a global meshless collocation particular solution method for solving the two dimensional navier stokes system of equations the two dimensional navier stokes system of equations for incompressible fluids is solved by the method of approximate particular solutions maps in its global formulation the fluid velocity and pressure fields are approximated by a linear superposition of particular solutions of a stokes non homogeneous system of equations with multiquadric mq radial basis function as the source term the nonlinear convective terms of the momentum equations are linearly approximated by using a guess value of the velocity field and the resulting linear system of equations is solved by a simple direct iterative scheme picard iteration with the velocity guess given by the solution at the previous iteration although the continuity equation is not explicitly imposed in the resulting formulation the scheme is mass conservative because the particular solutions exactly satisfy the mass conservation equation the proposed numerical scheme is validated by comparison of the obtained numerical results with the corresponding analytical solution of the kovasznay flow problem at different reynolds numbers re from this analysis it is observed that the maps results are stable and accurate for a wide range of shape parameter values in addition lid driven cavity flow problems in rectangular and triangular domains up to re 3200 and re 1000 respectively and the backward facing step at re 800 are solved and the results obtained are compared with corresponding benchmark numerical solutions showing excellent agreement

mdl denoising the so called denoising problem relative to normal models for noise is formalized such that noise is defined as the incompressible part in the data while the compressible part defines the meaningful information bearing signal such a decomposition is effected by minimization of the ideal code length called for by the minimum description length mdl principle and obtained by an application of the normalized maximum likelihood technique to the primary parameters their range and their number for any orthonormal regression matrix such as defined by wavelet transforms the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix

a numerical method for the incompressible navier stokes equations in three dimensional cylindrical geometry abstract we describe a numerical method for solving the steady three dimensional incompressible navier stokes equations in cylindrical geometry also we present results of computations in which this method is used to determine the flow in fluid filled cylinders undergoing spinning and coning motion second order accurate central finite difference formulas are used to approximate derivatives in the radial and axial directions and a fourier method is used to approximate the angular derivatives nonuniform grids are used to improve the resolution of the velocity and pressure near the cylinder walls the system of difference equations is solved using an iterative method based on successive over relaxation the method has been found to be very efficient in terms of both computer time and storage results of the numerical method applied to the flow in spinning and coning cylinders are presented for several cases for which experimental data are available in addition perturbation methods are used to study the data at small coning speeds and small coning angles numerical results of this no coning limit are compared with both the numerical data and experimental data at low coning conditions

stabilized finite element schemes with lbb stable elements for incompressible flows we study stabilized fe approximations of supg type to the incompressible navier stokes problem revisiting the analysis for the linearized model we show that for conforming lbb stable elements the design of the stabilization parameters for many practical flows differs from that commonly suggested in literature and initially designed for the case of equal order approximation then we analyze a reduced supg scheme often used in practice for lbb stable elements to provide the reduced scheme with appropriate stability estimates we introduce a modified lbb condition which is proved for a family of fe approximations the analysis is given for the linearized equations numerical experiments for some linear and nonlinear benchmark problems support the theoretical results

an edge based method for the incompressible navier stokes equations on polygonal meshes abstract a pressure based method is presented for discretizing the unsteady incompressible navier stokes equations using hybrid unstructured meshes the edge based data structure and assembly procedure adopted lead naturally to a strictly conservative discretization which is valid for meshes composed of n sided polygons particular attention is given to the construction of a pressure velocity coupling procedure which is supported by edge data resulting in a relatively simple numerical method that is consistent with the boundary and initial conditions required by the incompressible navier stokes equations edge formulas are presented for assembling the momentum equations which are based on an upwind biased linear reconstruction of the velocity field similar formulas are presented for assembling the pressure equation the method is demonstrated to be second order accurate in space and time for two navier stokes problems admitting an exact solution results for several other well known problems are also presented including lid driven cavity flow impulsively started cylinder flow and unsteady vortex shedding from a circular cylinder although the method is by construction minimalist it is shown to be accurate and robust for the problems considered

high order compact computation and nonuniform grids for streamfunction vorticity equations abstract fourth order compact difference schemes for steady streamfunction vorticity formulation of 2d incompressible navier stokes equations on nonuniform grids are derived using maple software package especially we deduce fourth order compact difference scheme of the first partial derivative terms in order to resolve boundary layers grid transformation techniques are used which maps a nonuniform grid onto a uniform one for use with the fourth order compact difference scheme a krylov subspace iterative method with an ilut preconditioning technique is employed to solve the resulting linear system the proposed high accuracy computation method is applied to two model problems computational results are compared with results computed by other schemes in the literature

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

implicit solutions of incompressible navier stokes equations using the pressure gradient method a modified pressure gradient method is developed for solving the incompressible twoand three dimensional navier stokes equations in primitive variables velocity and pressure gradient vectors rather than the velocity and pressure are considered as dependent variables this choice of the dependent variables is consistent with the flow physics as the velocity field of incompressible flows is not dependent on the pressure but rather the pressure gradient this introduces one and two additional dependent variables for two and three dimensions respectively to close the system of equations additional equations are obtained from the identity that the curl of the pressure gradient is zero this choice of dependent variables also leads to dirichlet boundary conditions for the pressure gradient which improves numerical stability and convergence rates the modified pressure gradient method includes a pressure gradient averaging term in the momentum equations to stabilize the solution this term is extended here to general curvilinear coordinates the system of equations is discritized using a conservative finite volume formulation time integration is achieved with a fully implicit scheme including implicit boundary conditions the implicit scheme guarantees that continuity is satisfied to machine zero numerical results compare well with solutions available in the literature for the cavity flow problem and flow about a circular cylinder at reynolds number 40

developing numerical techniques for solving low mach number fluid acoustic problems conservation equations applicable to this regime are derived by applying four simplifying assumptions to the fully compressible form of the navier stokes and energy equations isentropic state changes adiabatic flow negligible density variation inertial terms and stokes hypothesis the resulting equations termed acoustic compressible are similar to the traditional pseudocompressible equations except for two distinctions pseudocompressible solutions use artificially high mach numbers for computational convenience and neglect the pressure convection term in the mass conservation equation

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

tikhonov regularization and the l curve for large discrete ill posed problems discretization of linear inverse problems generally gives rise to very ill conditioned linear systems of algebraic equations typically the linear systems obtained have to be regularized to make the computation of a meaningful approximate solution possible tikhonov regularization is one of the most popular regularization methods a regularization parameter specifies the amount of regularization and in general an appropriate value of this parameter is not known a priori we review available iterative methods and present new ones for the determination of a suitable value of the regularization parameter by the l curve criterion and the solution of regularized systems of algebraic equations

a new family of 5 5 cc 4oc schemes applicable for unsteady navier stokes equations in this paper a new family of implicit compact finite difference schemes for computation of unsteady convection diffusion equation with variable convection coefficient is proposed the schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady navier stokes system the proposed schemes where transport variable and its first derivatives are carried as the unknowns combine virtues of compact discretization and pade scheme for spatial derivative these schemes which are based on a five point stencil with constant coefficients named as 5 5 constant coefficient 4th order compact 5 5 cc 4oc give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods these schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable they efficiently capture both transient and steady solutions of linear and nonlinear convection diffusion equations with dirichlet as well as neumann boundary conditions subsequently the proposed schemes are applied to problems governed by the incompressible navier stokes equations the results obtained are in excellent agreement with analytical and available numerical results in all cases establishing efficiency and accuracy of the proposed schemes

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

the empirical distribution of rate constrained source codes let x x sub 1 be a stationary ergodic finite alphabet source x sup n denote its first n symbols and y sup n be the codeword assigned to x sup n by a lossy source code the empirical kth order joint distribution q spl circ sup k x sup n y sup n spl rceil x sup k y sup k is defined as the frequency of appearances of pairs of k strings x sup k y sup k along the pair x sup n y sup n our main interest is in the sample behavior of this random distribution letting i q sup k denote the mutual information i x sup k y sup k when x sup k y sup k spl sim q sup k we show that for any sequence of lossy source code s of rate spl les r lim sup sub n spl rarr spl infin 1 k i q spl circ sup k x sup n y sup n spl rfloor spl les r 1 k h x sub 1 sup k h x a s where h x denotes the entropy rate of x this is shown to imply for a large class of sources including all independent and identically distributed i i d sources and all sources satisfying the shannon lower bound with equality that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve q spl circ sup k x sup n y sup n spl rfloor spl rarr sup d p x sup k y sup k a s whenever p sub x sup k sub y sup k is the unique distribution attaining the minimum in the definition of the kth order rate distortion function consequences of these results include a new proof of kieffer s sample converse to lossy source coding as well as performance bounds for compression based denoisers

ellipticity accuracy and convergence of the discrete navier stokes equations the introduction into the continuity equation of additional terms to recover grid scale ellipticity for the navier stokes equations discretised on a non staggered mesh results in an increase in the discretisation error the introduced error is a combination of the additional truncation error and a false source resulting from the inconsistent construction of the conservation equations used in the finite volume scheme considered the false source error component is removed by constructing the conservation terms consistently while the additional truncation error is shown to be of the same order as the leading order truncation error associated with the unmodified equations a method of reducing the magnitude of the additional terms thereby reducing the additional error is considered it is shown that although this does reduce the magnitude of the error it also reduces the ellipticity of the equations and leads to slower convergence

extrapolation techniques for ill conditioned linear systems in this paper the regularized solutions of an ill conditioned system of linear equations are computed for several values of the regularization parameter lambda then these solutions are extrapolated at lambda 0 by various vector rational extrapolations techniques built for that purpose these techniques are justified by an analysis of the regularized solutions based on the singular value decomposition and the generalized singular value decomposition numerical results illustrate the effectiveness of the procedures

optimal vorticity conditions for the node centred finite difference discretization of the second order vorticity velocity equations the present paper considers the 2d vorticity velocity navier stokes equations written as a second order system when a node centred finite difference discretization and a uniform cartesian grid are employed for such a formulation common vorticity boundary conditions yield much inferior solutions to those obtained in the node centred vorticity stream function or staggered grid vorticity velocity formulations however we demonstrate that these three formulations are formally equivalent in the sense that they all identically satisfy i the node centred finite difference form of the continuity equation ii the node centred finite difference form of the vorticity definition with respect to the mid cell or staggered velocity components and iii the cell centred finite volume integral form of the vorticity definition with respect to the nodal values of the velocity components this last property naturally provides the optimal boundary conditions for the wall vorticity in the node centred vorticity velocity formulation numerical solutions to the driven cavity flow problem are provided which confirm the equivalence of the three formulations

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

on the role of the helmholtz decomposition in mixed methods for incompressible flows and a new variational crime abstract according to the helmholtz decomposition the irrotational parts of the momentum balance equations of the incompressible navier stokes equations are balanced by the pressure gradient unfortunately nearly all mixed methods for incompressible flows violate this fundamental property resulting in the well known numerical instability of poor mass conservation the origin of this problem is the lack of l 2 orthogonality between discretely divergence free velocities and irrotational vector fields therefore a new variational crime for the nonconforming crouzeix raviart element is proposed where divergence free lowest order raviart thomas velocity reconstructions reestablish l 2 orthogonality this approach allows to construct a cheap flow discretization for general 2d and 3d simplex meshes that possesses the same advantageous robustness properties like divergence free flow solvers in the stokes case optimal a priori error estimates for the velocity gradients and the pressure are derived moreover the discrete velocity is independent of the continuous pressure several detailed linear and nonlinear numerical examples illustrate the theoretical findings

the ls stag method a new immersed boundary level set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties this paper concerns the development of a new cartesian grid immersed boundary ib method for the computation of incompressible viscous flows in two dimensional irregular geometries in ib methods the computational grid is not aligned with the irregular boundary and of upmost importance for accuracy and stability is the discretization in cells which are cut by the boundary the so called cut cells in this paper we present a new ib method called the ls stag method which is based on the mac method for staggered cartesian grids and where the irregular boundary is sharply represented by its level set function this implicit representation of the immersed boundary enables us to calculate efficiently the geometry parameters of the cut cells we have achieved a novel discretization of the fluxes in the cut cells by enforcing the strict conservation of total mass momentum and kinetic energy at the discrete level our discretization in the cut cells is consistent with the mac discretization used in cartesian fluid cells and has the ability to preserve the five point cartesian structure of the stencil resulting in a highly computationally efficient method the accuracy and robustness of our method is assessed on canonical flows at low to moderate reynolds number taylor couette flow flows past a circular cylinder including the case where the cylinder has forced oscillatory rotations finally we will extend the ls stag method to the handling of moving immersed boundaries and present some results for the transversely oscillating cylinder flow in a free stream

further results on moore penrose inverses of tensors with application to tensor nearness problems abstract the notion of the moore penrose inverse of a matrix has been extended to tensor case with einstein product recently in this paper we continue this work and propose the full rank decomposition of tensors by introducing a new kind of tensor rank which gives a novel representation of the moore penrose inverse moreover we also obtain several formulae related to the moore penrose inverse of a tensor and its i j k inverses in addition we consider the tensor nearness problem associated with a tensor equation a generalization of matrix nearness problems that arise in many areas of applied matrix computations it is shown that the unique solution to the tensor nearness problem can be represented by using the moore penrose inverses of the given tensors

the discrete continuity equation in primitive variable solutions of incompressible flow abstract the use of a non staggered computational grid for the numerical solutions of the incompressible flow equations has many advantages over the use of a staggered grid a penalty however is inherent in the finite difference approximations of the governing equations on non staggered grids in the primitive variable solutions the penalty is that the discrete continuity equation does not converge to machine accuracy rather it converges to a source term which is proportional to the fourth order derivative of the pressure the time increment and the square of the grid spacing an approach which minimizes the error in the discrete continuity equation is developed numerical results obtained for the driven cavity problem confirm the analytical developments

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

approximating rate distortion graphs of individual data experiments in lossy compression and denoising classical rate distortion theory requires specifying a source distribution instead we analyze rate distortion properties of individual objects using the recently developed algorithmic rate distortion theory the latter is based on the noncomputable notion of kolmogorov complexity to apply the theory we approximate the kolmogorov complexity by standard data compression techniques and perform a number of experiments with lossy compression and denoising of objects from different domains we also introduce a natural generalization to lossy compression with side information to maintain full generality we need to address a difficult searching problem while our solutions are therefore not time efficient we do observe good denoising and compression performance

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

on the generation of exact solutions for evaluating numerical schemes and estimating discretization error abstract in this paper we further develop the method of nearby problems mnp for generating exact solutions to realistic partial differential equations by extending it to two dimensions we provide an extensive discussion of the 2d spline fitting approach which provides ck continuity continuity of the solution value and its first k derivatives along spline boundaries and is readily extendable to higher dimensions a detailed one dimensional example is given to outline the general concepts then the two dimensional spline fitting approach is applied to two problems heat conduction with a distributed source term and the viscous incompressible flow in a lid driven cavity with both a constant lid velocity and a regularized lid velocity which removes the strong corner singularities the spline fitting approach results in very small spline fitting errors for the heat conduction problem and the regularized driven cavity whereas the fitting errors in the standard lid driven cavity case are somewhat larger due to the singular behaviour of the pressure near the driven lid the mnp approach is used successfully as a discretization error estimator for the driven cavity cases outperforming richardson extrapolation which requires two grid levels however mnp has difficulties with the simpler heat conduction case due to the discretization errors having the same magnitude as the spline fitting errors

discrete exterior calculus discretization of incompressible navier stokes equations over surface simplicial meshes a conservative discretization of incompressible navier stokes equations is developed based on discrete exterior calculus dec a distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product the governing equations are first rewritten using the exterior calculus notation replacing vector calculus differential operators by the exterior derivative hodge star and wedge product operators the discretization is then carried out by substituting with the corresponding discrete operators based on the dec framework numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured triangular meshes and first order accuracy for otherwise unstructured meshes by construction the method is conservative in that both mass and vorticity are conserved up to machine precision the relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step

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 anisotropic gls stabilized finite element method for incompressible flow problems abstract we consider a stabilized finite element approximation of incompressible flow problems in primitive velocity pressure variables which is based on a gls formulation equal order interpolation for the velocity and the pressure can be employed with this formulation the method introduced here is specially developed to be used on anisotropic finite element meshes with large element aspect ratios rather than using a single stabilization parameter within each element the jacobian matrix of the affine transformation from the reference element is employed for stabilization purposes stability and anisotropic error estimates in a suitable mesh dependent norm are proved for the linear stokes problem numerical results confirm the accuracy and robustness of the proposed method compared to similar previous stabilized schemes

a singularity avoiding moving least squares scheme for two dimensional unstructured meshes moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data in particular they are often employed when solving partial differential equations on unstructured meshes which are typically needed when the geometry defining the domain is complex it is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements however little research has specifically addressed this issue in this paper a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions and the precise conditions under which singularities occur are identified the theory is used to develop a stencil building algorithm which automatically detects singular stencils and corrects them in an efficient manner while attempting to maintain stencil symmetry as closely as possible finally the scheme is applied in a convection diffusion equation solver and an incompressible navier stokes solver and the results are shown to compare favourably with known analytical solutions and previously published results

arnoldi tikhonov regularization methods tikhonov regularization for large scale linear ill posed problems is commonly implemented by determining a partial lanczos bidiagonalization of the matrix of the given system of equations this paper explores the possibility of instead computing a partial arnoldi decomposition of the given matrix computed examples illustrate that this approach may require fewer matrix vector product evaluations and therefore less arithmetic work moreover the proposed range restricted arnoldi tikhonov regularization method does not require the adjoint matrix and hence is convenient to use for problems for which the adjoint is difficult to evaluate

feedback does not increase the capacity of discrete channels with additive noise we consider discrete time finite alphabet channels with additive random noise we show that output feedback does not increase the capacity of such channels this result holds in the most general case i e for arbitrary additive noise processes

a general reconstruction algorithm for simulating flows with complex 3d immersed boundaries on cartesian grids in the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on cartesian grids is presented in the proposed method an arbitrary three dimensional solid surface immersed in the fluid is discretized using an unstructured triangular mesh and all the cartesian grid nodes near the interface are identified then the solution at these nodes is reconstructed via linear interpolation along the local normal to the body in a way that the desired boundary conditions for both pressure and velocity fields are enforced the overall accuracy of the resulting solver is second order as it is demonstrated in two test cases involving laminar flow past a sphere

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

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

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

an overset grid method for 3d unsteady incompressible flows a composite grid numerical method is developed for simulating unsteady three dimensional 3d incompressible flows in complex geometries the governing equations are solved using a second order accurate finite volume method based on the dual time stepping artificial compressibility approach overset grids are employed to discretize arbitrarily complex geometries and a new interface algorithm is developed to facilitate communication between neighboring grids the algorithm is inspired by the necessary and sufficient conditions for satisfying global mass conservation in a composite domain and is simple to implement in 3d numerical experiments show that the new interpolation scheme is superior to straightforward trilinear interpolation of all flow variables as it minimizes non physical spurious oscillations in the overlap region is less sensitive to grid refinement and greatly enhances the computational efficiency of the iterative algorithm the advantages of the new method are especially pronounced when adjacent overset subdomains are discretized with different spatial resolutions the potential of the method as a powerful technique for simulating complex engineering flows is demonstrated by applying it to calculate vortex shedding from a circular cylinder mounted between two endplates and flow in a rectangular channel with two wall mounted obstacles

denoising via mcmc based lossy compression it has been established in the literature in various theoretical and asymptotic senses that universal lossy compression followed by some simple postprocessing results in universal denoising for the setting of a stationary ergodic source corrupted by additive white noise however this interesting theoretical result has not yet been tested in practice in denoising simulated or real data in this paper we employ a recently developed mcmc based universal lossy compressor to build a universal compression based denoising algorithm we show that applying this iterative lossy compression algorithm with appropriately chosen distortion measure and distortion level followed by a simple derandomization operation results in a family of denoisers that compares favorably both theoretically and in practice with other mcmc based schemes and with the discrete universal denoiser dude

a deferred correction multigrid algorithm based on a new smoother for the navier stokes equations abstract an algorithm which brings together the techniques of multigrid and deferred correction through their common relationship with imperfect newton iteration manages to combine the ease of calculation of a low order with the accuracy of a high order difference approximation of any given differential equation problem a stable explicit gauss seidel relaxation algorithm for the navier stokes equations based on an appropriate kind of upwinding of as well as derivatives especially developed for use as a multigrid smoother in this context is presented and the complete algorithm is tested on the standard conservative second order discretization of the driven cavity problem

explicit filtering and exact reconstruction of the sub filter stresses in large eddy simulation explicit filtering has the effect of reducing numerical or aliasing errors near the grid scale in large eddy simulation les we use a differential filter namely the inverse helmholtz operator which is readily applied to unstructured meshes the filter is invertible which allows the sub filter scale sfs stresses to be exactly reconstructed in terms of the filtered solution unlike eddy viscosity models the method of filtering and reconstruction avoids making any physical assumptions and is therefore valid in any flow regime the sub grid scale sgs stresses are not recoverable by reconstruction but the second order finite element method used here is an adequate source of numerical dissipation in lieu of an sgs model results for incompressible turbulent channel flow at re 180 are presented which show that explicit filtering and exact sfs reconstruction is a significant improvement over the standard les approach of implicit filtering and eddy viscosity sgs modelling

coupled fully implicit solution procedure for the steady incompressible navier stokes equations abstract this paper presents a new fully implicit procedure for the solution of the steady incompressible navier stokes equations in primitive variables the momentum equations are coupled with a poisson type equation for the pressure and solved using the beam and warming approximate factorization method the present formulation does not require the iterative solution of the pressure equation at each time step thus the major drawback of the pressure poisson approach which made it prohibitively expensive for complex three dimensional applications is eliminated numerical solutions for the problem of the two dimensional driven cavity are obtained using a non staggered grid at re 100 400 and 1000 all the computed results are obtained without any artificial dissipation this feature of the present procedure demonstrates its excellent convergence and stability characteristics those characteristics result from the coupling of the pressure equation which is elliptic in space with the momentum equations

vorticity boundary condition and related issues for finite difference schemes this paper discusses three basic issues related to the design of finite difference schemes forunsteadyviscous incompressible flows using vorticity formulations the boundary condition for vorticity an efficient time stepping procedure and the relation between these schemes and the ones based on velocity pressure formulation we show that many of the newly developed global vorticity boundary conditions can actually be written as some local formulas derived earlier we also show that if we couple a standard centered difference scheme with third or fourth order explicit runge kutta methods the resulting schemes havenocell reynolds number constraints for high reynolds number flows these schemes are stable under the cfl condition given by the convective terms finally we show that the classical mac scheme is the same as thom s formula coupled with second order centered differences in the interior in the sense that one can define discrete vorticity in a natural way for the mac scheme and get the same values as the ones computed from thom s formula we use this to derive an efficient fourth order runge kutta time discretization for the mac scheme from the one for thom s formula we present numerical results for driven cavity flow at high reynolds number 105

analysis of mismatched estimation errors using gradients of partition functions we consider the problem of signal estimation denoising from a statistical mechanical perspective in continuation to a recent work on the analysis of mean square error mse estimation using a direct relationship between optimum estimation and certain partition functions this paper consists of essentially two parts in the first part using the aforementioned relationship we derive single letter expressions of the asymptotic mismatched mse of a codeword from a randomly selected code corrupted by a gaussian vector channel in the second part we provide several examples to demonstrate phase transitions in the behavior of the mse these examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions

an implicit boundary approach for viscous compressible high reynolds flows using a hybrid remeshed particle hydrodynamics method abstract we present an implicit boundary particle method with background mesh adaptation we use a brinkman penalisation to represent the boundary of the domain and a remeshed particle method to simulate viscous flow with high reynolds numbers a penalty term is added to the navier stokes equations to impose the boundary conditions the boundary conditions are enforced to a specific precision with no need to modify the numerical method or change the grid achieving an implicit approach for flow around complex boundaries geometries simulation the main idea of the brinkman penalisation method is to model the solid obstacle as a porous medium the governing equations for the compressible fluid and penalised navier stokes for the porous medium are solved simultaneously without need for interface conditions the accuracy of the method is tested for a number of benchmark problems starting with simple cases such as a periodic laminar flow in a channel poiseuille flow to more complex problems such as the lid driven cavity with high reynolds numbers the reflection and propagation of a compressible shock wave and finally swirling flow in a model two stroke diesel engine the remeshed particle mesh method coupled with brinkman penalisation provides a good quality simulation and the results are in agreement with analytical or reference solutions

gas kinetic scheme with discontinuous derivative for low speed flow computation the present paper concerns the improvement of the gas kinetic scheme gks for low speed flow computation in the modified gks scheme the flow distributions with discontinuous derivatives are used as an initial condition at the cell interface for the flux evaluation this discontinuity is determined by considering both the flow characteristic and grid s resolution compared with gks method with a continuous slope for the flow variables at a cell interface the new scheme is more robust and accurate in the under resolved flow computation the new scheme presents much less numerical oscillation the extension of the current scheme to unstructured mesh is straightforward to validate the method both computations of 2d lid driven cavity flow and 3d flow past a sphere are performed the numerical results validate the current method

tetrahedral mesh optimisation and adaptivity for steady state and transient finite element calculations abstract a method for optimising a pre existing mesh of tetrahedral finite elements is described it is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality a riemannian metric reflecting the a posteriori error measure is used to calculate element size and shape a functional is defined which embodies both shape and size quality of an element with respect to the metric and is used to gauge mesh quality a heuristic based local search strategy is adopted local in the sense that it has no hill climbing abilities the paper presents applications of the method to complex steady state and time dependent problems which highlight its anisotropic feature capturing abilities numerical evidence is provided which suggests that the computational complexity time of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh

adaptive variational multiscale methods for incompressible flow based on two local gauss integrations we consider variational multiscale vms methods with h adaptive technique for the stationary incompressible navier stokes equations the natural combination of vms with adaptive strategy retains the best features of both methods and overcomes many of their deficits a reliable a posteriori projection error estimator is derived which can be computed by two local gauss integrations at the element level finally some numerical tests are presented to illustrate the method s efficiency

fixed slope universal lossy data compression corresponding to any lossless codeword length function l three universal lossy data compression schemes are presented one is with a fixed rate another is with a fixed distortion and a third is with a fixed slope the former two universal lossy data compression schemes are the generalization of yang kieffer s see ibid vol 42 no 1 p 239 45 1995 results to the general case of any lossless codeword length function l whereas the third is new in the case of fixed slope spl lambda 0 our universal lossy data compression scheme works as follows for any source sequence x sup n of length n the encoder first searches for a reproduction sequence y sup n of length n which minimizes a cost function n sup 1 l y sup n spl lambda spl rho sub n x sup n y sup n over all reproduction sequences of length n and then encodes x sup n into the binary codeword of length l y sup n associated with y sup n via the lossless codeword length function l where spl rho sub n x sup n y sup n is the distortion per sample between x sup n and y sup n under some mild assumptions on the lossless codeword length function l it is shown that when this fixed slope data compression scheme is applied to encode a stationary ergodic source the resulting encoding rate per sample and the distortion per sample converge with probability one to r sub spl lambda and d sub spl lambda respectively where d sub spl lambda r sub spl lambda is the point on the rate distortion curve at which the slope of the rate distortion function is spl lambda this result holds particularly for the arithmetic codeword length function and lempel ziv codeword length function the main advantage of this fixed slope universal lossy data compression scheme over the fixed rate fixed distortion universal lossy data compression scheme lies in the fact that it converts the encoding problem to a search problem through a trellis and then permits one to use some sequential search algorithms to implement it simulation results show that this fixed slope universal lossy data compression scheme combined with a suitable search algorithm is promising

square smoothing regularization matrices with accurate boundary conditions this paper is concerned with the solution of large scale linear discrete ill posed problems the determination of a meaningful approximate solution of these problems requires regularization we discuss regularization by the tikhonov method and by truncated iteration the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution the present paper describes the construction of square regularization matrices from finite difference equations with a focus on the boundary conditions the regularization matrices considered have a structure that makes them easy to apply in iterative methods including methods based on the arnoldi process numerical examples illustrate the properties and effectiveness of the regularization matrices described

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

a primitive variable method for the solution of three dimensional incompressible viscous flows abstract in this paper we present a new primitive variable method for the solution of the three dimensional incompressible reynolds averaged navier stokes equations in generalized curvilinear coordinates the governing equations are discretized on a non staggered grid and the discrete continuity equation is replaced by a discrete pressure poisson equation the discrete pressure equation is designed in such a way that i the compatibility condition for the poisson neumann problem is automatically satisfied and ii the discrete incompresibility constraint is satisfied to at least truncation error accuracy while the computed pressure is smooth the momentum equations are integrated in time using the four stage runge kutta algorithm while the pressure equation is solved using the point successive relaxation technique the method is applied to calculate the turbulent flow field over a ship model the computed results are in very good agreement with the experimental data

sph with the multiple boundary tangent method in this article we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics sph method benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries as well current sph boundary approaches do not properly treat curved boundaries in complicated flow domains these drawbacks have been remedied in a new boundary treatment method presented in this article called the multiple boundary tangent mbt approach in this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions the two benchmark problems chosen are the lid driven cavity problem and flow over a cylinder the sph solutions using the mbt approach and the results from literature are in very good agreement these solutions involved solid boundaries but the approach presented herein should be extendable to time evolving free surface boundaries copyright 2008 john wiley sons ltd

dilation free solutions for the incompressible flow equations on nonstaggered grids the present method employs a pressure poisson formulation that has the unique capability of satisfying the discrete continuity equation exactly while producing smooth pressure on nonstaggered grids a fourth order accurate discretization is employed for the pressure gradient operator in both the momentum equation and the pressure poisson equation the use of higher order accurate approximations for the pressure derivatives results in the enlargement of laplace operator which incorporates both odd and even grid points and thus spatially couples the pressure field the numerical solutions are compared to solutions obtained from the classic pressure poisson approach which uses artificial dissipation to couple the pressure field as well as benchmark results of a stream function vorticity formulation which automatically produces dilatation free solutions

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

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

numerical solutions for the incompressible navier stokes equations in primitive variables using a non staggered grid 11 abstract in part i of this study a method was developed for the solution of the pressure poisson equation with neumann boundary conditions on a non staggered grid this method was used to determine the pressure when given the velocity field from a stream function vorticity solution in part ii the pressure equation is solved iteratively with the momentum navier stokes equations on a non staggered grid in this case the solution of the pressure equation not only provides the pressure but also serves to indirectly satisfy the continuity equation this primitive variables formulation has a major advantage over the stream function vorticity method in its applicability for three dimensional flow numerical results are obtained and compared with the stream function vorticity results for the driven cavity of part i

a hybrid cartesian immersed boundary method for simulating flows with 3d geometrically complex moving bodies a numerical method is developed for solving the 3d unsteady incompressible navier stokes equations in cartesian domains containing immersed boundaries of arbitrary geometrical complexity moving with prescribed kinematics the governing equations are discretized on a hybrid staggered non staggered grid layout using second order accurate finite difference formulas the discrete equations are integrated in time via a second order accurate dual time stepping artificial compressibility iteration scheme unstructured triangular meshes are employed to discretize complex immersed boundaries the nodes of the surface mesh constitute a set of lagrangian control points used to track the motion of the flexible body at every instant in time the influence of the body on the flow is accounted for by applying boundary conditions at cartesian grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface grid convergence tests are carried out for the flow induced by an oscillating sphere in a cubic cavity which show that the method is second order accurate the method is validated by applying it to calculate flow in a cartesian domain containing a rigid sphere rotating at constant angular velocity as well as flow induced by a flapping wing the ability of the method to simulate flows in domains with arbitrarily complex moving bodies is demonstrated by applying to simulate flow past an undulating fish like body and flow past an anatomically realistic planktonic copepod performing an escape like maneuver euver

unstructured cartesian refinement with sharp interface immersed boundary method for 3d unsteady incompressible flows a novel numerical method is developed for solving the 3d unsteady incompressible navier stokes equations on locally refined fully unstructured cartesian grids in domains with arbitrarily complex immersed boundaries owing to the utilization of the fractional step method on an unstructured cartesian hybrid staggered non staggered grid layout flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero auxiliary hanging nodes are used to facilitate the discretization of the governing equations the second order accuracy of the solver is ensured by using multi dimension lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement the sharp interface immersed boundary method is augmented with local near boundary refinement to handle arbitrarily complex boundaries the discrete momentum equation is solved with the matrix free newton krylov method and the krylov subspace method is employed to solve the poisson equation the second order accuracy of the proposed method on unstructured cartesian grids is demonstrated by solving the poisson equation with a known analytical solution a number of three dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of reynolds numbers and flow regimes laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy the efficiency and the smooth transition of scales and coherent structures across refinement levels large eddy simulation les past a miniature wind turbine rotor parameterized using the actuator line approach indicates the ability of the fully unstructured solver to simulate complex turbulent flows finally a geometry resolving les of turbulent flow past a complete hydrokinetic turbine illustrates the potential of the method to simulate turbulent flows past geometrically complex bodies on locally refined meshes in all the cases the results are found to be in very good agreement with published data and savings in computational resources are achieved

a pseudospectral method for solution of the three dimensional incompressible navier stokes equations abstract a new chebyshev pseudospectral technique based on the projection method that was previously applied by the authors to the solution of two dimensional incompressible navier stokes equations in primitive variables for nonperiodic boundary conditions is extended to solve the three dimensional navier stokes equations the crucial point of the method is the requirement that the continuity equation be satisfied everywhere in the domain on the boundaries as well as in the interior the key feature of the work presented in this paper is that the computer storage requirements of the full matrix inversion resulting from direct solution of the pressure poisson equation in three dimensions is greatly reduced by considering an eigenfunction decomposition the method was tested on a two dimensional driven cavity flow and the results were compared with those of the most accurate finite difference calculation the three dimensional driven cavity flow was then calculated at the same reynolds numbers as the two dimensional cases i e re 100 400 and 1000 in the calculated results three dimensional boundary effects were observed in all cases and became more apparent with increasing reynolds number

regularization matrices determined by matrix nearness problems abstract this paper is concerned with the solution of large scale linear discrete ill posed problems with error contaminated data tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution this matrix should be chosen to promote the recovery of known important features of the desired solution such as smoothness and monotonicity we describe a novel approach to determine regularization matrices with desired properties by solving a matrix nearness problem the constructed regularization matrix is the closest matrix in the frobenius norm with a prescribed null space to a given matrix numerical examples illustrate the performance of the regularization matrices so obtained

on the roles of minimization and linearization in least squares finite element models of nonlinear boundary value problems in this paper we examine the roles of minimization and linearization in the least squares finite element formulations of nonlinear boundary values problems the least squares principle is based upon the minimization of the least squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations in the present case we consider l 2 norms since the least squares method is independent of the discretization procedure and the solution scheme the least squares principle suggests that minimization should be performed prior to linearization where linearization is employed in the context of either the picard or newton iterative solution procedures however in the least squares finite element analysis of nonlinear boundary value problems it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations the main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged the assessment is performed mathematically through an examination of the variational setting for the least squares formulation of an abstract nonlinear boundary value problem and also computationally through the numerical simulation of the least squares finite element solutions of both a nonlinear form of the poisson equation and also the incompressible navier stokes equations the assessment suggests that although the least squares principle indicates that minimization should be performed prior to linearization such an approach is often impractical and not necessary

on the role of polynomials in rbf fd approximations ii numerical solution of elliptic pdes rbf generated finite differences rbf fd have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of pdes we find in the present study that combining polyharmonic splines phs with multivariate polynomials offers an outstanding combination of simplicity accuracy and geometric flexibility when solving elliptic equations in irregular or regular regions in particular the drawbacks on accuracy and stability due to runge s phenomenon are overcome once the rbf stencils exceed a certain size due to an underlying minimization property test problems include the classical 2 d driven cavity and also a 3 d global electric circuit problem with the earth s irregular topography as its bottom boundary the results we find are fully consistent with previous results for data interpolation

parameter determination for tikhonov regularization problems in general form abstract tikhonov regularization is one of the most popular methods for computing an approximate solution of linear discrete ill posed problems with error contaminated data a regularization parameter 0 balances the influence of a fidelity term which measures how well the data are approximated and of a regularization term which dampens the propagation of the data error into the computed approximate solution the value of the regularization parameter is important for the quality of the computed solution a too large value of 0 gives an over smoothed solution that lacks details that the desired solution may have while a too small value yields a computed solution that is unnecessarily and possibly severely contaminated by propagated error when a fairly accurate estimate of the norm of the error in the data is known a suitable value of often can be determined with the aid of the discrepancy principle this paper is concerned with the situation when the discrepancy principle cannot be applied it then can be quite difficult to determine a suitable value of we consider the situation when the tikhonov regularization problem is in general form i e when the regularization term is determined by a regularization matrix different from the identity and describe an extension of the cose method for determining the regularization parameter in this situation this method has previously been discussed for tikhonov regularization in standard form i e for the situation when the regularization matrix is the identity it is well known that tikhonov regularization in general form with a suitably chosen regularization matrix can give a computed solution of higher quality than tikhonov regularization in standard form

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

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

implementations of range restricted iterative methods for linear discrete ill posed problems abstract this paper is concerned with iterative solution methods for large linear systems of equations with a matrix of ill determined rank and an error contaminated right hand side the numerical solution is delicate because the matrix is very ill conditioned and may be singular it is natural to require that the computed iterates live in the range of the matrix when the latter is symmetric because then the iterates are orthogonal to the null space computational experience indicates that it can be beneficial to require that the iterates live in the range of the matrix also when the latter is nonsymmetric we discuss the design and implementation of iterative methods that determine iterates with this property new implementations that are particularly well suited for use with the discrepancy principle are described

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

vorticity velocity formulation for three dimensional steady compressible flows the vorticity velocity formulation of the navier stokes equations is extended to the solution of three dimensional compressible fluid flow and heat transfer problems the basic governing equations are expressed in terms of three poisson like equations for the velocity components together with a vorticity transport equation and an energy equation the resulting seven coupled partial differential equations are solved by a finite difference method on a single grid and a discrete solution is obtained by combining a steady state and a time dependent newton s method once a converged solution is obtained one of the velocity equations can be removed from the system and replaced by the continuity equation and a conservative solution is obtained by using the previous solution as a starting estimate for newton s method with only a few additional iterations the numerical procedure is evaluated by applying it to natural and mixed convection problems the formulation is found to be stable at high rayleigh numbers and it may be applied to a wide variety of flow and heat transfer problems

occam filters for stochastic sources with application to digital images an occam filter employs lossy data compression to separate signal from noise previously it was shown that occam filters can filter random noise from deterministic signals here we show that occam filters can also separate two stochastic sources depending on their relative compressibility we also compare the performance of occam filters and wavelet based denoising on digital images

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