immersed interface finite element methods for elliptic interface problems with nonhomogeneous jump conditions in this work a class of new finite element methods called immersed interface finite element methods is developed to solve elliptic interface problems with nonhomogeneous jump conditions simple non body fitted meshes are used a single function that satisfies the same nonhomogeneous jump conditions is constructed using a level set representation of the interface with such a function the discontinuities across the interface in the solution and flux are removed and an equivalent elliptic interface problem with homogeneous jump conditions is formulated special finite element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate these methods are designed as an efficient component of the finite element level set methodology for fast simulation of interface dynamics that does not require remeshing

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

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 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

an immersed discontinuous finite element method for stokes interface problems abstract we present a discontinuous immersed finite element ife method for stokes interface problems on cartesian meshes that do not require the mesh to be aligned with the interface as such the method allows unfitted meshes with elements cut by the interface and thus may contain more than one fluid on these unfitted meshes we construct an immersed q 1 q 0 finite element space according to the location of the interface and pertinent interface jump conditions the proposed q 1 q 0 ife shape functions have several desirable features such as the unisolvence and the partition of unity we present several numerical examples to demonstrate that the proposed ife spaces maintain the optimal approximation capability with respect to the polynomials used we also show that related discontinuous ife solutions of stokes interface problems maintain the optimal convergence rates in both l 2 and broken h 1 norms

a study of a numerical solution of the steady two dimensions navier stokes equations in a constricted channel problem by a compact fourth order method we present a numerical solution for the steady 2d navier stokes equations using a fourth order compact type method the geometry of the problem is a constricted symmetric channel where the boundary can be varied via a parameter from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular the set of non linear equations is solved by the newton method results have been obtained for reynolds number up to 500 estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method

convergence of a compact scheme for the pure streamfunction formulation of the unsteady navier stokes system this paper is devoted to the analysis of a new compact scheme for the navier stokes equations in pure streamfunction formulation numerical results using that scheme have been reported in m ben artzi e j comput phys 205 2005 pp 640 664 the scheme discussed here combines the stephenson scheme for the biharmonic operator and ideas from box scheme methodology consistency and convergence are proved for the full nonlinear system instead of customary periodic conditions the case of boundary conditions is addressed it is shown that in one dimension the truncation error for the biharmonic operator is o h 4 at interior points and o h at near boundary points in two dimensions the truncation error is o h 2 at interior points due to the cross terms and o h at near boundary points hence the scheme is globally of order four in the one dimensional periodic case and of order two in the two dimensional periodic case but of order 3 2 for one and two dimensional nonperiodic boundary conditions we emphasize in particular that there is no special treatment of the boundary thus allowing robust use of the scheme the finite element analogy of the finite difference schemes is invoked at several stages of the proofs in order to simplify their verifications

an efficient compact difference scheme for solving the streamfunction formulation of the incompressible navier stokes equations recently a new paradigm for solving the steady navier stokes equations using a streamfunction velocity formulation was proposed by gupta and kalita m m gupta j c kalita a new paradigm for solving navier stokes equations streamfunction velocity formulation j comput phys 207 2005 52 68 which avoids difficulties inherent in the conventional streamfunction vorticity and primitive variable formulations it is discovered that this formulation can reached second order accurate and obtained accuracy solutions with little additional cost for a couple of fluid flow problems in this paper an efficient compact finite difference approximation named as five point constant coefficient second order compact 5pcc soc scheme is proposed for the streamfunction formulation of the steady incompressible navier stokes equations in which the grid values of the streamfunction and the values of its first derivatives velocities are carried as the unknown variables the derivation approach is simple and can be easily used to derive compact difference schemes for other similar high order elliptic differential equations numerical examples including the lid driven cavity flow problem and a problem of flow in a rectangular cavity with the hight width ratio of 2 are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme the results obtained are compared with ones by different available numerical methods in the literature the present scheme not only shows second order accurate but also proves more effective than the existing second order compact scheme of the streamfunction formulation in the aspect of computational cost

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

an efficient method for the incompressible navier stokes equations on irregular domains with no slip boundary conditions high order up to the boundary common efficient schemes for the incompressible navier stokes equations such as projection or fractional step methods have limited temporal accuracy as a result of matrix splitting errors or introduce errors near the domain boundaries which destroy uniform convergence to the solution in this paper we recast the incompressible constant density navier stokes equations with the velocity prescribed at the boundary as an equivalent system for the primary variables velocity and pressure equation for the pressure the key difference from the usual approaches occurs at the boundaries where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time this avoids the common difficulty of an apparently over determined poisson problem since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity the recast equations are ideal for numerical marching methods the new system can be discretized using a variety of methods including semi implicit treatments of viscosity and in principle to any desired order of accuracy in this work we illustrate the approach with a 2 d second order finite difference scheme on a cartesian grid and devise an algorithm to solve the equations on domains with curved non conforming boundaries including a case with a non trivial topology a circular obstruction inside the domain this algorithm achieves second order accuracy in the l norm for both the velocity and the pressure the scheme has a natural extension to 3 d

single cell discretizations of order two and four for biharmonic problems abstract new difference formulas are derived for solving the biharmonic problem in two dimensions over a rectangular domain these methods use only the nine grid points of a single mesh cell and do not require fictitious points in order to approximate the boundary conditions derivatives of the solution are obtained as a by product of the methods second order formulas are derived for both the first and second biharmonic problems in numerical experiments the new second order formulas compare favourably with the standard second order methods extensions to fourth order formulas are given the method of deriving these formulas can be used to derive similar formulas for arbitrarily shaped regions

essentially compact schemes for unsteady viscous incompressible flows a new fourth order accurate finite difference scheme for the computation of unsteady viscous incompressible flows is introduced the scheme is based on the vorticity stream function formulation it is essentially compact and has the nice features of a compact scheme with regard to the treatment of boundary conditions it is also very efficient at every time step or runge kutta stage only two poisson like equations have to be solved the poisson like equations are amenable to standard fast poisson solvers usually designed for second order schemes detailed comparison with the second order scheme shows the clear superiority of this new fourth order scheme in resolving both the boundary layers and the gross features of the flow this efficient fourth order scheme also made it possible to compute the driven cavity flow at reynolds number 106on a 10242grid at a reasonable cost fourth order convergence is proved under mild regularity requirements this is the first such result to our knowledge

a high order compact difference algorithm for half staggered grids for laminar and turbulent incompressible flows abstract the paper presents a novel efficient and accurate algorithm for laminar and turbulent flow simulations the spatial discretisation is performed with help of the compact difference schemes up to 10th order for collocated and half staggered grid arrangements the time integration is performed by a predictor corrector approach combined with the projection method for pressure velocity coupling at this stage a low order discretisation is introduced which considerably decreases the computational costs it is demonstrated that such approach does not deteriorate the solution accuracy significantly following boersma b j 13 the interpolation formulas developed for staggered uniform meshes are used also in the computations with a non uniform strongly varying nodes distribution in the proposed formulation of the projection method such interpolation is performed twice it is shown that it acts implicitly as a high order low pass filter and therefore the resulting algorithm is very robust its accuracy is first demonstrated based on simple 2d and 3d problems an inviscid vortex advection a decay of taylor green vortices a modified lid driven cavity flow and a dipole wall interaction in periodic flow problems the first two cases the solution accuracy exhibits the 10th order behaviour in the latter cases the 3rd and the 4th order is obtained robustness of the proposed method in the computations of turbulent flows is demonstrated for two classical cases a periodic channel with re 395 and re 590 and a round jet with re 21 000 the solutions are obtained without any turbulence model and also without any explicit techniques aiming to stabilise the solution the results are in a very good agreement with literature dns and les data both the mean and r m s values are predicted correctly

a fast direct solver for the biharmonic problem in a rectangular grid we present a fast direct solver methodology for the dirichlet biharmonic problem in a rectangle the solver is applicable in the case of the second order stephenson scheme j w stephenson j comput phys 55 1984 pp 65 80 as well as in the case of a new fourth order scheme which is discussed in this paper and is based on the capacitance matrix method b l buzbee and f w dorr siam j numer anal 11 1974 pp 1136 1150 p bjorstad siam j numer anal 20 1983 pp 59 71 the discrete biharmonic operator is decomposed into two components the first is a diagonal operator in the eigenfunction basis of the laplacian to which the fft algorithm is applied the second is a low rank perturbation operator given by the capacitance matrix which is due to the deviation of the discrete operators from diagonal form the sherman morrison formula g h golub and c f van loan matrix computations 3rd ed john hopkins university press baltimore md 1996 is applied to obtain a fast solution of the resulting linear system of equations

modeling and an immersed finite element method for an interface wave equation abstract the electromagnetic field which is governed by maxwell s equation plays a key role in plasma simulation in this article we first derive the interface conditions when we rewrite the interface maxwell s equation whose problem domain involves complex media such as objects of different materials into a parabolic hyperbolic type of interface model which is a modified wave equation by adding a first order time derivative term due to the lossy medium based on the interface conditions and the existing bilinear immersed finite element space for the interface poisson equation we propose an immersed finite element method for the spatial discretization of this parabolic hyperbolic interface equation on a cartesian mesh independent of the interface then we use a second order finite difference method for the temporal discretization in order to develop the full discretization scheme compared with the unstructured body fitting mesh which is needed by the traditional finite element method for interface problems the cartesian mesh independent of the interface will significantly benefit the plasma simulation in the electromagnetic field especially the particle models such as the particle in cell method this method provides a new efficient way to study varying electromagnetic field with objects of different materials on a cartesian mesh independent of the interface hence builds a solid foundation for the further study on the motion of plasma in this electromagnetic field numerical examples are provided to demonstrate the features of the proposed method

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

new cartesian grid methods for interface problems using the finite element formulation new finite element methods based on cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients the triangulations in these methods do not need to fit the interfaces the basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately both non conforming and conforming finite element spaces are considered corresponding interpolation functions are proved to be second order accurate in the maximum norm the conforming finite element method has been shown to be convergent with cartesian triangulations these new methods can be used as finite difference methods numerical examples are provided to support the methods and the theoretical analysis

a pure compact scheme for the streamfunction formulation of navier stokes equations a pure streamfunction formulation is introduced for the numerical simulation of the two dimensional incompressible navier stokes equations the idea is to replace the vorticity in the vorticity streamfunction evolution equation by the laplacian of the streamfunction the resulting formulation includes the streamfunction only thus no inter function relations need to be invoked a compact numerical scheme which interpolates streamfunction values as well as its first order derivatives is presented and analyzed a number of numerical experiments are presented including driven and double driven cavities where the reynolds numbers are sufficiently large leading to symmetry breaking of asymptotic solutions

high accuracy solutions of incompressible navier stokes equations abstract in recent years we have developed high accuracy finite difference approximations for partial differential equations of elliptic type with particular emphasis on the convection diffusion equation these approximations are of compact type have a local truncation error of fourth order and allow the use of standard iterative schemes to solve the resulting systems of algebraic equations in this paper we extend these high accuracy approximations to the solution of navier stokes equations solutions are obtained for the model problem of driven cavity and are compared with solutions obtained using other approximations and those obtained by other authors it is discovered that the high order approximations do indeed produce high accuracy solutions and have a potential for use in solving important problems of viscous fluid flows

immersed finite element methods for unbounded interface problems with periodic structures interface problems arise in many physical and engineering simulations involving multiple materials periodic structures often appear in simulations with large or even unbounded domain such as magnetostatic electrostatic field simulations immersed finite element ife methods are efficient tools to solve interface problems on a cartesian mesh which is desirable to many applications like particle in cell simulation of plasma physics in this article we develop an ife method for an interface problem with periodic structure on an infinite domain to cope with the periodic boundary condition we modify the stiffness matrix of the ife method the new matrix is maintained symmetric positive definite so that the linear system can be solved efficiently numerical examples are provided to demonstrate features of this method

convergence analysis of a colocated finite volume scheme for the incompressible navier stokes equations on general 2d or 3d meshes we study a colocated cell centered finite volume method for the approximation of the incompressible navier stokes equations posed on a 2d or 3d finite domain the discrete unknowns are the components of the velocity and the pressure all of them colocated at the center of the cells of a unique mesh such a configuration is known to lead to stability problems hence the need for a stabilization technique which we choose of the brezzi pitka ranta type the scheme features two essential properties the discrete gradient is the transpose of the divergence terms and the discrete trilinear form associated to nonlinear advective terms vanishes on discrete divergence free velocity fields as a consequence the scheme is proved to be unconditionally stable and convergent for the stokes problem and for the transient and the steady navier stokes equations in this latter case for a given sequence of approximate solutions computed on meshes the size of which tends to zero we prove up to a subsequence the l 2 convergence of the components of the velocity and in the steady case the weak l 2 convergence of the pressure the proof relies on the study of space and time translates of approximate solutions which allows the application of kolmogorov s theorem the limit of this subsequence is then shown to be a weak solution of the navier stokes equations numerical examples are performed to obtain numerical convergence rates in both the linear and nonlinear cases

partially penalized immersed finite element methods for elliptic interface problems this article presents new immersed finite element ife methods for solving the popular second order elliptic interface problems on structured cartesian meshes even if the involved interfaces have nontrivial geometries these ife methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in ife functions with the enhanced stability due to the added penalty not only can these ife methods be proven to have the optimal convergence rate in an energy norm provided that the exact solution has sufficient regularity but also numerical results indicate that their convergence rates in both the h 1 norm and the l 2 norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic ife methods in some situations trace inequalities are established for both linear and bilinear ife functions that are not only critical for the error analysis of these new ife methods but are also of a great potential to be useful in error analysis for other

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

a compact difference scheme for the biharmonic equation in planar irregular domains we present a finite difference scheme applicable to general irregular planar domains to approximate the biharmonic equation the irregular domain is embedded in a cartesian grid in order to approximate delta 2 phi at a grid point we interpolate the data on the irregular stencil by a polynomial of degree six the finite difference scheme is delta 2 q phi 0 0 where q phi is the interpolation polynomial the interpolation polynomial is not uniquely determined we present a method to construct such an interpolation polynomial and prove that our construction is second order accurate for a regular stencil m ben artzi j p croisille and d fishelov siam j sci comput 31 2008 pp 303 333 shows that the proposed interpolation polynomial is fourth order accurate we present some suitable numerical examples

block implicit multigrid solution of navier stokes equations in primitive variables abstract a calculation procedure for rapid computation of steady multidimensional viscous flows is presented the method solves the navier stokes equations in primitive variables using a coupled block implicit multigrid procedure the procedure is applicable to finite difference formulations using staggered locations of the flow variables a smoothing technique called symmetrical coupled gauss seidel scgs is proposed and is empirically observed to provide good smoothing rates the viscous flow in a square cavity with a moving top wall is calculated for a range of reynolds numbers calculations with finite difference grids as large as 321 321 nodes have been made to test the accuracy and efficiency of the calculation scheme the cpu times for these calculations are observed to be significantly smaller than other solution algorithms with primitive variable formulation the calculated flow fields in the cavity are in good agreement with earlier studies of the same flow situation

prior distributions for the bivariate binomial summary we derive prior distributions for the bivariate binomial model using bernardo s 1979 method these priors are compared to the jeffreys prior and to a prior proposed by crowder sweeting 1989 the priors possess desirable symmetry properties since we allow them to depend on the parameter of interest

a higher order compact finite difference algorithm for solving the incompressible navier stokes equations on the basis of the projection method a higher order compact finite difference algorithm which possesses a good spatial behavior is developed for solving the 2d unsteady incompressible navier stokes equations in primitive variable the present method is established on a staggered grid system and is at least third order accurate in space a third order accurate upwind compact difference approximation is used to discretize the non linear convective terms a fourth order symmetrical compact difference approximation is used to discretize the viscous terms and a fourth order compact difference approximation on a cell centered mesh is used to discretize the first derivatives in the continuity equation the pressure poisson equation is approximated using a fourth order compact difference scheme constructed currently on the nine point 2d stencil new fourth order compact difference schemes for explicit computing of the pressure gradient are also developed on the nine point 2d stencil for the assessment of the effectiveness and accuracy of the method particularly its spatial behavior a problem with analytical solution and another one with a steep gradient are numerically solved finally steady and unsteady solutions for the lid driven cavity flow are also used to assess the efficiency of this algorithm copyright c 2011 john wiley sons ltd

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

three dimensional immersed finite element methods for electric field simulation in composite materials this paper presents two immersed finite element ife methods for solving the elliptic interface problem arising from electric field simulation in composite materials the meshes used in these ife methods can be independent of the interface geometry and position therefore if desired a structured mesh such as a cartesian mesh can be used in an ife method to simulate 3 d electric field in a domain with non trivial interfaces separating different materials numerical examples are provided to demonstrate that the accuracies of these ife methods are comparable to the standard linear finite element method with unstructured body fit mesh copyright 2005 john wiley sons ltd

the sensitivity and accuracy of fourth order finite difference schemes on nonuniform grids in one dimension abstract we construct local fourth order finite difference approximations of first and second derivatives on nonuniform grids in one dimension the approximations are required to satisfy symmetry relationships that come from the analogous higher dimensional fundamental operators the divergence the gradient and the laplacian for example we require that the discrete divergence and gradient be negative adjoint of each other div grad and the discrete laplacian is defined as lap divgrad the adjointness requirement on the divergence and gradient guarantees that the laplacian is a symmetric negative operator the discrete approximations we derive are fourth order on smooth grids but the approach can be extended to create approximations of arbitrarily high order we analyze the loss of accuracy in the approximations when the grid is not smooth and include a numerical example demonstrating the effectiveness of the higher order methods on nonuniform grids

high accuracy iterative solution of convection diffusion equation with boundary layers on nonuniform grids abstract a fourth order compact finite difference scheme and a multigrid method are employed to solve the two dimensional convection diffusion equations with boundary layers the computational domain is first discretized on a nonuniform stretched grid to resolve the boundary layers a grid transformation technique is used to map the nonuniform grid to a uniform one the fourth order compact scheme is applied to the transformed uniform grid a multigrid method is used to solve the resulting linear system numerical experiments are used to show that a graded mesh and a grid transformation are necessary to compute high accuracy solutions for the convection diffusion problems with boundary layers and dicretized by the fourth order compact scheme

multigrid solution of automatically generated high order discretizations for the biharmonic equation in this work we use a symbolic algebra package to derive a family of finite difference approximations for the biharmonic equation on a 9 point compact stencil the solution and its first derivatives are carried as unknowns at the grid points dirichlet boundary conditions are thus incorporated naturally since the approximations use the 9 point compact stencil no special formulas are needed near the boundaries both second order and fourth order discretizations are derived the fourth order approximation produce more accurate results than the 13 point classical stencil or the commonly used system of two second order equations coupled with the boundary condition the method suffers from slow convergence when classical iteration methods such as gauss seidel or sor are employed in order to alleviate this problem we propose several multigrid techniques that exhibit grid independent convergence and solve the biharmonic equation in a small amount of computer time test results from three different problems including stokes flow in a driven cavity are reported

domain decomposition and schur complement approaches to coupling the well equations in reservoir simulation this note reports on the construction of preconditionings for bordered systems arising in compositional hydrocarbon reservoir modeling the main portion of the system represents the reservoir equations and the borders of the systems are associated with the production or injection constraints imposed on the active wells of the reservoir being modeled in general the simulation studies are sensitive to the accuracy of the solution at the wells this note describes strategies for extending a reservoir preconditioning to the well terms three alternatives are considered including borrowing ideas from domain decomposition with one domain being the reservoir and the other domain being the well terms the preconditioners were applied to several linear systems generated by a compositional reservoir simulator which included various choices for the number of oil wells the preconditioned iterative methods considered are minres and bi cgstab which are variants of the conjugate gradient method this note also rep

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

an explicit higher order difference scheme on a compact stencil for elliptic equations on curvilinear geometries abstract a fourth order explicit finite difference scheme on a compact stencil is proposed for a general steady convection diffusion equation on an arbitrary curvilinear coordinate system with computationally generated non uniform grid the method is dependent on the governing differential equation and attains higher order through consistent discretization and accurate evaluation of the transformation metrics extensive comparison of accuracy convergence rate and computation time is made with standard explicit and implicit schemes to highlight the relatively high efficiency of using the proposed scheme applicability of the scheme to irregular flows and geometries is validated by solving for i potential flow past a cambered airfoil at an angle of attack and ii full incompressible navier stokes calculations for flow past a cylinder performing rotary oscillations at low reynolds number

an improved immersed finite element particle in cell method for plasma simulation abstract the particle in cell pic method has been widely used for plasma simulation because of its noise reduction capability and moderate computational cost the immersed finite element ife method is efficient for solving interface problems on cartesian meshes which is desirable for the pic method the combination of these two methods provides an effective tool for plasma simulation with complex interface boundary this paper introduces an improved ife pic method that enhances the performance in both ife and pic aspects for the electric field solver we adopt the newly developed partially penalized ife method with enhanced accuracy for pic implementation we introduce a new interpolation technique to ensure the conservation of the charge numerical examples are provided to demonstrate the features of the improved ife pic method

meshfree point collocation method for the stream vorticity formulation of 2d incompressible navier stokes equations abstract meshfree point collocation method is developed for the stream vorticity formulation of two dimensional incompressible navier stokes equations particular emphasis is placed on the novel formulation of effective vorticity condition on no slip boundaries the moving least square approximation is employed to construct shape functions in conjunction with the framework of point collocation method the derivatives of an arbitrary function can be obtained by the linear combination of these shape functions which enables the vorticity boundary condition to vary linearly with the boundary velocity and the stream function together with the second order partial differential equations for the stream and vorticity functions this boundary condition of vorticity provides the efficient meshfree point collocation scheme for the two dimensional incompressible flow the accuracy and stability for the proposed scheme are demonstrated through a new type of application problem with complex geometry in addition to several typical examples of steady state flow simulation

a transformation free hoc scheme for incompressible viscous flows past an impulsively started circular cylinder in this paper we present a higher order compact scheme for the unsteady two dimensional 2d navier stokes equations on nonuniform polar grids specifically designed for the incompressible viscous flows past a circular cylinder the scheme is second order accurate in time and at least third order accurate in space the scheme very efficiently computes both unsteady and time marching steady state flow for a wide range of reynolds numbers re ranging from 10 to 9500 for the impulsively started cylinder the robustness of the scheme is highlighted when it accurately captures the vortex shedding for moderate re represented by the von karman street and the so called and s phenomena for higher re comparisons are made with established numerical and experimental results and excellent agreement is found in all the cases both qualitatively and quantitatively

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

a new fourth order compact scheme for the navierstokes equations in irregular domains we present a high order finite difference scheme for navierstokes equations in irregular domains the scheme is an extension of a fourth order scheme for navierstokes equations in streamfunction formulation on a rectangular domain ben artzi etal 2010 the discretization offered here contains two types of interior points the first is regular interior points where all eight neighboring points of a grid point are inside the domain and not too close to the boundary the second is interior points where at least one of the closest eight neighbors is outside the computational domain or too close to the boundary in the second case we design discrete operators which approximate spatial derivatives of the streamfunction on irregular meshes using discretizations of pure derivatives in the x y and along the diagonals of the element

accurate ω ψ spectral solution of the singular driven cavity problem this article provides accurate spectral solutions of the driven cavity problem calculated in the vorticity stream function representation without smoothing the corner singularities a prima facie impossible task as in a recent benchmark spectral calculation by primitive variables of botella and peyret closed form contributions of the singular solution for both zero and finite reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form the method employed is based on a split approach to the vorticity and stream function equations a galerkin legendre approximation of the problem for the perturbation and an evaluation of the nonlinear terms by gauss legendre numerical integration results computed for re 0 100 and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation chebyshev projection method the validity of the proposed singularity subtraction scheme for computing time dependent solutions is also established

a compact streamfunction velocity scheme on nonuniform grids for the 2d steady incompressible navier stokes equations in this paper an effective compact finite difference approximation which carries streamfunction and its first derivatives velocities as the unknown variables for the streamfunction velocity formulation of the steady two dimensional incompressible navier stokes equation is developed on non uniform orthogonal cartesian grids to solve the resulting system of equations a multigrid iterative strategy on nonuniform grids is introduced by using the interpolation techniques numerical experiments involving two test problems with analytical solutions and the lid driven square cavity flow problem are carried out to display the superiority of the currently developed method on nonuniform grid numerical results show that the present method on nonuniform grids gets as similarly efficient convergence rate as on uniform grids viz second order accuracy and the resolution of the computed solutions for the problems with the sharp changes can be significantly improved when the nonuniform grid strategy is utilized the backward facing step flow is also calculated by the present method to exhibit the capability to simulate the distant field using fewer grid points the solution for the natural convection problem reveals further the wide applications of the present method not only in the flow problems but also in the heat transfer problems all of these numerical results demonstrate the accuracy and efficiency of the currently proposed schemes

a laplace method for under determined bayesian optimal experimental designs abstract in long et al 2013 a new method based on the laplace approximation was developed to accelerate the estimation of the post experimental expected information gains kullback leibler divergence in model parameters and predictive quantities of interest in the bayesian framework a closed form asymptotic approximation of the inner integral and the order of the corresponding dominant error term were obtained in the cases where the parameters are determined by the experiment in this work we extend that method to the general case where the model parameters cannot be determined completely by the data from the proposed experiments we carry out the laplace approximations in the directions orthogonal to the null space of the jacobian matrix of the data model with respect to the parameters so that the information gain can be reduced to an integration against the marginal density of the transformed parameters that are not determined by the experiments furthermore the expected information gain can be approximated by an integration over the prior where the integrand is a function of the posterior covariance matrix projected over the aforementioned orthogonal directions to deal with the issue of dimensionality in a complex problem we use either monte carlo sampling or sparse quadratures for the integration over the prior probability density function depending on the regularity of the integrand function we demonstrate the accuracy efficiency and robustness of the proposed method via several nonlinear under determined test cases they include the designs of the scalar parameter in a one dimensional cubic polynomial function with two unidentifiable parameters forming a linear manifold and the boundary source locations for impedance tomography in a square domain where the unknown parameter is the conductivity which is represented as a random field

hopf bifurcation of the unsteady regularized driven cavity flow abstract a numerical simulation of the unsteady incompressible flow in the unit cavity is performed by using a chebyshev tau approximation for the space variables the high accuracy of the spectral methods and the condensed distribution of the chebyshev collocation points near the boundary enable us to obtain reliable results for high reynolds numbers with a moderate number of modes it is found that the flow converges to a stationary state for reynolds numbers re up to 10 000 for reynolds numbers larger than a critical value 10 000

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

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

a two level finite element discretization of the streamfunction formulation of the stationary quasi geostrophic equations of the ocean in this paper we proposed a two level finite element discretization of the nonlinear stationary quasi geostrophic equations which model the wind driven large scale ocean circulation optimal error estimates for the two level finite element discretization were derived numerical experiments for the two level algorithm with the argyris finite element were also carried out the numerical results verified the theoretical error estimates and showed that for the appropriate scaling between the coarse and fine mesh sizes the two level algorithm significantly decreases the computational time of the standard one level algorithm

an iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity interface problems involving the non homogeneous flux jump condition are critical for engineering designs in the magnetostatic electrostatic field in applications such as plasma simulation we often only know the total electric quantity on the surface of the object not the charge density distribution on the surface which appears as the non homogeneous flux jump condition in the usual interface problems considered in the literature for the magnetostatic electrostatic field based on structured meshes independent of the interface this article proposes an iterative method that employs both the immersed finite element ife method with non homogeneous flux jump conditions and the regular finite element method with ghost nodes introduced in the object to solve the 2d interface problem for the potential field according to the given total electric quantity on the surface of the object numerical experiments are provided to illustrate the accuracy and efficiency of the proposed method

linear and bilinear immersed finite elements for planar elasticity interface problems this article is to discuss the linear which was proposed in 18 19 and bilinear immersed finite element ife methods for solving planar elasticity interface problems with structured cartesian meshes basic features of linear and bilinear ife functions including the unisolvent property will be discussed while both methods have comparable accuracy the bilinear ife method requires less time for assembling its algebraic system our analysis further indicates that the bilinear ife functions are guaranteed to be applicable to a larger class of elasticity interface problems than linear ife functions numerical examples are provided to demonstrate that both linear and bilinear ife spaces have the optimal approximation capability and that numerical solutions produced by a galerkin method with these ife functions for elasticity interface problem also converge optimally in both l 2 and semi h 1 norms

a cartesian grid method for solving the two dimensional streamfunction vorticity equations in irregular regions we describe a method for solving the two dimensional navier stokes equations in irregular physical domains our method is based on an underlying uniform cartesian grid and second order finite difference finite volume discretizations of the streamfunction vorticity equations geometry representing stationary solid obstacles in the flow domain is embedded in the cartesian grid and special discretizations near the embedded boundary ensure the accuracy of the solution in the cut cells along the embedded boundary we determine a distribution of vorticity sources needed to impose the no slip flow conditions this distribution appears as a right hand side term in the discretized fluid equations and so we can use fast solvers to solve the linear systems that arise to handle the advective terms we use the high resolution algorithms in clawpack we show that our stokes solver is second order accurate for steady state solutions and that our full navier stokes solver is between first and second order accurate and reproduces results from well studied benchmark problems in viscous fluid flow finally we demonstrate the robustness of our code on flow in a complex domain

a central difference scheme for a pure stream function formulation of incompressible viscous flow we present a numerical scheme for incompressible viscous flow formulated as an equation for the stream function the pure stream function formulation obviates the difficulty associated with vorticity boundary conditions the resulting biharmonic equation is discretized with a compact scheme and solved with an algebraic multigrid solver the advection of vorticity is implemented with a high resolution central scheme that remains stable and accurate in the presence of large gradients the accuracy and robustness of the method are demonstrated for high reynolds number flows in a lid driven cavity

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

very high order compact finite difference schemes on non uniform grids for incompressible navier stokes equations this article presents a family of very high order non uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible navier stokes equations the high order compact schemes on non uniform grids developed in shukla and zhong r k shukla x zhong derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation j comput phys 204 2005 404 for linear model equations are extended to the full navier stokes equations in the vorticity and streamfunction formulation two methods for the solution of helmholtz and poisson equations using high order compact schemes on non uniform grids are developed the schemes are constructed so that they maintain a high order of accuracy not only in the interior but also at the boundary second order semi implicit temporal discretization is achieved through an implicit backward differentiation scheme for the linear viscous terms and an explicit adam bashforth scheme for the non linear convective terms the boundary values of vorticity are determined using an influence matrix technique the resulting discretized system with boundary closures of the same high order as the interior is shown to be stable when applied to the two dimensional incompressible navier stokes equations provided enough grid points are clustered at the boundary the resolution characteristics of the high order compact finite difference schemes are illustrated through their application to the one dimensional linear wave equation and the two dimensional driven cavity flow comparisons with the benchmark solutions for the two dimensional driven cavity flow thermal convection in a square box and flow past an impulsively started cylinder show that the high order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary

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

high order compact scheme for the steady stream function vorticity equations a higher order compact scheme that is o h4 on the nine point 2 d stencil is formulated for the steady stream function vorticity form of the navier stokes equations the resulting stencil expressions are presented and hence this new scheme can be easily incorporated into existing industrial software we also show that special treatment of the wall boundary conditions is required the method is tested on representative model problems and compares very favourably with other schemes in the literature

ordered group reference priors with application to the multinomial problem summary noninformative priors are developed using the reference prior approach for multiparameter problems in which there may be parameters of interest and nuisance parameters for a given grouping of parameters and ordering of the groups intuitively according to inferential importance an algorithm for determining the associated reference prior is presented the algorithm is illustrated on the multinomial problem with discussion of the variety and success of various groupings and ordering strategies

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

an upwind compact difference scheme for solving the streamfunction velocity formulation of the unsteady incompressible navier stokes equation abstract in this paper an upwind compact difference method with second order accuracy both in space and time is proposed for the streamfunction velocity formulation of the unsteady incompressible navier stokes equations the first derivatives of streamfunction velocities are discretized by two type compact schemes viz the third order upwind compact schemes suggested with the characteristic of low dispersion error are used for the advection terms and the fourth order symmetric compact scheme is employed for the biharmonic term as a result a five point constant coefficient second order compact scheme is established in which the computational stencils for streamfunction only require grid values at five points at both n th and n 1 th time levels the new scheme can suppress non physical oscillations moreover the unconditional stability of the scheme for the linear model is proved by means of the discrete von neumann analysis four numerical experiments involving a test problem with the analytic solution doubly periodic double shear layer flow problem lid driven square cavity flow problem and two sided non facing lid driven square cavity flow problem are solved numerically to demonstrate the accuracy and efficiency of the newly proposed scheme the present scheme not only shows the good numerical performance for the problems with sharp gradients but also proves more effective than the existing second order compact scheme of the streamfunction velocity formulation in the aspect of computational cost

estimating a product of means bayesian analysis with reference priors abstract suppose that we observe x n 1 and independently y n 1 and are concerned with inference mainly estimation and confidence statements about the product of means this problem arises most obviously in situations of determining area based on measurements of length and width it also arises in other practical contexts however for instance in gypsy moth studies the hatching rate of larvae per unit area can be estimated as the product of the mean of egg masses per unit area times the mean number of larvae hatching per egg mass approximately independent samples can be obtained for each mean see southwood 1978 noninformative prior bayesian approaches to the problem are considered in particular the reference prior approach of bernardo 1979 an appropriate reference prior for the problem is developed and relatively easily implementable formulas for posterior moments e g the posterior mean and variance and credible sets are derived comparisons with alternative noninf

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

hopf bifurcation in the driven cavity abstract incompressible two dimensional calculations are reported for the impulsively started lid driven cavity with aspect ratio two the algorithm is based on the time dependent stream function equation with a crank nicolson differencing scheme for the diffusion terms and with an adams bashforth scheme for the convection terms a multigrid method is used to solve the linear implicit equations at each time step periodic asymptotic solutions have been found for re 10000 and for re 5000 the re 5000 results are validated by grid refinement calculations the solutions are shown to be precisely periodic and care is taken to demonstrate that asymptotic states have been reached a discussion is included about the indicators that are used to show that an asymptotic state has been reached and to show that the asymptotic state is indeed periodic

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

noninformative priors and nuisance parameters abstract we study the conflict between priors that are noninformative for a parameter of interest versus priors that are noninformative for the whole parameter our investigation leads us to maximize a functional that has two terms an asymptotic approximation to a standardized expected kullback leibler distance between the marginal prior and marginal posterior for a parameter of interest and a penalty term measuring the distance of the prior from the jeffreys prior a positive constant multiplying the second terms determines the tradeoff between noninformativity for the parameter of interest and noninformativity for the entire parameter as the constant increases the prior tends to the jeffreys prior when the constant tends to 0 the prior becomes degenerate except in special cases this prior does not have a closed form solution but we present a simple numerical algorithm for finding the prior we compare this prior to the berger bernardo prior

information theoretic asymptotics of bayes methods in the absence of knowledge of the true density function bayesian models take the joint density function for a sequence of n random variables to be an average of densities with respect to a prior the authors examine the relative entropy distance d sub n between the true density and the bayesian density and show that the asymptotic distance is d 2 log n c where d is the dimension of the parameter vector therefore the relative entropy rate d sub n n converges to zero at rate log n n the constant c which the authors explicitly identify depends only on the prior density function and the fisher information matrix evaluated at the true parameter value consequences are given for density estimation universal data compression composite hypothesis testing and stock market portfolio selection

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