optimum sensitivity derivatives of objective functions in nonlinear programming the feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated this elimination restricts the sensitivity analysis to the first order sensitivity derivatives of the objective function it is also shown that when a complete first order sensitivity analysis is performed second order sensitivity derivatives of the objective function are available at little additional cost an expression is derived whose application to linear programming is presented

reversible watermark using the difference expansion of a generalized integer transform a reversible watermarking algorithm with very high data hiding capacity has been developed for color images the algorithm allows the watermarking process to be reversed which restores the exact original image the algorithm hides several bits in the difference expansion of vectors of adjacent pixels the required general reversible integer transform and the necessary conditions to avoid underflow and overflow are derived for any vector of arbitrary length also the potential payload size that can be embedded into a host image is discussed and a feedback system for controlling this size is developed in addition to maximize the amount of data that can be hidden into an image the embedding algorithm can be applied recursively across the color components simulation results using spatial triplets spatial quads cross color triplets and cross color quads are presented and compared with the existing reversible watermarking algorithms these results indicate that the spatial quad based algorithm allows for hiding the largest payload at the highest signal to noise ratio

experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

approximation method for configuration optimization of trusses an efficient method for truss configuration optimization is presented elastic trusses are designed for minimum weight by varying the areas of the members and the location of the joints constraints on member stresses and euler buckling are imposed and multiple loading conditions are considered the method presented here utilizes an approximate structural analysis based on first order taylor series expansions of the member forces the force approximation succeeds in reducing the degree of coupling between the sizing and geometry design variables and thereby increases the accuracy of the approximation a numerical optimizer uses information from the approximate structural analysis as it minimizes the weight of the truss

improving the efficiency of aerodynamic shape optimization the computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements the first improvement involves replacing a grid point based approach for surface representation with a bezier bernstein polynomial parameterization of the surface explicit analytical expressions for the grid sensitivity terms are developed for both approaches the second improvement proposes the use of newton s method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

geometric programming for aircraft design optimization formulating conceptual stage aircraft design problems as geometric programs which are a specific type of convex optimization problem is proposed recent advances in convex optimization offer sign

reversible data hiding based on block median preservation this paper proposes a reversible data hiding scheme for gray level images it exploits the high correlation among image block pixels to produce a difference histogram secret data is embedded based on a multi level histogram shifting mechanism with reference to the integer median of each block the image blocks are divided into four categories due to four corresponding embedding strategies aiming at preserving the medians during data embedding in decoder the median pixels are retrieved first followed by the hidden data extraction and the host image can be accurately recovered via an inverse histogram shifting mechanism after removing the secret data from the marked image experimental results validate the effectiveness of our scheme and demonstrate that it outperforms several previous methods in terms of capacity and marked image s quality

lsb steganographic method based on reversible histogram transformation function for resisting statistical steganalysis statistical steganalysis schemes detect the existence of secret information embedded by steganography the x 2 detection and regular singular rs attack methods are two well known statistical steganalysis schemes used against lsb least significant bit steganography the embedded message length can be estimated accurately by these two steganalysis schemes for secret communication the resistance of steganography against steganalysis is very important for information security to avoid the enemy s attempts the statistical features between stego images and cover images should be as similar as possible for better resistance to steganalysis in this manuscript a reversible histogram transformation function based lsb steganographic method is proposed to resist statistical steganalysis the experimental results show that the proposed method resists not only rs attack but also x 2 detection methods

aerodynamic design optimization using sensitivity analysis and computational fluid dynamics a new and efficient method is presented for aerodynamic design optimization which is based on a computational fluid dynamics cfd sensitivity analysis algorithm the method is applied to design a simplified scramjet afterbody configuration for an optimized axial thrust the euler equations are solved for the inviscid analysis of the flow which provides the objective function and the constraints of the optimization problem the cfd analysis is then coupled with the optimization procedure that used a constrained minimization method the sensitivity coefficients i e gradients of the objective function and the constraints needed for the optimization are obtained using a quasi analytic al method rather than the traditional finite difference approximations during the one dimensional search of the optimization procedure an approximate flow analysis predicted flow based on a first order taylor series expansion is used to reduce the computational cost finally the sensitivity of the optimum objective function to various flowfield problem parameters such as the mach number which are kept constant during the optimization is computed to predict new optimum solutions the flow analysis of the demonstrative example are compared with the experimental data it is shown that the method is more efficient than the traditional methods

problem formulation for multidisciplinary optimization this paper is about multidisciplinary design optimization or mdo the coupling of two or more analysis disciplines with numerical optimization the paper has three goals first it is an expository introduction to mdo aimed at those who do research on optimization algorithms since the optimization community has much to contribute to this important class of computational engineering problems second this paper presents to the mdo research community a new abstraction for multidisciplinary analysis and design problems as well as new decomposition formulations for these problems third the individual discipline feasible idf approaches introduced here make use of existing specialized analysis codes and they introduce significant opportunities for coarse grained computational parallelism particularly well suited to heterogeneous computing environments the key distinguishing characteristic of the three fundamental approaches to mdo formulation discussed here is the kind of disciplinary feasibility that

sensitivity analysis of the aeroacoustic response of turbomachinery blade rows a method for computing the change or sensitivity of the aeroacoustic response of a cascade to small changes in airfoil and cascade geometry is presented the steady flow is modeled by the full potential equation which is discretized using a variational finite element technique a streamline computational grid is generated as part of the steady solution newton iteration is used to solve for the nonlinear steady flow and grid equations with lower upper lu matrix decomposition plus one forward and one back substitution used to solve the resulting matrix equations similarly the unsteady small disturbance flow about the nonlinear mean flow is modeled by the linearized potential equation together with rapid distortion theory to account for vortical gusts these linearized equations are discretized using finite elements and solved with a single lu decomposition the sensitivities of the steady and unsteady flowfields to small changes in geometry are computed by perturbing the discretized equations about the nominal solutions the resulting linear system of equations can be solved very efficiently because the lu factors of the resulting matrix equations are computed as part of the nominal steady and unsteady solution results are presented in this paper to show the accuracy and efficiency of the method and the implications for aeroacoustic design of turbomachinery blades are discussed

an efficient feasible directions algorithm for design synthesis a nonlinear optimization algorithm is described that combines the best features of the method of feasible directions and the generalized reduced gradient method the algorithm uses the direction finding subproblem from the method of feasible directions to find a search direction that is equivalent to that of the generalized reduced gradient method but without the need to add a large number of slack variables associated with inequality constraints this leads to a core efficient algorithm for the solution of optimization problems with a large number of inequality constraints also during the one dimensional search it is not necessary to separate the design space into dependent and independent variables using the present method the concept of infrequent gradient calculations is introduced as a means of gaining further optimization efficiency finally it is shown that using the basic direction finding algorithm contained in this method the sensitivity of the optimum design with respect to problem parameters can be obtained without the need for second derivatives or lagrange multipliers the optimization algorithm and sensitivity analysis is demonstrated by numerical example

adaptive lossless steganographic scheme with centralized difference expansion in this paper a novel adaptive lossless data hiding scheme is presented that is capable of offering greater embedding capacity than the existing schemes unlike the fixed hiding capacity each block provides in most of the currently available lossless data hiding approaches the proposed method utilizes a block based lossless data embedding algorithm where the quantity of the hidden information each block bears is variable to both reduce the image distortion and increase the hiding capacity the payload of each block depends on its cover image complexity due to the fact that schemes with difference expansion tend to damage the image quality seriously in the edge areas in the proposed scheme smoother areas are chosen to conceal more secret bits this way a better balance can be reached between the embedding ratio and the stego image quality in addition when recovered the cover image can came back to its old self to the last bit without any distortion at all experimental results as this paper will show have demonstrated that the proposed method is capable of hiding more secret data while maintaining imperceptible stego image quality degradation

comparison of newton s and quasi newton s method solvers for the navier stokes equations the results of a computational evaluation of several newton s and quasi newton s method solvers are discussed and analyzed computer time and memory requirements for iterating a solution to the steady state are recorded for each method roe s flux difference splitting together with the spekreijse van albada continuous limiter is used for the spatial discretization sparse matrix inversions are performed using a modified version of the boeing real sparse library routines and the conjugate gradient squared algorithm the methods are applied to exact and approximate newton s method jacobian systems for flat plate and flat plate wedge type ge ometries results indicate that the quasi newton s method solvers do not exhibit quadratic convergence but can be more efficient than the exact newton s method in select cases consistent goal of computational fluid dynamics cfd research has been to improve the efficiency of numerical algorithms one measure of this efficiency is the log of the residual which varies linearly with iteration count for typical cfd techniques these methods can be expected to converge at the same rate no matter how close they are to the final solution an exception to this behavior is the quadratic convergence newton s method for which the convergence rate actually increases as the final solution is approached when quadratic convergence has been attained the number of cor rect digits in the solution doubles with each iteration this behavior has been illustrated by several researchers who have obtained solutions of the potential equation 1 the euler equa tions 2 5 and the navier stokes equations 2 4 6 13 unfortu nately the number of iterations is a less important measure of the efficiency of a code than the total computation time quadratic convergence rates are typically accompanied by significant increases in algorithm complexity and hence in creased per iteration computational requirements it was the intent of this research to explore how the conver gence rate and per iteration efficiency vary for similar new ton s and quasi newton s method solvers so that the most efficient computational strategy can be identified to accom plish this goal the quadratic convergence newton s method solver developed by orkwis and mcrae6 8 was modified to create several quasi newton s method solvers approxima tions were made to the form of the jacobian and to the jacobian matrix inversion process the resulting schemes are evaluated based on their robustness and efficiency for two test problems

three dimensional adaptive grid method a three dimensional solution adaptive grid scheme is described which is suitable for complex fluid flows this method using tension and torsion spring analogies was previously developed and successfully applied for two dimensional flows in the present work a collection of three dimensional flow fields are used to demonstrate the feasibility and versatility of this concept to include an added dimension flow fields considered include 1 supersonic flow past an aerodynamic afterbody with a propulsive jet at incidence to the free stream 2 supersonic flow past a blunt fin mounted on a solid wall and 3 supersonic flow over a bump in addition to generating three dimensional solution adapted grids the method can also be used effectively as an initial grid generator the utility of the method lies in 1 optimum distribution of discrete grid points 2 improvement of accuracy 3 improved computational efficiency 4 minimization of data base sizes and 5 simplified three dimensional grid generation

high performance jpeg steganography using complementary embedding strategy a high performance jpeg steganography should be secure enough to resist modern steganalysis in this paper we propose a high performance jpeg steganographic method the proposed method adopts the complementary embedding strategy to avoid the detections of several statistical attacks to show the effectiveness of the proposed method several statistical attacks are simulated and used to detect the stego images created by the proposed method several famous jpeg steganographic algorithms are also simulated for comparisons with the proposed method experimental results show that the proposed steganographic method has superior performance both in capacity and security and is practical for the application of secret communication

probabilistic diffusion tractography with multiple fibre orientations what can we gain we present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations using automatic relevance determination we are able to perform online selection of the number of fibre orientations supported by the data at each voxel simplifying the problem of tracking in a multi orientation field we then apply the identical probabilistic algorithm to tractography in the multi and single fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single fibre tractography we show that multi fibre tractography offers significant advantages in sensitivity when tracking non dominant fibre populations but does not dramatically change tractography results for the dominant pathways

wavelet based copyright protection scheme for digital images based on local features a lossless robust copyright protection scheme for digital images based on cryptography and watermarking is proposed in the proposed wavelet based scheme the logo image is not embedded into the protected image the secret key is generated during the embedding process using local features extracted from the perceptually prominent components of the host image after the digital wavelet transform digital signature and time stamping technologies are then used for further protection with the secret key the logo image extraction process can be completed without the host image experimental results show that the proposed scheme is effective and robust against common image processing and geometric distortions

a reduced hessian method for large scale constrained optimization we propose a quasi newton algorithm for solving large optimization problems with nonlinear equality constraints it is designed for problems with few degrees of freedom and is motivated by the need to use sparse matrix factorizations the algorithm incorporates a correction vector that approximates the cross term z t wy p y in order to estimate the curvature in both the range and null spaces of the constraints the algorithm can be considered to be in some sense a practical implementation of an algorithm of coleman and conn we give conditions under which local and superlinear convergence is obtained

reversible data embedding into images using wavelet techniques and sorting the proliferation of digital information in our society has enticed a lot of research into data embedding techniques that add information to digital content like images audio and video in this paper we investigate high capacity lossless data embedding methods that allow one to embed large amounts of data into digital images or video in such a way that the original image can be reconstructed from the watermarked image we present two new techniques one based on least significant bit prediction and sweldens lifting scheme and another that is an improvement of tian s technique of difference expansion the new techniques are then compared with various existing embedding methods by looking at capacity distortion behavior and capacity control

three dimensional aerodynamic shape optimization using discrete sensitivity analysis an aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three dimensional geometries the function of sensitivity analysis is to directly couple computational fluid dynamics cfd with numerical optimization techniques which facilitates the construction of efficient direct design methods the development of a practical three dimensional design procedures entails many challenges such as 1 the demand for significant efficiency improvements over current design methods 2 a general and flexible three dimensional surface representation and 3 the efficient solution of very large systems of linear algebraic equations it is demonstrated that each of these challenges is overcome by 1 employing fully implicit newton methods for the cfd analyses 2 adopting a bezier bernstein polynomial parameterization of two and three dimensional surfaces and 3 using preconditioned conjugate gradient like linear system solvers whereas each of these extensions independently yields an improvement in computational efficiency the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use the new aerodynamic shape optimization procedure is demonstrated in the design of both two and three dimensional inviscid aerodynamic problems including a two dimensional supersonic internal external nozzle two dimensional transonic airfoils resulting in supercritical shapes three dimensional transport wings and three dimensional supersonic delta wings each design application results in realistic and useful optimized shapes

self adaptive grid method with application to airfoil flow a self adaptive grid method that is suitable for multidimensional steady and unsteady computations is described based on variational principles a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error user specified parameters denoting both maximum and minimum permissible grid spacings are used to define the all important constants thereby minimizing the empiricism and making the method self adaptive operator splitting and one sided controls for orthogonality and smoothness are used to make the method practical robust and efficient examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions as well as for a steady inviscid flow computation and a one dimensional case these examples illustrate the precise control the user has with the self adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions

a bayesian approach for stochastic white matter tractography white matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging mri images in this paper a novel bayesian modeling approach for white matter tractography is presented the uncertainty associated with estimated white matter fiber paths is investigated and a method for calculating the probability of a connection between two areas in the brain is introduced the main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way theory for estimating global connectivity is also presented as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile

a comparison of optimization based approaches for a model computational aerodynamics design problem abstract the objective of this paper is to compare three optimization based methods for solving aerodynamic design problems we use the euler equations for one dimensional duct flow as a model problem the optimization methods are i the black box method with finite difference gradients ii a modification where gradients are found by an algorithm based on the implicit function theorem and iii an all atonce method where the flow and design variables are simultaneously altered the three methods are applied to the model problem and compared for efficiency robustness and implementation difficulty we also show that the black box implicit gradient method is equivalent to applying the variational or optimal control approach to design optimization directly to the discretized analysis problem rather than to the continuous problem as is usually done the black box method with implicit gradients seems to provide a good compromise of features and can be retrofitted to most existing analysis codes to turn them into design codes although the all at once method was found to be less robust than the black box methods when it succeeded it was considerably more efficient

optimal shape design of a two dimensional asymmetric diffuser in turbulent flow an optimal shape of two dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm the initial diffuser is taken to be a two dimensional asymmetric diffuser for which much experimental and numerical data are available the reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1 8 10 4 f rom this initial shape optimal diffuser shapes are designed for six different geometric constraints such as the streamwise length and height of the diffuser the optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall the turbulent flow inside the diffuser is predicted using the k v2 f model and optimal shapes are obtained through iterative procedures to satisfy the optimality condition with the shape design flow separation that appeared in the initial diffuser is completely removed or significantly reduced for one of the optimal diffuser shapes obtained large eddy simulation is carried out to validate the result of the shape design the wall shear stress wall pressure mean velocity and turbulence quantities obtained from large eddy simulation are in good agreement with those from the simulation using the turbulence model

a reversible data hiding scheme using complementary embedding strategy obtaining good visual quality and high hiding capacity with reversible data hiding systems is a technically challenging problem in this paper we propose a simple reversible data hiding scheme that uses a complementary hiding strategy the proposed method embeds one secret bit horizontally and vertically into one cover pixel of a grayscale cover image by decreasing odd valued pixels and increasing even valued pixels by one experimental results show that the hiding capacity measured by bit per pixel bpp of the proposed scheme is at least 1 21bpp with a psnr peak signal to noise ratio value greater than 52db for all standard test images especially in the case of four layer embedding the psnr value of the proposed method is still greater than 51db at a hiding capacity of about 5bpp for all standard test images in addition the proposed method is quite simple because it primarily uses additions and subtractions these results indicate that the proposed scheme is superior to many existing reversible data hiding schemes introduced in the literature

cfd shape optimization using an incomplete gradient adjoint formulation a design methodology based on the adjoint approach for flow problems governed by the incompressible euler equations is presented the main feature of the algorithm is that it avoids solving the adjoint equations which saves an important amount of cpu time furthermore the methodology is general in the sense it does not depend on the geometry representation all the grid points on the surface to be optimized can be chosen as design parameters in addition the methodology can be applied to any type of mesh the partial derivatives of the flow equations with respect to the design parameters are computed by finite differences in this way this computation is independent of the numerical scheme employed to obtain the flow solution once the design parameters have been updated the new solid surface is obtained with a pseudo shell approach in such a way that local singularities which can degrade or inhibit the convergence to the optimal solution are avoided some 2d and 3d numerical examples are shown to demonstrate the proposed methodology copyright 2001 john wiley sons ltd

algorithm developments for discrete adjoint methods this paper presents a number of algorithm developments for adjoint methods using the discrete approach in which the discretisation of the non linear equations is linearised and the resulting matrix is then transposed with a new iterative procedure for solving the adjoint equations exact numerical equivalence is maintained between the linear and adjoint discretisations the incorporation of strong boundary conditions within the discrete approach is discussed as well as a new application of adjoint methods to linear unsteady flow in turbomachinery

lossless data hiding for vq indices based on neighboring correlation data hiding is one of the protective techniques for authentication or secret communication through a public and open channel such as the internet in this study a novel lossless data hiding by embedding secret data into a vector quantization vq compressed image is proposed to achieve secret communication and data compression simultaneously the correlation of neighboring blocks of a vq compressed image is explored it is shown that the neighboring blocks of a vq compressed image normally have high mutual correlation thus this scheme employs the neighboring processed compression indices to generate specific sub codebooks required for encoding and hiding data simultaneously since the sizes of sub codebooks are smaller than that of the original vq codebook the encoded size of each index can be significantly reduced as a result a great deal of extra free space can be created moreover the original vq compressed images can be perfectly recovered after data extraction to evaluate the effectiveness of this approach various test images are employed in the experiments as documented in the experimental results it is shown that the performance of the proposed scheme is superior to the former schemes in terms of compression ratio embedding rate execution time and embedding capacity

filtered multitensor tractography we describe a technique that uses tractography to drive the local fiber model estimation existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit we formulate fiber tracking as recursive estimation at each step of tracing the fiber the current estimate is guided by those previous to do this we perform tractography within a filter framework and use a discrete mixture of gaussian tensors to model the signal starting from a seed point each fiber is traced to its termination using an unscented kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction despite the presence of noise and uncertainty this provides a causal estimate of the local structure at each point along the fiber using two and three fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings in vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

using an adjoint approach to eliminate mesh sensitivities in computational design an adjoint algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced the method eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables an expense that has hindered large scale design optimization for practical applications the effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation followed by an explicit matrix vector product whose cost scales with the number of design variables and the resolution of the parameterized surface grid the methodology augments the current practice of using adjoints solely for the flowfield and leads to a dramatic computational savings the accuracy of the implementation is established and several sample design optimizations are shown

efficient aerodynamic design method using a tightly coupled algorithm an efe cient aerodynamic design optimization method for the compressible euler equations is presented a gradient based optimization method is used to e nd the optimal design in conjunction with a continuous adjoint sensitivity analysis method to improve the efe ciency of the design method a tightly coupled algorithm based on a step size estimation isproposed the efe ciency of thepresentmethod is demonstrated through drag minimizations of a wing and an airfoil the result shows that the cost of the present method is signie cantly lower than that of the loosely coupled algorithm nomenclature ci e ux jacobian matrix in the computational domain d design variables vector fi e ux vector in the computational domain fi e ux vector in the physical domain g gradient vector of the object function i object function q conservative e ow variables vector r residual vector in the computational domain s searching direction step size along the searching direction s a lagrangian multiplier vector subscript face value at cell face superscript t transpose of vector or matrix

mesh movement for a discrete adjoint newton krylov algorithm for aerodynamic optimization a grid movement algorithm based on the linear elasticity method with multiple increments is presented the methodisrelativelycomputationallyexpensivebutisexceptionallyrobust producinghigh qualityelementsevenfor large shape changes it is integrated with an aerodynamic shape optimization algorithm that uses an augmented adjoint approach for gradient calculation the discrete adjoint equations are augmented to explicitly include the sensitivities of the mesh movement resulting in an increase in efficiency and numerical accuracy this gradient computation method requires less computational time than a function evaluation and leads to significant computational savings as dimensionality is increased the results of the application of these techniques to several large deformation and optimization cases are presented

space marching calculations about hypersonic configurations using a solution adaptive mesh algorithm a solution adaptive marching algorithm is developed and applied to a three dimensional parabolized navierstokes equation solver the resulting algorithm obtains accurate solutions by using a spatial marching adaptivegrid procedure the adaptation step redistributes grid points line by line in both crossflow directions with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions the solution adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations the first of these is an all body type geometry with elliptical cross sections and is studied at angles of attack of 0 5 and 15 deg the second geometry is a generic blended vv ing body design results are presented that demonstrate the improvements in flow field resolution obtainable with the solution adaptive marching procedure over conventional fixed grid techniques computed pitot pressure profiles obtained using the solution adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid

parametric spherical deconvolution inferring anatomical connectivity using diffusion mr imaging the human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail even at the macroscopic level the advent of diffusion mr imaging has enabled the exploration of the structural properties of white matter in vivo in this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water diffusion process and further onto the measured mr signals our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of bingham distributions in addition we define the term anatomical connectivity taking the underlying image modality into account this neurophysiological metric may represent the proportion of the nerve fibers originating in the source area which intersect a given target region the specified inverse problem is solved by bayesian statistics posterior probability maps denote the probability that the connectivity value exceeds a chosen threshold conditional upon the noisy observations these maps allow us to draw inferences about the structural organization of the cerebral cortex moreover we will demonstrate the proposed approach with diffusion weighted data sets featuring high angular resolution

continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes a continuous adjoint approach is developed to obtain the sensitivity derivatives for the euler equations the completederivationofthecostateequations andtheirtransversality boundary conditionsarepresented both the state and the costate equations are second order e nite volume discretized for unstructured meshes and they are coupled with a constrained optimization algorithm also integrated into the overall methodology are a geometry parameterization method for the shape optimization and a dynamic unstructured mesh method for the shape evolution and the consequent volume mesh adaptations for the proof of concept three transonic airfoil optimization problems are presented this method accepts general cost functionals which are not necessarily functions of pressure only it is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivativesof the state variables thisapproach eliminates the need fornormal derivativecomputations that can be erroneous

a numerical approach for shape optimization of fluid flow domains abstract a numerical method for the shape optimization of fluid flow domains is presented and analyzed the procedure is based on a flow solver a mathematical optimization tool and a technique for shape variation which are combined into an integrated procedure the flow solver relies on the discretization of the incompressible navier stokes equations by means of the finite volume method for block structured boundary fitted grids with multi grid acceleration the optimization tool is an implementation of a trust region based derivative free method it is designed to minimize smooth functions whose evaluations are considered expensive and whose derivatives are not available or not desirable to approximate the shape variation is obtained by deforming the computational grid employed by the flow solver for this purpose displacement fields scaled by the design variables are added to the initial grid the displacement vectors are computed once before starting the optimization cycle by using a free form deformation technique applications illustrating the functionality and the properties of the method are presented for some examples of engineering interest such as the minimization of a pressure drop the maximization of a lift force and the optimization of a wall temperature

a path optional lossless data hiding scheme based on vq joint neighboring coding data hiding is an important technique for covert communication that embeds secret data into a cover image with minimal perceptible degradation lossless data hiding is a special type of data hiding technique that guarantees not only the secret data but the cover media can be reconstructed without any distortion in this paper a novel path optional lossless data hiding scheme based on the joint neighboring coding jnc of the vector quantization vq index table is proposed the proposed scheme generates a vq index table based on the cover image first next according to an initial key and secret data content different adjacent indices may be chosen to perform joint neighboring coding for each index and hide secret data finally an appropriate output codestream is generated based on the minimal length principle our main contributions lie in three aspects 1 the method combines the novel path based shift method with the traditional jnc method to improve the capacity and stego image quality simultaneously 2 the secret data extraction and cover image recovering processes are separated and both can be publicized to users 3 the method is path optional to meet various users requirements to testify the superiority of the proposed method we compare it with the side match vq smvq based and modified fast correlation vq mfcvq based algorithms according to the experimental results the proposed scheme outperforms the smvq based and mfcvq based algorithms in four aspects i e hiding capacity stego image quality transmission efficiency and security level

digital watermarking based on chaotic map and reference register in this paper we present a new digital watermarking technique based on chaotic map and reference register rr we develop a block based chaotic map which outperforms the traditional one by breaking local spatial similarity to increase the amount of significant coefficients in the transformed image a rr is then employed to locate specific coefficients of a container efficiently for watermark embedding and extraction we demonstrate the superiority of the proposed scheme in terms of better embedding capacity and lower message error rate furthermore we show the proposed algorithm works well under some image processing distortions such as the jpeg compression gaussian noise and low pass filter

resolution of complex tissue microarchitecture using the diffusion orientation transform dot this article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion weighted magnetic resonance mr data this novel approach utilizes the fourier transform relationship between the water displacement probabilities and diffusion attenuated mr signal expressed in spherical coordinates the radial part of the fourier integral is evaluated analytically under the assumption that mr signal attenuates exponentially the values of the resulting functions are evaluated at a fixed distance away from the origin the spherical harmonic transform of these functions yields the laplace series coefficients of the probabilities on a sphere of fixed radius alternatively probability values can be computed nonparametrically using legendre polynomials orientation maps calculated from excised rat nervous tissue data demonstrate this technique s ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm this proposed methodology has a trivial extension to multiexponential diffusion weighted signal decay the developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

aerodynamic shape optimization using preconditioned conjugate gradient methods in an effort to further improve upon the latest advancements made in aerodynamic shape optimization procedures a systematic study is performed to examine several current solution methodologies as applied to various aspects of the optimization procedure it is demonstrated that preconditioned conjugate gradient like methodologies dramatically decrease the computational efforts required for such procedures the design problem investigated is the shape optimization of the upper and lower surfaces of an initially symmetric naca 0012 airfoil in inviscid transonic flow and at zero degrees angle of attack the complete surface shape is represented using a bezier bernstein polynomial

design sensitivity analysis and optimization of nonlinear structuralresponse using incremental procedure this paper describes procedures for design sensitivity analysis of nonlinear structural response using the incremental solution scheme the total and updated lagrangian approaches are discussed sensitivity analyses for the stress strain and displacement constraints are developed in the optimization process the buckling load constraint is also imposed numerical aspects of design sensitivity analysis are discussed three numerical examples are solved to illustrate the design sensitivity analysis and optimization process the numerical procedures are stable and work well they can be applied to more complex structures to optimize them

intelligent reversible watermarking and authentication hiding depth map information for 3d cameras in this paper we propose an application for 3d cameras by reversibly hiding the depth map in the corresponding 2d images the proposed technique is prospective in cameras capable of capturing simultaneously the 2d image and resultant depth map of an object 3d cameras equipped with self embedding capability can serve two additional purposes protection of the captured image and secure transmission of its depth map the reversible watermarking in addition to other features guarantees the lossless recovery of an original image and separation of its depth map when required for this purpose a reversible watermarking scheme based on genetic algorithm ga has been proposed which computes suitable threshold for each block of coefficients in the wavelet domain thus a tradeoff is made between watermark imperceptibility and capacity using ga the threshold map is embedded in addition to the actual payload and thus the proposed approach does not require histogram pre processing in order to avoid overflow underflow the same threshold map has been used for authentication purpose by correlating it with the low frequency coefficients of the 2d transformed image further to exploit the inherent redundancy in the depth map which is the actual payload in this case lossless compression has been employed before its embedding similarly besides secret key based permutation a cryptographic layer is overlaid on the watermarking layer for security purposes experiments conducted on images and depth maps obtained using a 3d camera and an optical microscopic system validate the proposed concept

shape optimization for delay of laminar turbulent transition a method using gradient based optimization is introduced for the design of wing profiles with the aim of natural laminar flow as well as minimum wave drag the euler equations of gasdynamics the laminar boundary layer equations for compressible flows on infinite swept wings and the linear parabolized stability equations pse are solved to analyze the evolution of convectively unstable disturbances laminar turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance which is computed using the pse the shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named numerical tests are carried out to optimize the rae 2822 airfoil with the aim to delay simultaneously the transition reduce the pressure drag coefficient and maintain the coefficients of lift and pitch moments constraints are also applied on the geometry results show a reduction of the total amplification of a large number of disturbances which is assumed to represent a delay of the transition in the boundary layer because delay of the transition implies reduction of the viscous drag the present method enables shape optimization to perform viscous drag reduction

infeasible path optimal design methods with applications to aerodynamic shape optimization we consider optimal design of physical systems described by a nonlinear boundary value problem we propose a sequential quadratic programming method specifically tailored to the solution of this class of design problems a particular representation of the null space of the constraint jacobian that exploits its specific structure is employed the resulting method avoids resolution of nonlinear behavior at the optimization iterations while keeping the size of the problem as small as that of conventional approaches three variants of the method are developed and discussed these entail the solution of either two or three linear systems involving the jacobian matrix of the discretized form of the boundary value problem the method is used to solve aerodynamic design problems involving nonlinear transonic flow no special provisions are made for treating discontinuities and therefore the present implementation of the method is limited to problems with no shocks problems with up to 90 shape design variables are solved numerical results demonstrate a substantial performance improvement over conventional methods

optimized nonuniform rational b spline geometrical representation for aerodynamic design of wings the geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation in an attempt to reduce the number of design variables while preserving good smoothness properties the present research investigates the performance of an optimized nonuniform rational b spline nurbs geometrical representation for the aerodynamic design of wings as a first step an approach is described whereby optimal spatial positions and weights of a fixed number of nurbs control points is determined using a quasi newton optimization algorithm to approximate a general airfoil section the resulting optimized nurbs representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties in a second step the nurbs control point positions and weights are used as design variables in an aerodynamic optimization problem this methodology results in a rapid and robust design process as illustrated by examples of aerodynamic optimization for two and three dimensional cases

multigrid and upwind viscous flow solver on three dimensional overlapped and embedded grids a computationally efficient method is presented for solving the three dimensional governing equations of the viscous compressible flows about complex configurations with geometrically nonsimilar components the physical domain is decomposed into regions for which the grid generation is relatively simple and virtually without significant restrictions the navier stokes equations are solved by an implicit upwind finite volume scheme the convergence is accelerated by a multigrid algorithm despite the holes created in the computational domain by the overlapped grids which are completely or partially embedded within one another the block inversions and the diagonalized scalar inversions of the coefficient matrices are modified to allow the existence of such holes the method is tested through two demonstrative csises the solution for a supersonic flow past a blunt nose cylinder at a high angle of attack is obtained using a c o grid embedded in a global cartesian grid this solution is successfully compared with the one obtained using a single c o grid and the experimental data then supersonic interference flows past an ogive nose cylinder in the close proximity of a flat plate are solved using overlapped and topologically nonsimilar but simple grids

a lossless data hiding scheme based on three pixel block differences this paper proposes a data hiding scheme that losslessly embeds a message into a cover image using the two differences between the first and the second pixel as well as between the second and the third pixel in a three pixel block in the cover image an absolute difference between a pair of pixels is selected to embed the message if the number of pixel pairs with the difference in the image is the largest to embed a bit 1 or 0 the selected difference is increased by 1 or left unchanged respectively in the best case a three pixel block can embed two bits 11 and only the central pixel needs to be increased or decreased by 1 the average payload capacity among the test images can be up to 2 08 bits per pixel bpp

geometrically invariant image watermarking using polar harmonic transforms this paper presents an invariant image watermarking scheme by introducing the polar harmonic transform pht which is a recently developed orthogonal moment method similar to zernike moment zm and pseudo zernike moment pzm approaches pht is defined on a circular domain the magnitudes of phts are invariant to image rotation and scaling furthermore the phts are free of numerical instability so they are more suitable for watermarking in this paper the invariant properties of phts are investigated during embedding a subset of the accurate phts are modified according to the binary watermark sequence then a compensation image is formatted by reconstructing the modified pht vector the final watermarked image is obtained by adding the compensation image to the original image in the decoder the watermark can be retrieved from the magnitudes of the phts directly experimental results illustrate that the proposed scheme outperforms zm pzm based schemes in terms of embedding capacity and watermark robustness and is also robust to both geometric and signal processing based attacks

sensitivity analysis of unsteady aerodynamic loads in cascades a method for computing the effect perturbations in the shape of airfoils in a cascade have on the steady and unsteady flow through the cascade is presented first the full potential equation is used to describe the behavior of the nonlinear steady flow and the small disturbance unsteady flow through the cascade the steady flow and small disturbance unsteady flow versions of the full potential equation are then discretized on a computational grid of quadrilateral cells using a variational finite element technique the resulting discretized equations describing the nonlinear steady flow are solved using newton iteration with lower upper decomposition at each iteration similarly the discretized unsteady small disturbance equations which are linear are solved using a single lower upper decomposition next a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the steady and unsteady flowfields the sensitivity analysis makes use of the nominal steady and unsteady flow lower upper decompositions so that no additional matrices need to be factored hence the present method is computationally very efficient

an approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives in this study involving advanced fluid flow codes an incremental iterative formulation also known as the delta or correction form together with the well known spatially split approximate factorization algorithm is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis for smaller 2d problems a direct method can be applied to solve these linear equations in either the standard or the incremental form in which case the two are equivalent iterative methods are needed for larger 2d and future 3d applications however because direct methods require much more computer memory than is currently available iterative methods for solving these equations in the standard form are generally unsatisfactory due to a lack of diagonal dominance and perhaps ill conditioning of the coefficient matrix this problem can be overcome when these equations are cast in the incremental form these and other benefits are discussed herein the methodology is successfully implemented and tested in 2d using an upwind cell centered finite volume formulation applied to the thin layer navier stokes equations results are presented for two sample airfoil problems 1 subsonic low reynolds number laminar flow and 2 transonic high reynolds number turbulent flow

a bayesian framework for global tractography we readdress the diffusion tractography problem in a global and probabilistic manner instead of tracking through local orientations we parameterise the connexions between brain regions at a global level and then infer on global and local parameters simultaneously in a bayesian framework this approach offers a number of important benefits the global nature of the tractography reduces sensitivity to local noise and modelling errors by constraining tractography to ensure a connexion is found and then inferring on the exact location of the connexion we increase the robustness of connectivity based parcellations allowing parcellations of connexions that were previously invisible to tractography the bayesian framework allows a direct comparison of the evidence for connecting and non connecting models to test whether the connexion is supported by the data crucially by explicit parameterisation of the connexion between brain regions we infer on a parameter that is shared with models of functional connectivity this model is a first step toward the joint inference on functional and anatomical connectivity

a novel high capacity data embedding system in this paper we present a novel data embedding system with high embedding capacity the embedding algorithm is based on the quantized projection embedding method with some enhancement to achieve high embedding rates in particular our system uses a random permutation of the columns of a hadamard matrix as projection vectors and a fixed perceptual mask based on the jpeg default quantization table for the quantization step design as a result the data embedding system achieves 1 167 1 bit out of 167 raw image bits to 1 84 hiding ratios with a ber of around 0 1 in the presence of jpeg compression attacks while maintaining visual distortion at a minimum

adaptive embedding techniques for vq compressed images an embedding algorithm which can adaptively embed a binary message into a vq compressed image is proposed in this paper the proposed algorithm is divided into three phases in the codeword grouping phase a new group of codewords is initiated by the two most similar codewords which do not belong to any group for each codeword which does not belong to any group if the codeword is similar to all of the codewords in the group it will be added to the group in the embedding phase each codeword in a group will be assigned to embed a certain sub message whose length is determined by the number of codewords in the group the more codewords a group has the higher the embedding capacity of a codeword in the group will be in the extracting phase given a codeword and the number of codewords in the group to which the codeword belongs the embedded message can be extracted from the codeword by simply determining the order of the codeword in the group experimental results show that the proposed algorithm performs better than previous algorithms with regard to embedding capacity and image quality for the test images when the embedding capacity is less than 5bits per codeword index the difference of the psnr values between the stego image and its vq compressed cover image will be no more than 5db on average

expansion embedding techniques for reversible watermarking reversible watermarking enables the embedding of useful information in a host signal without any loss of host information tian s difference expansion technique is a high capacity reversible method for data embedding however the method suffers from undesirable distortion at low embedding capacities and lack of capacity control due to the need for embedding a location map we propose a histogram shifting technique as an alternative to embedding the location map the proposed technique improves the distortion performance at low embedding capacities and mitigates the capacity control problem we also propose a reversible data embedding technique called prediction error expansion this new technique better exploits the correlation inherent in the neighborhood of a pixel than the difference expansion scheme prediction error expansion and histogram shifting combine to form an effective method for data embedding the experimental results for many standard test images show that prediction error expansion doubles the maximum embedding capacity when compared to difference expansion there is also a significant improvement in the quality of the watermarked image especially at moderate embedding capacities

reduction of the adjoint gradient formula for aerodynamic shape optimization problems we present a new continuous adjoint method for aerodynamic shape optimization using the euler equations which reduces the computational cost of the gradients by reducing the volume integral part of the adjoint gradient formula to a surface integral the savings are particularly significant for three dimensional aerodynamic shape optimization problems on general unstructured and overset meshes to validate the concept the new gradient equations have been tested for various aerodynamic shape optimization problems including an inverse problem for three dimensional wing configurations and drag minimization problems of a single element airfoil and a three dimensional wing fuselage configuration

efficient reversible data hiding for color filter array images a reversible data hiding algorithm which uses prediction errors in the color difference domain for mosaic images with the bayer color filter array cfa is proposed furthermore the proposed algorithm can be extended to deal with the digital time delay and integration dtdi mosaic images and lukac and plataniotis lp mosaic images experimental results on cfa dtdi and lp mosaic images demonstrate that the proposed algorithm can achieve high embedding capacity while maintaining good image quality

solution adaptive grid procedure for high speed parabolic flow solvers a solution adaptive grid procedure based bn an error equidistribution scheme is developed and applied to a parabolized navier stokes solver an improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point the scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability a grid fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure

visual exploration of hardi fibers with probabilistic tracking high angular resolution diffusion imaging hardi is an effective method for characterizing complex neural fiber paths in the human brain however visualizing and analyzing the fibers is often challenging because of the complexity of the fiber orientation distribution function used to describe the crossing kissing and fanning fibers in this paper we propose a novel visual analytics approach to study brain fiber paths that allows users to explore fiber bundles to reveal the probability of fiber paths using a new visual classification method first we use a spherical deconvolution model for diffusion estimation and a bayesian theorem for fiber tractography second each fiber is subjected to a cluster analysis using pixel based visual encoding this result is shown in a pixel based visual representation where each pixel bar maps opacity color and length to the probability direction and length of a fiber fiber bundles can then be acquired via a two step classification routine that uses dbscan to group fibers based on similarities then the user can further refine fiber bundle selection using probabilistic information from the pixel bars therefore the proposed approach shows not only the shape but also the confidence of the fiber paths we demonstrate the resulting hardi fiber bundles and compare a brain with tumor and normal brain using our system experiments and an empirical user study verify the effectiveness of our approach

sparse approach to simultaneous analysis and design of geometricallynonlinear structures this method to increase the efficiency of the opimization process for nonlinear structures considers the equilibrium equations as equality constraints of the nonlinear mathematical programming problem

use of analytical flow sensitivities in static aeroelasticity modern computational fluid dynamics tools can be used to predict sensitivities for flows encountered by aircraft and missiles throughout the flight regime in this study we describe one important multidisciplinary application of aerodynamic sensitivity analysis namely the coupling of the aerodynamic sensitivities with a structural dynamics analysis and optimization code

nonlinear programming via an exact penalty function asymptotic analysis in this paper we consider the final stage of a global method to solve the nonlinear programming problem we prove 2 step superlinear convergence in the process of analyzing this asymptotic behavior we compare our method theoretically to the popular successive quadratic programming approach

integrated nonlinear structural analysis and design proposition d une approche integree de l optimisation de structures mecaniques necessitant une analyse non lineaire le processus d optimisation part d une reponse linearisee de la structure les non linearites etant introduites au fur et a mesure de la convergence verification de la reduction du cout de l analyse par cette methode traitement de deux exemples de structure en treillis

an intelligent chaotic embedding approach to enhance stego image quality steganography s role in secret communication extends from concealing information to communication as one of several possible approaches to embed confidential information in digital images the least significant bit lsb technique has been widely used however maintaining the imperceptibility of the stego image is still a serious concern in this paper an adaptive random ar k bit embedding approach has been attempted to enhance the quality of stego images the original cover is divided into nonoverlapping blocks of equal size the encrypted confidential data are embedded in each block through four different random walks the best random walk which provides the minimum degradation for a particular block is identified and is fixed for that block the decision on the fixed random walk for each block is recorded and kept as the secret key the ar method has also been combined with the inverted pattern approach referred to as the adaptive random inverted pattern arip approach to further enhance the quality of the stego image the estimated peak signal to noise ratio psnr value for the arip method yields 1db enhancement

response surface techniques for diffuser shape optimization the design of incompressible diffusers for maximum pressure recovery is used to demonstrate the utility of response surface approximations for design optimization of eow devices two examples involving two and eve design variables are treated with the diffuser wall shapes described by polynomials and b splines in both cases monotonicity conditions drastically reduce the design space in this irregularly shaped space a pool of designs is selected by a d optimality criterion and analyzed by a e nite volume computational euid dynamics cfd code quadratic polynomial response surfaces are then e tted to the pressure recovery coefe cients to improve the prediction accuracy uncertain regressor terms and possible outlier design points are excluded based on statistical tests a standard optimization algorithm is used to e nd the optimal diffuser design from the response surface approximations the optimum diffusers exhibit minimal e ow separation and yield similar wall shapes for the two parameterizations a main asset of the response surface optimization approach lies in the smoothing of noisy response functions therefore theissueofnumericalnoiseincfd results basedon theuseof two different analysis codes is addressed

solution adaptive grid procedure for the parabolized navier stokes equations a solution adapt ive grid procedure based on an error equidistribution principle is developed and applied to a three dimensional parabolized navier stokes solver the scheme redistributes grid points line by line in both crossflow directions with grid point motion controlled by forces analogous to tensional and torsional spring forces the tensional force is proportional to the error measure or a weighting function related to the error measure the torsional force is used to control grid skewness relative to the upstream and cross stream coordinate lines weighting functions are selected by first normalizing flowfield gradients and or curvature of a number of dependent variables and then selecting the largest at each point the hypersonic flow over a right circular cone at three different yaw angles is studied to demonstrate the performance of the solution adaptive grid procedure pitot pressure profiles and surface pressure computed using the solution adaptive algorithm are compared with experimental results as well as with numerical results obtained using a fixed grid pitot pressure predictions using the adaptive grid algorithm show better agreement with experiment than those obtained using a fixed grid