symmetry preserving discretization of navier stokes equations on collocated unstructured grids a fully conservative discretization is presented in this paper the same principles followed by verstappen and veldman 2003 3 are generalized for unstructured meshes here a collocated mesh scheme is preferred over a staggered one due to its simpler form for such meshes the basic idea behind this approach remains the same mimicking the crucial symmetry properties of the underlying differential operators i e the convective operator is approximated by a skew symmetric matrix and the diffusive operator by a symmetric positive definite matrix a novel approach to eliminate the checkerboard spurious modes without introducing any non physical dissipation is proposed to do so a fully conservative regularization of the convective term is used the supraconvergence of the method is numerically showed and the treatment of boundary conditions is discussed finally the new discretization method is successfully tested for a buoyancy driven turbulent flow in a differentially heated cavity

on spectral multigrid methods for the time dependent navier stokes equations a new splitting scheme is proposed for the numerical solution of the time dependent incompressible navier stokes equations by spectral methods a staggered grid is used for the pressure improved intermediate boundary conditions are employed in the split step for the velocity and spectral multigrid techniques are used for the solution of the implicit equations

fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations a new finite difference scheme on a non uniform staggered grid in cylindrical coordinates is proposed for incompressible flow the scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error provided that the discrete continuity equation is satisfied a novel pole treatment is also introduced where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole the pole singularity is removed properly using analytical and numerical techniques the kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates the pole treatment is verified for inviscid pipe flow mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow

the optimal sampling pattern for linear control systems in digital control systems the state is sampled at given sampling instants and the input is kept constant between two consecutive instants with the optimal sampling problem we mean the selection of sampling instants and control inputs such that a given function of the state and input is minimized in this paper we formulate the optimal sampling problem and we derive a necessary condition for the optimality of a set of sampling instants in the linear quadratic regulator problem since the numerical solution of the optimal sampling problem is very time consuming we also propose a new quantization based sampling strategy that is computationally tractable and capable of achieving near optimal cost finally and probably most interesting of all we prove that the quantization based sampling is optimal in first order systems for a large number of samples experiments demonstrate that quantization based sampling has near optimal performance even when the system has a higher order however it is still an open question whether quantization based sampling is asymptotically optimal in any case

a ghost fluid level set methodology for simulating multiphase electrohydrodynamic flows with application to liquid fuel injection in this paper we present the development of a sharp numerical scheme for multiphase electrohydrodynamic ehd flows for a high electric reynolds number regime the electric potential poisson equation contains ehd interface boundary conditions which are implemented using the ghost fluid method gfm the gfm is also used to solve the pressure poisson equation the methods detailed here are integrated with state of the art interface transport techniques and coupled to a robust high order fully conservative finite difference navier stokes solver test cases with exact or approximate analytic solutions are used to assess the robustness and accuracy of the ehd numerical scheme the method is then applied to simulate a charged liquid kerosene jet

a current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number part i on a rectangular collocated grid system a consistent conservative and accurate scheme has been designed to calculate the current density and the lorentz force by solving the electrical potential equation for magnetohydrodynamics mhd at low magnetic reynolds numbers and high hartmann numbers on a finite volume structured collocated grid in this collocated grid velocity u pressure p and electrical potential f are located in the grid center while current fluxes are located on the cell faces the calculation of current fluxes on the cell faces is conducted using a conservative scheme which is consistent with the discretization scheme for the solution of electrical potential poisson equation a conservative interpolation is used to get the current density at the cell center which is used to conduct the calculation of lorentz force at the cell center for momentum equations we will show that both conservative and consistent are important properties of the scheme to get an accurate result for high hartmann number mhd flows with a strongly non uniform mesh employed to resolve the hartmann layers and side layers of hunt s conductive walls and shercliff s insulated walls a general second order projection method has been developed for the incompressible navier stokes equations with the lorentz force included this projection method can accurately balance the pressure term and the lorentz force for a fully developed core flow this method can also simplify the pressure boundary conditions for mhd flows

regularity preserving image interpolation assumptions about image continuity lead to oversmoothed edges in common image interpolation algorithms a wavelet based interpolation method that imposes no continuity constraints is introduced the algorithm estimates the regularity of edges by measuring the decay of wavelet transform coefficients across scales and preserves the underlying regularity by extrapolating a new subband to be used in image resynthesis the algorithm produces visibly sharper edges than traditional techniques and exhibits an average peak signal to noise ratio psnr improvement of 2 5 db over bilinear and bicubic techniques

the error amended sharp edge ease scheme for image zooming this paper proposes a new interpolation method called the error amended sharp edge ease scheme which is a modified bilinear method in order to remove reduce interpolation artifacts such as image blur and the checkerboard effect ringing ease tries to amend the interpolation error by employing the classical interpolation error theorem in an edge adaptive fashion ease is applied for image zooming by both integer and noninteger magnification factors the new interpolation scheme has proved to result in high resolution images having clearer and sharper edges than linear interpolation methods for all synthetic and natural images we have tested ease can be implemented with ease it turns out to be similarly efficient as cubic interpolation 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

a time aggregation approach to markov decision processes we propose a time aggregation approach for the solution of infinite horizon average cost markov decision processes via policy iteration in this approach policy update is only carried out when the process visits a subset of the state space as in state aggregation this approach leads to a reduced state space which may lead to a substantial reduction in computational and storage requirements especially for problems with certain structural properties however in contrast to state aggregation which generally results in an approximate model due to the loss of markov property time aggregation suffers no loss of accuracy because the markov property is preserved single sample path based estimation algorithms are developed that allow the time aggregation approach to be implemented on line for practical systems some numerical and simulation examples are presented to illustrate the ideas and potential computational savings

on the role of exponential splines in image interpolation a sobolev reproducing kernel hilbert space approach to image interpolation is introduced the underlying kernels are exponential functions and are related to stochastic autoregressive image modeling the corresponding image interpolants can be implemented effectively using compactly supported exponential b splines a tight l2 upper bound on the interpolation error is then derived suggesting that the proposed exponential functions are optimal in this regard experimental results indicate that the proposed interpolation approach with properly tuned signal dependent weights outperforms currently available polynomial b spline models of comparable order furthermore a unified approach to image interpolation by ideal and nonideal sampling procedures is derived suggesting that the proposed exponential kernels may have a significant role in image modeling as well our conclusion is that the proposed sobolev based approach could be instrumental and a preferred alternative in many interpolation tasks

locally adaptive wavelet based image interpolation we describe a spatially adaptive algorithm for image interpolation the algorithm uses a wavelet transform to extract information about sharp variations in the low resolution image and then implicitly applies interpolation which adapts to the image local smoothness singularity characteristics the proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper better performance comes at the expense of higher complexity

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

energy conserving runge kutta methods for the incompressible navier stokes equations energy conserving methods have recently gained popularity for the spatial discretization of the incompressible navier stokes equations in this paper implicit runge kutta methods are investigated which keep this property when integrating in time firstly a number of energy conserving runge kutta methods based on gauss radau and lobatto quadrature are constructed these methods are suitable for convection dominated problems such as turbulent flows because they do not introduce artificial diffusion and are stable for any time step secondly to obtain robust time integration methods that work also for stiff problems the energy conserving methods are extended to a new class of additive runge kutta methods which combine energy conservation with l stability in this class the radau iia b method has the best properties results for a number of test cases on two stage methods indicate that for pure convection problems the additive radau iia b method is competitive with the gauss methods however for stiff problems such as convection dominated flows with thin boundary layers both the higher order gauss and radau iia b method suffer from order reduction overall the gauss methods are the preferred method for energy conserving time integration of the incompressible navier stokes equations

a new alternating bi diagonal compact scheme for non uniform grids a new compact scheme has been developed for any non uniform grid the compact scheme has been developed for spatial discretization and is analyzed here in conjunction with four stage fourth order runge kutta rk4 scheme for time integration while solving the one dimensional convection equation the space time discretization combination is calibrated by subjecting the system to global spectral analysis gsa which was developed by the authors group here the compact scheme has been obtained by using a combination of two bi diagonal schemes the novel aspect of this scheme is its application in the physical plane directly without the necessity of mapping or transformations some typical cases for problems in acoustics as well as fluid mechanics have been studied here and potential use in large eddy simulations les has been demonstrated by solving navier stokes equation for lid driven cavity

adaptive map error concealment for dispersively packetized wavelet coded images in this paper we present an adaptive maximum a posteriori map error concealment algorithm for dispersively packetized wavelet coded images we model the subbands of a wavelet coded image as markov random fields and use the edge characteristics in a particular subband and regularity properties of subband wavelet samples across scales to adapt the potential functions locally the resulting adaptive map estimation gives psnr advantages of up to 0 7 db compared to the competing algorithms the advantage is most evident near the edges which helps improve the visual quality of the reconstructed images

curvature interpolation method for image zooming we introduce a novel image zooming algorithm called the curvature interpolation method cim which is partial differential equation pde based and easy to implement in order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect the cim first evaluates the curvature of the low resolution image after interpolating the curvature to the high resolution image domain the cim constructs the high resolution image by solving a linearized curvature equation incorporating the interpolated curvature as an explicit driving force it has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and pde based methods of no curvature information various results are given to prove effectiveness and reliability of the new method

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

a high order low dispersion symmetry preserving finite volume method for compressible flow on curvilinear grids a new high order finite volume method is presented that preserves the skew symmetry of convection for the compressible flow equations the method is intended for large eddy simulations les of compressible turbulent flows in particular in the context of hybrid rans les computations the method is fourth order accurate and has low numerical dissipation and dispersion due to the finite volume approach mass momentum and total energy are locally conserved furthermore the skew symmetry preservation implies that kinetic energy sound velocity and internal energy are all locally conserved by convection as well the method is unique in that all these properties hold on non uniform curvilinear structured grids due to the conservation of kinetic energy there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection this enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid scale model by minimizing the numerical dispersion the numerical errors are reduced by an order of magnitude compared to a standard fourth order finite volume method

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

construction of explicit and implicit dynamic finite difference schemes and application to the large eddy simulation of the taylor green vortex a general class of explicit and implicit dynamic finite difference schemes for large eddy simulation is constructed by combining taylor series expansions on two different grid resolutions after calibration for re the dynamic finite difference schemes allow to minimize the dispersion errors during the calculation through the real time adaption of a dynamic coefficient in case of dns resolution these dynamic schemes reduce to taylor based finite difference schemes with formal asymptotic order of accuracy whereas for les resolution the schemes adapt to dispersion relation preserving schemes both the explicit and implicit dynamic finite difference schemes are tested for the large eddy simulation of the taylor green vortex flow and numerical errors are investigated as well as their interaction with the dynamic smagorinsky model and the multiscale smagorinsky model very good results are obtained

approximate factorization as a high order splitting for the implicit incompressible flow equations abstract we apply the method of approximate factorization to derive a second order accurate splitting of the incompressible flow equations stokes or navier stokes equations this is novel because the method of approximate factorization was believed inapplicable to this type of equation system we demonstrate the resulting splitting on a second order crank nicolson discretization and point out its intimate relationship to some existing second order accurate splitting projection methods further we use the approximate factorization method to derive entirely new splittings we first develop a new generalized second order accurate splitting which may be specialized to a variety of applications we indicate its application to finite elements checker board free cell centered discretizations and ocean modeling we then generalized the original splitting to an arbitrarily high order scheme

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

image denoising based on wavelets and multifractals for singularity detection this paper presents a very efficient algorithm for image denoising based on wavelets and multifractals for singularity detection a challenge of image denoising is how to preserve the edges of an image when reducing noise by modeling the intensity surface of a noisy image as statistically self similar multifractal processes and taking advantage of the multiresolution analysis with wavelet transform to exploit the local statistical self similarity at different scales the pointwise singularity strength value characterizing the local singularity at each scale was calculated by thresholding the singularity strength wavelet coefficients at each scale were classified into two categories the edge related and regular wavelet coefficients and the irregular coefficients the irregular coefficients were denoised using an approximate minimum mean squared error mmse estimation method while the edge related and regular wavelet coefficients were smoothed using the fuzzy weighted mean fwm filter aiming at preserving the edges and details when reducing noise furthermore to make the fwm based filtering more efficient for noise reduction at the lowest decomposition level the mmse based filtering was performed as the first pass of denoising followed by performing the fwm based filtering experimental results demonstrated that this algorithm could achieve both good visual quality and high psnr for the denoised images

optimal linear estimation with square based sampling this paper is concerned with the problem of event based sampling for the purpose of reducing the number of data transferred in control systems and the corresponding modified kalman filter a mathematical description based upon square based sampling is proposed in which the sampling occured when the accumulated difference between two adjacent sampling points satisfies the specified event condition then by utilizing the square based sampling method a modified kalman filter algorithm is adopted in which the measurement is sent when the output exceeds a given event the simulation results illustrate the advantage of the new event based sampling scheme and the effectiveness of modified kalman filter

image interpolation by adaptive 2 d autoregressive modeling and soft decision estimation the challenge of image interpolation is to preserve spatial details we propose a soft decision interpolation technique that estimates missing pixels in groups rather than one at a time the new technique learns and adapts to varying scene structures using a 2 d piecewise autoregressive model the model parameters are estimated in a moving window in the input low resolution image the pixel structure dictated by the learnt model is enforced by the soft decision estimation process onto a block of pixels including both observed and estimated the result is equivalent to that of a high order adaptive nonseparable 2 d interpolation filter this new image interpolation approach preserves spatial coherence of interpolated images better than the existing methods and it produces the best results so far over a wide range of scenes in both psnr measure and subjective visual quality edges and textures are well preserved and common interpolation artifacts blurring ringing jaggies zippering etc are greatly reduced

kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow the collocated mesh scheme is often favored over the staggered mesh scheme for turbulence simulation in complex geometries due to its simpler form in curvilinear coordinates the collocated mesh scheme does not conserve kinetic energy however and few careful checks of the impact of these errors have been made in this work analysis is used to identify two sources of kinetic energy conservation error in the collocated mesh scheme 1 errors arising from the interpolations used to estimate the velocity on the cell faces and 2 errors associated with the slightly inconsistent pressure field used to ensure mass conservation for the cell face volume fluxes it is shown that the interpolation error can be eliminated through the use of first order accurate centered interpolation operators with mesh independent weights the pressure error appears to be intrinsic to the scheme and it is shown to scale as o t2 x2 the effects of the conservation errors are investigated numerically through simulations of inviscid flow over an airfoil and in large eddy simulations of turbulent channel flow neither the interpolation error nor the pressure error appear to lead to significant problems in the channel flow simulations where viscous dissipation is present and where the cartesian mesh is stretched in only one direction the inviscid airfoil simulations performed on a curvilinear mesh show a much greater sensitivity to the interpolation error the standard second order centered interpolation is shown to lead to severe numerical oscillations while the kinetic energy conserving first order centered interpolation produces solutions that are almost as smooth as those obtained with a third order upwind interpolation when compared in channel flow simulations however the first order centered interpolation is shown to be far superior to the third order upwind interpolation the latter being adversely affected by numerical dissipation only slight differences were noted when comparing channel flow simulations using first order and second order centered interpolations these results suggest that numerical oscillations can be controlled in curvilinear coordinates through the use of properly constructed non dissipative centered interpolations

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

analysis of stability and accuracy of finite difference schemes on a skewed mesh numerical stability and accuracy of finite difference schemes on a skewed non uniform mesh are investigated to provide guidelines for mesh design and for devising appropriate solution methods when mesh skewness is unavoidable in the current analysis a linear advection diffusion equation in a cartesian coordinate system is transformed into a curvilinear one corresponding to a skewed mesh a finite difference approximation of the transformed equation leads to the leading order error terms which are responsible for time step restrictions and numerical instability a truncation error analysis of central difference approximation reveals the effects of mesh non uniformity and skewness on the solution quality in addition a modified wavenumber analysis is performed for the central and upwind difference schemes coupled with time integration methods to examine the effects of mesh skewness angle and flow direction relative to the mesh angle on the numerical stability in general severe mesh skewness leads to restrictions on the allowable cell peclet number and time step size and also increases phase and amplitude errors

lebesgue approximation model of continuous time nonlinear dynamic systems traditional model based approaches are based on periodic iterations where the continuous time model is discretized with a fixed period despite the easiness in analysis and design such periodic approximation model may be undesirable from the computation efficiency point of view this paper presents the lebesgue approximation model lam of continuous time nonlinear systems where the iteration is activated on an as needed basis but not periodically we show that the proposed lam behaves exactly the same as a specific event triggered feedback system through which the properties of the lam can be studied we provide a sufficient condition to ensure asymptotic stability of the lam and derive theoretical bounds on the difference between the states of the lam and the original continuous time system the lam is then integrated in the particle filtering approach for fault prognosis simulation results show that the lam can dramatically reduce the number of iterations in prognosis without sacrificing accuracy and precision

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

adaptive image resizing based on continuous domain stochastic modeling we introduce an adaptive continuous domain modeling approach to texture and natural images the continuous domain image is assumed to be a smooth function and we embed it in a parameterized sobolev space we point out a link between sobolev spaces and stochastic auto regressive models and exploit it for optimally choosing sobolev parameters from available pixel values to this aim we use exact continuous to discrete mapping of the auto regressive model that is based on symmetric exponential splines the mapping is computationally efficient and we exploit it for maximizing an approximated gaussian likelihood function we account for non gaussian levy type processes by deriving a more robust estimator that is based on the sample auto correlation sequence both estimators use multiple initialization values for overcoming the local minima structure of the fitting criteria experimental image resizing results indicate that the auto correlation criterion can cope better with non gaussian processes and model mismatch our work demonstrates the importance of the auto correlation function in adaptive image interpolation and image modeling tasks and we believe it is instrumental in other image processing tasks as well

boundary treatment for fourth order staggered mesh discretizations of the incompressible navier stokes equations harlow and welch phys fluids 8 1965 2182 2189 introduced a discretization method for the incompressible navier stokes equations conserving the secondary quantities kinetic energy and vorticity besides the primary quantities mass and momentum this method was extended to fourth order accuracy by several researchers 25 14 21 in this paper we propose a new consistent boundary treatment for this method which is such that continuous integration by parts identities including boundary contributions are mimicked in a discrete sense in this way kinetic energy is exactly conserved even in case of non zero tangential boundary conditions we show that requiring energy conservation at the boundary conflicts with order of accuracy conditions and that the global accuracy of the fourth order method is limited to second order in the presence of boundaries we indicate how non uniform grids can be employed to obtain full fourth order accuracy

high order pole treatment in cylindrical coordinates for incompressible flow simulations with finite difference collocated schemes abstract a finite difference collocated scheme is proposed for the simulation of unsteady incompressible flows in cylindrical coordinates the rhie chow flux interpolation technique is used to avoid the odd even decoupling of the pressure field it is shown that the calculation of the coriolis and centrifugal acceleration terms based on the cell center values lead to numerical instabilities near the pole in the inviscid regime to avoid this issue a new formulation based on the combination of cell center and cell face velocity components is proposed for the calculation of these terms furthermore a new pole treatment methodology is introduced to calculate the viscous terms resulting single valued properties at the pole as regards the extensions of the present scheme to higher orders of accuracy a fourth order spatial discretization is also introduced and verified moreover it is shown that for higher order extensions the present pole treatment is able to preserve the order of accuracy and the l 2 norm and l norm errors are greatly improved in comparison with the previous schemes the robustness of the present method is assessed via five different numerical tests including laminar flows in a polar cavity vortex wall interaction evolution of a monopole vortex system to a tripole vortex system advection of the lamb dipole and large eddy simulation les of turbulent pipe flows compared to the previous les results for turbulent pipe flows significant improvement is obtained for the mean and fluctuating velocities especially at the core region of the channel similarly at the wall region the fluctuating axial and azimuthal velocities and the skewnesses of the axial and radial velocities are very close to the previous direct numerical simulation and experimental data

solving average cost markov decision processes by means of a two phase time aggregation algorithm abstract this paper introduces a two phase approach to solve average cost markov decision processes which is based on state space embedding or time aggregation in the first phase time aggregation is applied for policy optimization in a prescribed subset of the state space and a novel result is applied to expand the evaluation to the whole state space this evaluation is then used in the second phase in a policy improvement step and the two phases are then alternated until convergence is attained some numerical experiments illustrate the results

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

image resolution enhancement by using discrete and stationary wavelet decomposition in this correspondence the authors propose an image resolution enhancement technique based on interpolation of the high frequency subband images obtained by discrete wavelet transform dwt and the input image the edges are enhanced by introducing an intermediate stage by using stationary wavelet transform swt dwt is applied in order to decompose an input image into different subbands then the high frequency subbands as well as the input image are interpolated the estimated high frequency subbands are being modified by using high frequency subband obtained through swt then all these subbands are combined to generate a new high resolution image by using inverse dwt idwt the quantitative and visual results are showing the superiority of the proposed technique over the conventional and state of art image resolution enhancement techniques

learning algorithms for markov decision processes with average cost this paper gives the first rigorous convergence analysis of analogues of watkins s q learning algorithm applied to average cost control of finite state markov chains we discuss two algorithms which may be viewed as stochastic approximation counterparts of two existing algorithms for recursively computing the value function of the average cost problem the traditional relative value iteration rvi algorithm and a recent algorithm of bertsekas based on the stochastic shortest path ssp formulation of the problem both synchronous and asynchronous implementations are considered and analyzed using the ode method this involves establishing asymptotic stability of associated ode limits the ssp algorithm also uses ideas from two time scale stochastic approximation

spectral methods for the navier stokes equations with one infinite and two periodic directions abstract two numerical methods were designed to solve the time dependent three dimensional incompressible navier stokes equations in boundary layers method a semi infinite domain and mixing layers or wakes method b fully infinite domain their originality lies in the use of rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions combined with one method a or two method b slowly decaying extra functions for each wave vector that exactly represent the irrotational component of the solution at large distances both methods eliminate the pressure term as part of the formulation thus avoiding fractional step time integration they yield rapid convergence and are free of spurious modes in the orr sommerfeld spectra they are also efficient although the operation count is of order n 2 n is the number of modes in the infinite direction these methods have been used for extensive direct numerical simulations of transition and turbulence a new time integration scheme with low storage requirements and good stability properties is also described

a geometric approach to pulse width modulated control in nonlinear dynamical systems the author demonstrates under the assumption of high frequency control switchings the existence of an ideal equivalence among sliding regimes of variable structure feedback control and pulse width modulated pwm control responses in nonlinear dynamical systems this equivalence constitutes the basis for a geometric approach approach to pwm control loops design an illustrate example of energy conversion in a lossless switched controlled bilinear network is presented

time reversibility of the euler equations as a benchmark for energy conserving schemes the three dimensional incompressible euler equations are time reversible this property should be preserved as well as possible by numerical discretizations this article investigates the time reversibility properties of various solvers designed for incompressible navier stokes computations the test case is the inviscid taylor green vortex which becomes turbulent before the time is reversed to try to recover the initial condition the simulations are performed using high and low order finite difference solvers as well as using a pseudo spectral solver various time stepping schemes are also investigated although the flow statistics are significantly affected by the accuracy of the space discretization the time reversibility is not because most space discretizations are time reversible for an exact time stepping the crucial factor for time reversibility is the accuracy of the time stepping scheme and its interaction with the space discretization furthermore an important practical requirement for the solver is to be energy conserving in order to avoid numerical instability an energy conserving solver using an accurate time stepping is then able to go back almost perfectly from a complex turbulent flow to the simple initial condition therefore we propose that this constitutes a severe and useful benchmark that navier stokes solvers should challenge the present investigations and their conclusions are also supported by parallel 1 d investigations using the non linear convection equation inviscid burgers and the linear convection equation

an adaptable k nearest neighbors algorithm for mmse image interpolation we propose an image interpolation algorithm that is nonparametric and learning based primarily using an adaptive k nearest neighbor algorithm with global considerations through markov random fields the empirical nature of the proposed algorithm ensures image results that are data driven and hence reflect ldquoreal worldrdquo images well given enough training data the proposed algorithm operates on a local window using a dynamic k nearest neighbor algorithm where k differs from pixel to pixel small for test points with highly relevant neighbors and large otherwise based on the neighbors that the adaptable k provides and their corresponding relevance measures a weighted minimum mean squared error solution determines implicitly defined filters specific to low resolution image content without yielding to the limitations of insufficient training additionally global optimization via single pass markov approximations similar to cited nearest neighbor algorithms provides additional weighting for filter generation the approach is justified in using a sufficient quantity of training per test point and takes advantage of image properties for in depth analysis we compare to existing methods and draw parallels between intuitive concepts including classification and ideas introduced by other nearest neighbor algorithms by explaining manifolds in low and high dimensions

nonlinear image upsampling method based on radial basis function interpolation in this paper we present a novel edge directed upsampling method based on radial basis function rbf interpolation in order to remove artifacts such as blurred edges or blocking effects we suggest a nonlinear method capable of taking edge information into account the resampling evaluation is determined according to the edge orientation the proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods the algorithm is compared with some well known linear schemes as well as recently developed nonlinear schemes the resulting images demonstrate the new algorithm s ability to magnify an image while preserving the edge features

contrast guided image interpolation in this paper a contrast guided image interpolation method is proposed that incorporates contrast information into the image interpolation process given the image under interpolation four binary contrast guided decision maps cdms are generated and used to guide the interpolation filtering through two sequential stages 1 the 45 and 135 cdms for interpolating the diagonal pixels and 2 the 0 and 90 cdms for interpolating the row and column pixels after applying edge detection to the input image the generation of a cdm lies in evaluating those nearby non edge pixels of each detected edge for re classifying them possibly as edge pixels this decision is realized by solving two generalized diffusion equations over the computed directional variation dv fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges respectively the amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge the diffused dv fields are then thresholded for yielding the binary cdms respectively therefore the decision bands with variable widths will be created on each cdm the two cdms generated in each stage will be exploited as the guidance maps to conduct the interpolation process for each declared edge pixel on the cdm a 1 d directional filtering will be applied to estimate its associated to be interpolated pixel along the direction as indicated by the respective cdm otherwise a 2 d directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non edge pixel extensive simulation results have clearly shown that the proposed contrast guided image interpolation is superior to other state of the art edge guided image interpolation methods in addition the computational complexity is relatively low when compared with existing methods hence it is fairly attractive for real time image applications

image enhancement by nonlinear extrapolation in frequency space a technique for enhancing the perceptual sharpness of an image is described the enhancement algorithm augments the frequency content of the image using shape invariant properties of edges across scale by using a nonlinearity that generates phase coherent higher harmonics the procedure utilizes the laplacian transform and the laplacian pyramid image representation results are presented depicting the power spectra augmentation and the visual enhancement of several images simplicity of computations and ease of implementation allow for real time applications such as high definition television hdtv

a simple approach to discretize the viscous term with spatially varying eddy viscosity a simple approach to discretize the viscous dissipation term in the incompressible navier stokes equations with spatially varying viscosity is presented unlike the case where the viscosity remains constant its discretization may be quite cumbersome especially for high order staggered formulations to circumvent this problem we propose an alternative form of the viscous term whose discretization is straightforward notice that this approach is also suitable for eddy viscosity models for large eddy simulation moreover since it is based on already available operators it can be easily implemented on any structured or unstructured code the supra convergence of the method is numerically shown on both a fourth order cartesian staggered and an unstructured collocated formulation

highly energy conservative finite difference method for the cylindrical coordinate system a highly energy conservative second order accurate finite difference method for the cylindrical coordinate system is developed it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used this argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on cartesian coordinates numerical tests are undertaken for an inviscid flow with various schemes and it turns out that the proposed scheme offers a superior energy conservation property and greater stability than the intuitive and previously proposed methods for both equally spaced and unequally spaced meshes

policy iteration based feedback control it is well known that stochastic control systems can be viewed as markov decision processes mdps with continuous state spaces in this paper we propose to apply the policy iteration approach in mdps to the optimal control problem of stochastic systems we first provide an optimality equation based on performance potentials and develop a policy iteration procedure then we apply policy iteration to the jump linear quadratic problem and obtain the coupled riccati equations for their optimal solutions the approach is applicable to linear as well as nonlinear systems and can be implemented on line on real world systems without identifying all the system structure and parameters

symmetry preserving discretization of turbulent flow we propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the underlying differential operators i e the convective operator is represented by a skew symmetric coefficient matrix and the diffusive operator is approximated by a symmetric positive definite matrix mimicking crucial properties of differential operators forms in itself a motivation for discretizing them in a certain manner we give it a concrete form by noting that a symmetry preserving discretization of the navier stokes equations is stable on any grid and conserves the total mass momentum and kinetic energy for the latter the physical dissipation is to be turned off of coarse being stable on any grid the choice of the grid may be based on the required accuracy solely and the main question becomes how accurate is a symmetry preserving discretization its accuracy is tested for a turbulent flow in a channel by comparing the results to those of physical experiments and previous numerical studies the comparison is carried out for a reynolds number of 5600 which is based on the channel width and the mean bulk velocity based on the channel half width and wall shear velocity the reynolds number becomes 180 the comparison shows that with a fourth order symmetry preserving method a 64 64 32 grid suffices to perform an accurate numerical simulation

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

a fully conservative second order finite difference scheme for incompressible flow on nonuniform grids a second order accurate finite difference discretization of the incompressible navier stokes is presented that discretely conserves mass momentum and kinetic energy in the inviscid limit in space and time the method is thus completely free of numerical dissipation and potentially well suited to the direct numerical simulation or large eddy simulation of turbulent flow the method uses a staggered arrangement of velocity and pressure on a structured cartesian grid and retains its discrete conservation properties for both uniform and nonuniform gird spacing the predicted conservation properties are confirmed by inviscid simulations on both uniform and nonuniform grids the capability of the method to resolve turbulent flow is demonstrated by repeating the turbulent channel flow simulations of h choi and p moin 1994 j comput phys 113 1 where the effect of computational time step on the computed turbulence was investigated the present fully conservative scheme achieved turbulent flow solutions over the entire range of computational time steps investigated t tu2 0 4 to 5 0 little variation in statistical turbulence quantities was observed up to t 1 6 the present results differ significantly from those reported by choi and moin who observed significant discrepancies in the turbulence statistics above t 0 4 and the complete laminarization of the flow at and above t 1 6

image zooming method using edge directed moving least squares interpolation based on exponential polynomials this paper presents a nonlinear image interpolation algorithm the suggested method is based on the moving least squares mls projection technique but introduces a fundamental modification the algebraic polynomial based mls methods provide very satisfactory results however the associated approximation space is shift and scale invariant so that it cannot be adjusted according to the characteristic of a given data as a result when upsampling images it has a limitation in producing sharp edges such that edges are often blurred in the magnified images to recover sharper edges we need to reduce smoothing parameter or adapt a new parameter sharpening the edges motivated by this observations we propose a novel mls method governed by a set of exponential polynomials with tension parameters such that they can be tuned to the characteristic of given data moreover for a better match to the local structures around the edges the suggested algorithm uses weights which consider the edge orientation numerical results are presented and compared visually and by using some quantitative fidelity measures psnr epsnr ssim and fsim to the bicubic spline interpolation and other recently developed nonlinear methods the results demonstrate the new algorithm s ability to magnify an image while preserving edge features

higher order mimetic methods for unstructured meshes a higher order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer mimetic discretization methods create discrete versions of the partial differential operators such and the gradient and divergence that are exact in some sense and therefore mimic the important mathematical properties of their continuous counterparts the proposed numerical method is an interesting mixture of both finite volume and finite element ideas while the ideas presented can be applied to arbitrarily high order accuracy we focus in this work on the details of creating a third order accurate method the proposed method is shown to be exact for piecewise quadratic solutions and shows third order convergence on arbitrary triangular tetrahedral meshes the numerical accuracy of the method is confirmed on both two dimensional and three dimensional unstructured meshes the computational cost required for a desired accuracy is analyzed against lower order mimetic methods

lebesgue sampling based optimal control problems with time aggregation we formulate the lebesgue sampling based optimal control problem we show that the problem can be solved by the time aggregation approach in markov decision processes mdp theory policy iteration based and reinforcement learning based methods are developed for the optimal policies both analytical solutions and sample path based algorithms are given compared to the periodic sampling scheme the lebesgue sampling scheme improves system performance

skew symmetric form of convective terms and fully conservative finite difference schemes for variable density low mach number flows the form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by morinishi et al y morinishi t s lund o v vasilyev p moin fully conservative higher order finite difference schemes for incompressible flow j comput phys 124 1998 90 and fully conservative finite difference schemes suitable for shock free unsteady compressible flow simulations are proposed commutable divergence advective and skew symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow these forms are analytically equivalent if the continuity is satisfied and the skew symmetric form is secondary conservative without the aid of the continuity while the divergence form is primary conservative the relations between the present and existing quasi skew symmetric forms are also revealed commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system and they are fully conservative provided that the corresponding discrete continuity is satisfied in addition a semi discrete convection scheme suitable for compact finite difference is presented based on the skew symmetric form the conservation properties of the present schemes are demonstrated numerically in a three dimensional periodic inviscid flow the proposed fully discrete fully conservative second order accurate scheme is also used to perform the dns of compressible isotropic turbulence and the simulation of open cavity flow

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

high order finite difference schemes on non uniform meshes with good conservation properties numerical simulation of turbulent flows dns or les requires numerical methods that are both stable and free of numerical dissipation one way to achieve this is to enforce additional constraints such as discrete conservation of mass momentum and kinetic energy the objective of this work is to generalize the high order schemes of morinishi et al to non uniform meshes while maintaining conservation properties of the schemes as much as possible this generalization is achieved by preserving symmetries of the uniform mesh case the proposed schemes do not simultaneously conserve mass momentum and kinetic energy however depending on the form of the convective term conservation of either momentum or energy in addition to mass can be achieved it is shown that the conservation properties of the generalized schemes are as good as those of the standard second order finite difference scheme on non uniform meshes while the accuracy of the new schemes is definitely superior the predicted conservation properties are demonstrated numerically in inviscid flow simulations

mass momentum and energy conserving mamec discretizations on general grids for the compressible euler and shallow water equations the paper explains a method by which discretizations of the continuity and momentum equations can be designed such that they can be combined with an equation of state into a discrete energy equation the resulting mamec discretizations conserve mass momentum as well as energy although no explicit conservation law for the total energy is present essential ingredients are i discrete convection that leaves the discrete energy invariant and ii discrete consistency between the thermodynamic terms of particular relevance is the way in which finite volume fluxes are related to nodal values the method is an extension of existing methods based on skew symmetry of discrete operators because it allows arbitrary equations of state and a larger class of grids than earlier methods the method is first illustrated with a one dimensional example on a highly stretched staggered grid in which the mamec method calculates qualitatively correct results and a non skew symmetric finite volume method becomes unstable a further example is a two dimensional shallow water calculation on a rectilinear grid as well as on an unstructured grid the conservation of mass momentum and energy is checked and losses are found negligible up to machine accuracy

an edge guided image interpolation algorithm via directional filtering and data fusion preserving edge structures is a challenge to image interpolation algorithms that reconstruct a high resolution image from a low resolution counterpart we propose a new edge guided nonlinear interpolation technique through directional filtering and data fusion for a pixel to be interpolated two observation sets are defined in two orthogonal directions and each set produces an estimate of the pixel value these directional estimates modeled as different noisy measurements of the missing pixel are fused by the linear minimum mean square error estimation lmmse technique into a more robust estimate using the statistics of the two observation sets we also present a simplified version of the lmmse based interpolation algorithm to reduce computational cost without sacrificing much the interpolation performance experiments show that the new interpolation techniques can preserve edge sharpness and reduce ringing artifacts

a generalized interpolative vector quantization method for jointly optimal quantization interpolation and binarization of text images this paper presents an approach for the effective combination of interpolation with binarization of gray level text images to reconstruct a high resolution binary image from a lower resolution gray level one we study two nonlinear interpolative techniques for text image interpolation these nonlinear interpolation methods map quantized low dimensional 2 spl times 2 image blocks to higher dimensional 4 spl times 4 possibly binary blocks using a table lookup operation the first method performs interpolation of text images using context based nonlinear interpolative vector quantization nlivq this system has a simple training procedure and has performance for gray level high resolution images that is comparable to our more sophisticated generalized interpolative vq givq approach which is the second method in it we jointly optimize the quantizer and interpolator to find matched codebooks for the low and high resolution images then to obtain the binary codebook that incorporates binarization with interpolation we introduce a binary constrained optimization method using givq in order to incorporate the nearest neighbor constraint on the quantizer while minimizing the distortion in the interpolated image a deterministic annealing based optimization technique is applied with a few interpolation examples we demonstrate the superior performance of this method over the nlivq method especially for binary outputs and other standard techniques e g bilinear interpolation and pixel replication

finite volume compact schemes on staggered grids compact finite difference schemes have been recently used in several direct numerical simulations of turbulent flows since they can achieve high order accuracy and high resolution without exceedingly increasing the size of the computational stencil the development of compact finite volume schemes is more revolved due to the appearance of surface and volume integrals while pereira et al j comput phys 167 2001 and smirnov et al aiaa paper 2546 2001 focused on collocated grids in this paper we use the staggered grid arrangement compact schemes can be tuned to achieve very high resolution for a given formal order of accuracy we develop and test high resolution schemes by following a procedure proposed by lele j comput phys 103 1992 which to the best of our knowledge has not yet been applied to compact finite volume methods on staggered grids results from several one and two dimensional simulations for the scalar transport and navier stokes equations are presented showing that the proposed method is capable to accurately reproduce complex steady and unsteady flows

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

a staggered grid high order accurate method for the incompressible navier stokes equations a high order accurate finite difference method for the numerical solution of the incompressible navier stokes equations is presented fourth order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite difference formulas high order accuracy in time is obtained by marching the solution with runge kutta methods the incompressibility constraint is enforced for each runge kutta stage iteratively either by local pressure correction or by a poisson equation based global pressure correction method local pressure correction is carried out on cell by cell basis using a local fourth order accurate discrete analog of the continuity equation the global pressure correction is based on the numerical solution of a poisson type equation which is discretized to fourth order accuracy and solved using gmres in both cases the updated pressure is used to recompute the velocities in order to satisfy the incompressibility constraint to fourth order accuracy the accuracy and efficiency of the proposed method is demonstrated in test problems

a computational error assessment of central finite volume discretizations in large eddy simulation using a smagorinsky model we present a framework for the computational assessment and comparison of large eddy simulation methods we apply this to large eddy simulation of homogeneous isotropic decaying turbulence using a smagorinsky subgrid model and investigate the combined effect of discretization and model errors at coarse subgrid resolutions we compare four different central finite volume methods these discretization methods arise from the four possible combinations that can be made with a second order and a fourth order central scheme for either the convective and the viscous fluxes by systematically varying the simulation resolution and the smagorinsky coefficient we determine parameter regions for which a desired number of flow properties is simultaneously predicted with approximately minimal error we include both physics based and mathematics based error definitions leading to different error measures designed to emphasize either errors in large or in small scale flow properties it is shown that the evaluation of simulations based on a single physics based error may lead to inaccurate perceptions on quality we demonstrate however that evaluations based on a range of errors yields robust conclusions on accuracy both for physics based and mathematics based errors parameter regions where all considered errors are simultaneously near optimal are referred to as multi objective optimal parameter regions the effects of discretization errors are particularly important at marginal spatial resolution such resolutions reflect local simulation conditions that may also be found in parts of more complex flow simulations under these circumstances the asymptotic error behavior as expressed by the order of the spatial discretization is no longer characteristic for the total dynamic consequences of discretization errors we find that the level of overall simulation errors for a second order central discretization of both the convective and viscous fluxes the 2 2 method and the fully fourth order 4 4 method is equivalent in their respective multi objective optimal regions mixed order methods i e the 2 4 and 4 2 combinations yield errors which are considerably higher

policy iteration algorithm for singular controlled diffusion processes in this paper the infinite horizon optimal control problems for singular diffusion processes are considered from the viewpoints of markov decision processes and perturbation analysis where the singularity of diffusion means that the covariance matrix of the system noise is allowed to be degenerate a formula of performance difference under two different controls is derived and leads to a comparison theorem by the comparison theorem starting from a control a so called better control can be selected therefore a control policy iteration algorithm is developed by which the performance improves step by step and converges to the optimal one when this applies to the stochastic affine nonlinear regulator and stochastic linear quadratic optimal control problems better control can be constructed in a closed form it is also shown that when the considered stochastic systems degenerate to the deterministic ones the proposed algorithm reduces to the adaptive dynamic programming algorithm j j murray c j

edge forming methods for color image zooming this paper introduces edge forming schemes for image zooming of color images by general magnification factors in order to remove reduce artifacts arising in image interpolation such as image blur and the checkerboard effect an edge forming method is suggested to be applied as a postprocess of standard interpolation methods the method is based on nonconvex nonlinear partial differential equations the equations are carefully discretized incorporating numerical schemes of anisotropic diffusion to be able to form reliable edges satisfactorily the alternating direction implicit adi method is employed for an efficient simulation of the model it has been numerically verified that the resulting algorithm can form clear edges in 2 to 3 adi iterations various results are given to show th effectiveness and reliability of the algorithm