer anal 33 3 937 970 1996 the coarser scale basis function has larger support while the finer scale basis function has smaller support with these variable supports in full resolution the basis functions serve as large to small windows so that the global and local information can be incorporated concurrently for image matching especially for recovering motion vectors containing large displacements to evaluate the accuracy of the wavelet based method two sets of test images were experimented using both the wavelet based method and a leading pyramid spline based method by szeliski et al international journal of computer vision 22 3 199 218 1996 one set of test images taken from barron et al international journal of computer vision 12 43 77 1994 contains small displacements the other set exhibits low texture or spatial aliasing after image blurring and contains large displacements the experimental results showed that our wavelet based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation

a rational high order compact difference method for the steady state stream functionvorticity formulation of the navierstokes equations a rational high order compact rhoc finite difference fd method on the nine point stencil is proposed for solving the steady state two dimensional navierstokes equations in the stream functionvorticity form the resulting system of algebra equations can be solved by using the point successive over or under relaxation sor iteration numerical experiments involving two linear and two nonlinear problems with their analytical solutions and two flow problems including the lid driven cavity and backward facing step flows are carried out to validate the performance of the newly proposed method numerical solutions of the driven cavity problem with different grid mesh sizes maximum being 513513 for reynolds numbers ranging from 0 to 17500 are obtained and compared with some of the accurate results available in the literature

intensity and gradient based stereo matching using hierarchical gaussian basis functions we propose a stereo correspondence method by minimizing intensity and gradient errors simultaneously in contrast to conventional use of image gradients the gradients are applied in the deformed image space although a uniform smoothness constraint is imposed it is applied only to nonfeature regions to avoid local minima in the function minimization we propose to parameterize the disparity function by hierarchical gaussians both the uniqueness and the ordering constraints can be easily imposed in our minimization framework besides we propose a method to estimate the disparity map and the camera response difference parameters simultaneously experiments with various real stereo images show robust performances of our algorithm

on defining functions and cores for unbounded domains i we show that every strictly pseudoconvex domain omega with smooth boundary in a complex manifold mathcal m admits a global defining function i e a smooth plurisubharmonic function varphi u rightarrow mathbb r defined on an open neighbourhood u subset mathcal m of overline omega such that omega varphi 0 d varphi ne 0 on b omega and varphi is strictly plurisubharmonic near b omega we then introduce the notion of the core mathfrak c omega of an arbitrary domain omega subset mathcal m as the set of all points where every smooth and bounded from above plurisubharmonic function on omega fails to be strictly plurisubharmonic if omega is not relatively compact in mathcal m then in general mathfrak c omega is nonempty even in the case when mathcal m is stein it is shown that every strictly pseudoconvex domain omega subset mathcal m with smooth boundary admits a global defining function that is strictly plurisubharmonic precisely in the complement of mathfrak c omega we then investigate properties of the core in particular we prove that the core is always 1 pseudoconcave

spline based image registration the problem of image registration subsumes a number of problems and techniques in multiframe image analysis including the computation of optic flow general pixel based motion stereo correspondence structure from motion and feature tracking we present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems in particular we show how to compute local flow global parametric flow rigid flow resulting from camera egomotion and multiframe versions of the above problems using a spline based description of the flow removes the need for overlapping correlation windows and produces an explicit measure of the correlation between adjacent flow estimates we demonstrate our algorithm on multiframe image registration and the recovery of 3d projective scene geometry we also provide results on a number of standard motion sequences

a sequential regularization method for time dependent incompressible navier stokes equations the objective of the paper is to present a method called the sequential regularization method srm for the nonstationary incompressible navier stokes equations from the viewpoint of regularization of differential algebraic equations daes and to provide a way to apply a dae method to partial differential algebraic equations pdaes the srm is a functional iterative procedure it is proved that its convergence rate is o epsilon m where m is the number of the srm iterations and epsilon is the regularization parameter the discretization and implementation issues of the method are considered in particular a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes it appears that the srm formulation is new in the navier stokes context unlike other regularizations or pseudocompressibility methods in the navier stokes context the regularization parameter epsilon in the srm need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any epsilon hence the stability condition is independent of epsilon even for explicit time discretization numerical experiments are given to verify our theoretical results

complex interpolation of normed and quasinormed spaces in several dimensions ii properties of harmonic interpolation this paper is a continuation of the study of harmonic interpolation families of normed or quasinormed spaces parametrized by points of a domain in ck it is shown among other things that each of the following properties holds for all the intermediate quasinormed spaces if it holds for all given boundary spaces 1 being a normed space 2 being a hilbert space 3 satisfying the triangle inequality by the rth power of the quasinorm 4 being uniformly convex and 5 being uniformly smooth as a principal tool the notion of a harmonic set valued function a generalization of analytic multifunction is introduced and studied

an efficient transient navier stokes solver on compact nonuniform space grids in this paper we propose an implicit higher order compact hoc finite difference scheme for solving the two dimensional 2d unsteady navier stokes n s equations on nonuniform space grids this temporally second order accurate scheme which requires no transformation from the physical to the computational plane is at least third order accurate in space which has been demonstrated with numerical experiments it efficiently captures both transient and steady state solutions of the n s equations with dirichlet as well as neumann boundary conditions the proposed scheme is likely to be very useful for the computation of transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variation numerical results are presented and compared with analytical as well as established numerical data excellent comparison is obtained in all the cases

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

a transformation free ψ v formulation of the navier stokes equations on compact nonuniform grids abstract in this work we have developed a second order accurate compact finite difference scheme for the biharmonic form of the steady state navier stokes n s equations on nonuniform cartesian grids without transformation contrary to the schemes developed on rectangular cartesian grids for n s equations that could handle only rectangular boundaries the proposed scheme can easily accommodate bluff bodies with curved boundary the scheme is applied to one problem having analytical solution and three fluid flow problems having different complexities while one of them viz the lid driven cavity depict internal flows the flow past a circular cylinder and a flat plate immersed in uniform flow represents external flows the scheme is shown to handle both dirichlet and neumann boundary conditions with equal ease the efficiency of the scheme is demonstrated not only by its ability to capture smaller scales up to post quaternary level of vortices for the flow in lid driven cavity but also its robustness in handling non rectangular boundaries of immersed bodies while the scheme has handled the boundary of an immersed body not necessarily aligned to the grid lines for one of the problems for another it has tackled a curved boundary on cartesian grid without the need of roping in any immersed interface in the process its efficiency is further asserted by the proximity of the computed solutions to available experimental results

boundary layer separation and adverse pressure gradient for 2 d viscous incompressible flow we study the detailed process of bifurcation in the flow s topological structure for a two dimensional 2 d incompressible flow subject to no slip boundary conditions and its connection with boundary layer separation the boundary layer separation theory of m ghil t ma and s wang based on the structural bifurcation concept is translated into vorticity form the vorticity formulation of the theory shows that structural bifurcation occurs whenever a degenerate singular point for the vorticity appears on the boundary this singular point is characterized by nonzero tangential second order derivative and nonzero time derivative of the vorticity furthermore we prove the presence of an adverse pressure gradient at the critical point due to reversal in the direction of the pressure force with respect to the basic shear flow at this point a numerical example of 2 d driven cavity flow governed by the navier stokes equations is presented boundary layer separation occurs the bifurcation criterion is satisfied and an adverse pressure gradient is shown to be present

fully compact higher order computation of steady state natural convection in a square cavity the flow in a thermally driven square cavity with adiabatic top and bottom walls and differentially heated vertical walls for a wide range of rayleigh numbers 10 3 or ra or 10 7 has been computed with a fourth order accurate higher order compact scheme which was used earlier only for the stream function vorticity psi omega form of the two dimensional steady state navier stokes equations the boundary conditions used are also compact and of identical accuracy in particular a compact fourth order accurate neumann boundary condition has been developed for temperature at the adiabatic walls the treatment of the derivative source term is also compact and has been done in such a way as to give fourth order accuracy and easy assimilation with the solution procedure as the discretization for the psi omega formulation boundary conditions and source term treatment are all fourth order accurate highly accurate solutions are obtained on relatively coarser grids unlike other compact solution procedure in literature for this physical configuration the present method is fully compact and fully higher order accurate also use of conjugate gradient and hybrid biconjugate gradient stabilized algorithms to solve the symmetric and nonsymmetric algebraic systems at every outer iteration ensures good convergence behavior of the method even at higher rayleigh numbers

on convex hulls and pseudoconvex domains generated by q plurisubharmonic functions part iii we study the properties of hulls of compact sets in mathbb c n that are generated by certain subfamilies of q plurisubharmonic functions we consider in particular those functions that are plurisubharmonic on the level sets of holomorphic mappings defined from mathbb c n into mathbb c q we also compare the above mentioned hulls against the generalised polynomially and rationally convex hulls already defined in the literature our main result yields that the hulls defined by q plurisubharmonic functions or q pseudoconvex sets are all q maximum so that their complement is relatively n text q text 2 pseudoconvex

a transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular in this paper we propose an implicit high order compact hoc finite difference scheme for solving the two dimensional 2d unsteady navier stokes n s equations on irregular geometries on orthogonal grids our scheme is second order accurate in time and fourth order accurate in space it is used to solve three pertinent fluid flow problems namely the flow decayed by viscosity the lid driven square cavity and the flow in a constricted channel it is seen to efficiently capture both transient and steady state solutions of the n s equations with dirichlet as well as neumann boundary conditions apart from including the good features of hoc schemes our formulation has the added advantage of capturing transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations detailed comparison data produced by the scheme for all the three test cases are provided and compared with analytical as well as established numerical results excellent comparison is obtained in all the cases