a note on the set theoretical defuzzification the set theoretic defuzzification sd method has been claimed to be a rational defuzzification method which is exclusively based on the fuzzy set theory j valente de oliveira fuzzy sets and systems 76 1995 63 however this paper shows the examples that the method is not applicable with general t norms and t conorms for normal fuzzy sets we show that the sd values of a normalized fuzzy set are located outside the support of the given fuzzy set with the min type t norm operator for non normal fuzzy sets we show that the defuzzification values of certain kinds of non normal fuzzy sets are unit value regardless of the support of the fuzzy set finally we show that the sd method does not satisfy two of three basic constraints for rational defuzzification operator which is proposed by runkler and glesner proc 2nd ieee internat conf on fuzzy systems p 1161

a 6th order staggered compact finite difference method for the incompressible navier stokes and scalar transport equations in a previous paper we have developed a staggered compact finite difference method for the compressible navier stokes equations in this paper we will extend this method to the case of incompressible navier stokes equations in an incompressible flow conservation of mass is ensured by the well known pressure correction method 7 21 the advection and diffusion terms are discretized with 6th order spatial accuracy the discrete poisson equation which has to be solved in the pressure correction step has the same spatial accuracy as the advection and diffusion operators the equations are integrated in time with a third order adams bashforth method results are presented for a 1d advection diffusion equation a 2d lid driven cavity at a reynolds number of 1000 and 10 000 and finally a 3d fully developed turbulent duct flow at a bulk reynolds number of 5400 in all cases the methods show excellent agreement with analytical and other numerical and experimental work

practical aspects of higher order numerical schemes for wave propagation phenomena this paper examines practical issues related to the use of compact difference based fourth and sixth order schemes for wave propagation phenomena with focus on maxwell s equations of electromagnetics an outline of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches transformed plane method and physical space differencing in the first technique the truncation error expansion for the sixth order compact scheme confirms that the order of accuracy is preserved if a consistent mesh refinement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available physical space differencing formulas are derived for the five point stencil by expressing the coefficients in terms of local spacing ratios the order of accuracy of the reconstruction operator is then verified with a numerical experiment on stretched meshes to ensure stability for a broad range of problems fourier analysis is employed to develop a single parameter family of up to tenth order tridiagonal based spatial filters the implementation of these filters is discussed in terms of their effect on the interior scheme as well as in a 1 d cavity where they are employed to suppress a late time instability the paper concludes after demonstrating the application of the scheme to several 3 d canonical problems utilizing cartesian as well as curvilinear meshes published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

interface conditions of finite difference compact schemes for computational aeroacoustics the interface condition provides flexibility to handle complex geometries on a set of structured grids however when used with a compact scheme to apply in computational aeroacoustics its accuracy and stability may be degraded seriously by the boundary treatment that arises at a grid interface to minimize this effect a modified characteristic condition is incorporated in the finite difference compact scheme by using an explicit difference form at the boundary the extension of this approach is naturally attained through the coordinate transformation of convective terms across an interface in multidimensions the validity of current development is demonstrated through a simulation of trailing edge noise generation from an airfoil at a low mach number

a unifying approach to defuzzification and comparison of the outputs of fuzzy controllers this paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective this is done by emphasizing the fuzzy controller as a decision making system based on the extensive study and justification of the fuzzy set comparison criteria that were developed and published elsewhere by the author a ranking and thus a defuzzification index is introduced this index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful in addition the proposed index is based on the generalization of the hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases

finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains a finite difference time dependent numerical method for the wave equation supported by recently derived novel elliptic grids is analyzed the method is successfully applied to single and multiple two dimensional acoustic scattering problems including soft and hard obstacles with complexly shaped boundaries the new grids have nearly uniform cell area j grids and nearly uniform grid line spacing email protected numerical experiments reveal the positive impact of these two grid properties on the scattered field convergence to its harmonic steady state the restriction imposed by stability conditions on the time step size is relaxed due to the near uniformity cell areas and grid line spacing as a consequence moderately large time steps can be used for relatively fine spatial grids resulting in greater accuracy at a lower computational cost also numerical solutions for wave problems inside annular regions of complex shapes are obtained the use of the new grids results in late time stability in contrast with other classical finite difference time dependent methods

effects of periodic excitation on turbulent flow separation from a flap the effects of periodic perturbations on delaying separation or promoting reattachment of initially separated flow were experimentally investigated the leading parameters affecting the flow are the flap deflection the input momentum and its reduced frequency the sensitivity of the flow to the imposed oscillations depends on its initial state and this leads to hysteresis with respect to changes in any of the aforementioned parameters for example the most effective frequency required to attach the flow to the surface is much lower than the one required to prevent its separation the amplitude needed to force reattachment may be an order of magnitude larger than the amplitude required to prevent separation at a given inclination of the flap nevertheless periodic forcing is much more effective than steady blowing for boundary layer control

a low dimensional model of separation bubbles in this work motivated by the problem of model based predictive control of separated flows we identify the key variables and the requirements on a model based observer and construct a prototype low dimensional model to be embedded in control applications namely using a phenomenological physics based approach and dynamical systems and singularity theories we uncover the low dimensional nature of the complex dynamics of actuated separated flows and capture the crucial bifurcation and hysteresis inherent in separation phenomena this new look at the problem naturally leads to several important implications such as firstly uncovering the physical mechanisms for hysteresis secondly predicting a finite amplitude instability of the bubble and thirdly to new issues to be studied theoretically and tested experimentally

some properties of defuzzification neural networks abstract fuzzy systems have gained more and more attention from researchers and practitioners of various fields in such systems the output represented by a fuzzy set sometimes needs to be transformed into a scalar value and this task is known as the defuzzification process several analytic methods have been proposed for this problem but lately the neural network approach has been used for this purpose when employed as defuzzifiers a neural network is called a defuzzification neural network in this paper some preliminary results on properties of such defuzzification networks will be reported

a fuzzy linguistic approach to a multi criteria sequencing problem abstract in this paper a fuzzy approach to a single machine scheduling problem is considered in this approach the system s variables are defined using linguistic terms each of these variables may take values described via fuzzy triangular numbers the scheduling criteria are the common due date the total earliness and tardiness and the controllable duration of the jobs processing times the aim is to determine the length of the processing times to sequence the jobs in the machine and finally to determine the common due date in a near optimal way the problem is solved using an algorithmic procedure which is illustrated by means of an example

a set theoretical defuzzification method a defuzzification method coinciding with the result of the subsethood theorem and including a family of averaging methods like mean of maxima and center of gravity as special cases is presented the defuzzification method named subsethood defuzzification sd method has the advantage of being exclusively based on set theoretical operations giving thus an insight on the nature of the computations involved in one of the most controversial stages of the fuzzy controller architecture in addition the sd method allows its customization also in the aim of set theory customization is believed as a necessary feature as the defuzzification problem seems ill defined and application dependent

quasi disjoint pentadiagonal matrix systems for the parallelization of compact finite difference schemes and filters this paper proposes a novel systematic approach for the parallelization of pentadiagonal compact finite difference schemes and filters based on domain decomposition the proposed approach allows a pentadiagonal banded matrix system to be split into quasi disjoint subsystems by using a linear algebraic transformation technique as a result the inversion of pentadiagonal matrices can be implemented within each subdomain in an independent manner subject to a conventional halo exchange process the proposed matrix transformation leads to new subdomain boundary sb compact schemes and filters that require three halo terms to exchange with neighboring subdomains the internode communication overhead in the present approach is equivalent to that of standard explicit schemes and filters based on seven point discretization stencils the new sb compact schemes and filters demand additional arithmetic operations compared to the original serial ones however it is shown that the additional cost becomes sufficiently low by choosing optimal sizes of their discretization stencils compared to earlier published results the proposed sb compact schemes and filters successfully reduce parallelization artifacts arising from subdomain boundaries to a level sufficiently negligible for sophisticated aeroacoustic simulations without degrading parallel efficiency the overall performance and parallel efficiency of the proposed approach are demonstrated by stringent benchmark tests

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

patched characteristic interface condition for high order multiblock aeroacoustic computation a patched grid technique is proposed with the aim of increasing the flexibility and efficiency of high order finite difference schemes for multiblock computational aeroacoustics the patched characteristic interface conditions allow arbitrarily positioned nonmatching grid points along each side of the internal block boundaries the work extendsthecharacteristicinterfaceconditionsoriginally proposedtotreattheproblemofgridsingularityassociated with structured grids and high order finite difference schemes a simple method of generalizing the original characteristic interface conditions theory for arbitrary block coordinate alignments is also outlined the new interface condition is implemented into a high order computational aeroacoustics code to solve either the euler or navier stokes equations the patch algorithm makes use of a high order optimized interpolation method to approximatethecharacteristicconvectiontermsatcorrespondinglocationsalongtheblockinterface theresultisan interface condition that provides better management of cell distribution in the computational domain while at the same time providing a treatment to the grid singularity problem associated with complex geometries several test casesareusedtodemonstratethe flexibilityofthenewinterfaceconditionandtoinvestigatevariousparameters the computed results are shown to be in excellent agreement with exact solutions

high order immersed boundary method for incompressible flows in this work a high order numerical approach based on the immersed boundary method to simulate viscous incompressible flows involving arbitrary boundaries is described the idea is to combine compact finite difference schemes and a high order direct forcing approach of the sharp interface immersed boundary method in this approach a particular challenge is to solve the pressure poisson equation using the compact stencil this issue is addressed by introducing an efficient approach based on high order corrections to the right hand side of the poisson equation that is the source term while retaining the second order short stencil for the laplace operator the two dimensional implementation is described for which third order global convergence is achieved when an immersed boundary is present

a dispersion relation preserving optimized upwind compact difference scheme for high accuracy flow simulations in this work we have derived an optimized upwind compact difference scheme for achieving excellent spatial resolution the derived numerical scheme adds numerical diffusion which is strictly restricted to a high wavenumber region in order to control numerical instabilities as well as to achieve de aliasing ability more importantly the derived numerical scheme has excellent dispersion relation preserving drp property the applicability of the proposed scheme in simulating real flow problems has been demonstrated by solving flow inside a lid driven cavity a transitional flow past ag24 aerofoil and a two dimensional decaying turbulence flow

grid stabilization of high order one sided differencing ii second order wave equations we demonstrate the stable boundary closure of difference methods of order up through 16 for the solution of wave equations in second order form our method combines the introduction of 1 2 judiciously placed subcell grid points near the boundary with minimal stencil one sided difference operators of the same order as the interior scheme the method is tested on a variety of problems including the scalar wave equation discretized on mapped grids and overlapping composite grids as well as an integrable nonlinear system

the stability of numerical boundary treatments for compact high order finite difference schemes the stability characteristics of various compact fourth and sixth order spatial operators are assessed with the theory of gustafsson kreiss and sundstrom g k s for the semidiscrete initial boundary value problem these results are generalized to the fully discrete case with a recently developed theory of kreiss and wu in all cases favorable comparisons are obtained between g k s theory eigenvalue determination and numerical simulation the conventional definition of stability then is sharpened to include only those spatial discretizations that are asymptotically stable bounded left half plane eigenvalues many of the higher order schemes that are g k s stable are not asymptotically stable a series of compact fourth and sixth order schemes that are both asymptotically and g k s stable for the scalar case are then developed

upper bound on the characters of the symmetric groups let c be a conjugacy class in the symmetric group s n and be a partition of n let f be the degree of the irreducible representation s c the character of s at c and r c the normalized character c f we prove that there exist constants b 0 and 1 q 0 such that for n 4 for every conjugacy class c in s n and every irreducible representation s of s n r c max q 1 n 1 n b supp c where supp c is the number of non fixed digits under the action of a permutation in c 1 is the size of the largest part in and 1 is the number of parts in the proof is obtained by enumeration of rim hook tableaux the hook formula and probabilistic arguments combinatorial algebraic and statistical applications follow this result in particular we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes

flow control predictions using unsteady reynolds averaged navier stokes modeling a parametric study t he effective control of flow separation promises substantial performance improvements for a wide variety of air vehicles although the methods are well known there is very little by way of theory or numerical models that can adequately predict lift enhancements drag reduction etc an attemptwasmade to address this problem by conducting a computational fluid dynamics cfd validation workshop for synthetic jets and turbulent separation control 1 where one casewas dedicated to predicting the nominally two dimensional flow over a hump the baseline uncontrolled case was considered in addition to control by means of steady suction 2 and zero net mass flux oscillatory blowing 3 the workshop determined that cfd with steady or unsteady reynolds averaged navier stokes rans or urans consistently overpredicted the reattachment location regardless of turbulence model or method within the separation bubble most computations predicted velocity profiles well but considerably underpredicted the magnitude of turbulent shear stresses large eddy simulations and other costly methods appear capable of overcoming this deficiency but the focus of the current study is on the more affordable rans and urans methodologies see for example krishnan et al 4 morgan et al 5 and saric et al 6 although these individual test cases were challenging to cfd codes only a single test case was considered for both steady suction and zero net mass flux blowing during the course of the experimental investigation however steady and unsteady surface pressures were acquired for a wide variety of control parameters including reynolds number suction flow rate and frequency and blowing amplitude in the zero net mass flux case significant variations or changes in control authority were observed depending upon the control input or prevailing reynolds numbers for example varying the suction flow rate at different reynolds numbers indicated an increase in the rate of drag reduction in contrast no reynolds number effect could be detected with regard to zero net mass flux blowing in addition for the oscillatory case the flow was seen to be highly dependent on control frequency and peak blowing amplitude different sometimes counteracting mechanisms dominated the separated flowfield during different parts of the control cycle comparisons of these changes or trends with numerical results will clearly facilitate more precise evaluation of cfd s value for predictive purposes this is because the uncontrolled or baseline state is usually known and hence the correct prediction of changes to the baseline state as a result of a particular control strategy would be of great value for assessing different concepts or downselection to address this need rumsey and greenblatt 7 undertook a detailed parametric study and this note presents a summary of the main findings

active flow separation control on wall mounted hump at high reynolds numbers an active separation control experiment was conducted in a cryogenic pressurized wind tunnel on a wall mounted bump at chord reynolds numbers from 2 4 x 10 6 to 26 x 106 and a mach number of 0 25 the model simulates the upper surface of a 20 thick glauert goldschmied type airfoil at zero incidence the turbulent boundary layer of the tunnel sidewall flows over the model and eliminates laminar turbulent transition from the problem indeed the reynolds number either based on the chord or boundary layer thickness had a negligible effect on the flow and its control without control a large turbulent separation bubble is formed at the lee side of the model periodic excitation and steady suction or blowing were applied to eliminate gradually the separation bubble detailed effects due to variations in the excitation frequency amplitude and the steady mass flux are described and compared to those of steady suction or blowing

on discretely entropy stable weight adjusted discontinuous galerkin methods curvilinear meshes abstract we construct entropy conservative and entropy stable discontinuous galerkin dg discretizations for time dependent nonlinear hyperbolic conservation laws on curvilinear meshes the resulting schemes preserve a semi discrete quadrature approximation of a continuous global entropy inequality the proof requires the satisfaction of a discrete geometric conservation law which we enforce through an appropriate polynomial approximation we extend the construction of entropy conservative and entropy stable dg schemes to the case when high order curvilinear mass matrices are approximated using low storage weight adjusted approximations and describe how to retain global conservation properties under such an approximation for certain types of curvilinear meshes these weight adjusted approximations deliver optimal rates of convergence finally the high order accuracy local conservation and discrete conservation or dissipation of entropy for under resolved solutions are verified through numerical experiments for the compressible euler equations on triangular and tetrahedral meshes

artificial dissipation models for the euler equations various artificial dissipation models that are used with central difference algorithms for the euler equations are analyzed for their effect on accuracy stability and convergence rates in particular linear and nonlinear models are investigated using an implicit approximate factorization code arc2d for transonic airfoils fully implicit application of the dissipation models is shown to improve robustness and convergence rates the treatment of dissipation models at boundaries will be examined it will be shown that accurate error free solutions with sharp shocks can be obtained using a central difference algorithm coupled with an appropriate nonlinear artificial dissipation model i introduction t he solution of the euler equations using numerical techniques requires the use of either a differencing method with inherent dissipation or the addition of dissipation terms to a nondissipative scheme this is because the euler equations do not provide any natural dissipation mechanism such as viscosity in the navier stokes equations that would eliminate high frequencies which are caused by nonlinearitie s and especially shocks a variety of numerical algorithms and computer codes for the euler equations have been developed methods such as maccormack s1 explicit

a quantum walk inspired adiabatic algorithm for solving graph isomorphism problems we present a quantum algorithm for solving graph isomorphism problems that is based on an adiabatic protocol we use a collection of continuous time quantum walks each one generated by an xy hamiltonian to visit the configuration space in this way we avoid a diffusion over all the possible configurations and significantly reduce the dimensionality of the accessible hilbert space within this restricted space the graph isomorphism problem can be translated into searching for a satisfying assignment to a 2 sat satisfiable formula and mapped onto a 2 local hamiltonian without resorting to perturbation gadgets or projective techniques we present an analysis of the time for execution of the algorithm on small graph isomorphism problem instances and discuss the issue of an implementation of the proposed adiabatic scheme on current quantum computing hardware

a time spectral approximate jacobian based linearized compressible navier stokes solver for high speed boundary layer receptivity and stability abstract a numerical method for conducting linear receptivity and stability investigations of high speed wall bounded flows based on the linearized compressible navier stokes equations is presented the current approach is directly applicable for stability investigations of arbitrarily complex geometries the left hand side operator for the linear system of equations is obtained by computing numerical right hand side jacobians while the right hand side is build from exact flux jacobians utilizing the numerical right hand side jacobian approach avoids lengthy error prone derivation of the stability equations in the context of generalized curvilinear coordinates the governing equations are solved using either time stepping or time spectral discretizations three different time spectral approaches i e direct inversion unfactored and factored schemes are presented and their numerical characteristics for the solution of the linearized navier stokes equations for linear receptivity and stability analysis for large scale transition problems are explored linear receptivity and stability calculations results are provided for different solver options performance comparison of the three schemes are presented for a wide range of test cases an incompressible cross flow for a swept flat plate boundary layer for a supersonic shock boundary layer interaction for hypersonic boundary layers on a flat plate and flared cone and finally for the receptivity of a hypersonic boundary layer for a right sharp cone

a hybrid method and unified analysis of generalized finite differences and lagrange finite elements abstract finite differences finite elements and their generalizations are widely used for solving partial differential equations and their high order variants have respective advantages and disadvantages traditionally these methods are treated as different strong vs weak formulations and are analyzed using different techniques fourier analysis or green s functions vs functional analysis except for some special cases on regular grids recently the authors introduced a hybrid method called adaptive extended stencil fem or aes fem conley et al 2016 which combines features of generalized finite differences and lagrange finite elements to achieve second order accuracy over unstructured meshes however its analysis was incomplete due to the lack of existing mathematical theory that unifies the formulations and analysis of these different methods in this work we introduce the framework of generalized weighted residuals to unify the formulation of finite differences finite elements and aes fem in addition we propose a unified analysis of the well posedness convergence and mesh quality dependency of these different methods we also report numerical results with aes fem to verify our analysis we show that aes fem improves the accuracy of generalized finite differences while reducing the mesh quality dependency and simplifying the implementation of high order finite elements

a spectral difference lattice boltzmann method for solution of inviscid compressible flows on structured grids in this work a spectral difference lattice boltzmann method sdlbm is developed and applied for an accurate simulation of two dimensional inviscid compressible flows on structured grids the compressible form of the discrete boltzmann bgk equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid here the 2d compressible lattice boltzmann lb model proposed by watari is applied the spectral difference sd method is implemented for the solution of the lb equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function for time accurate solutions the fourth order runge kutta scheme is used to discretize the temporal term in the lb equation note that the procedure of implementing the sd method to solve the lb equation is nearly the same as that procedure developed in the literature for the solution of the euler equations the accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems a sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size distribution on the accuracy and performance of the solution at first three inviscid compressible flow problems namely the stationary isentropic vortex the shock tube and the shock vortex interaction are solved by using the sdlbm to demonstrate the accuracy and robustness of the present solution methodology results computed for these test cases are in good agreement with the analytical and the available numerical solutions to more assess the accuracy and robustness of the sdlbm a third order finite volume lbm fvlbm is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other it is demonstrated that the sdlbm is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible lb based flow solvers as the final problem the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the sdlbm in reaching to a steady state solution

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

a subexponential time quantum algorithm for the dihedral hidden subgroup problem we present a quantum algorithm for the dihedral hidden subgroup problem dhsp with time and query complexity 2 o sqrt log n in this problem an oracle computes a function f on the dihedral group d n which is invariant under a hidden reflection in d n by contrast the classical query complexity of dhsp is o sqrt n the algorithm also applies to the hidden shift problem for an arbitrary finitely generated abelian group the algorithm begins as usual with a quantum character transform which in the case of d n is essentially the abelian quantum fourier transform this yields the name of a group representation of d n which is not by itself useful and a state in the representation which is a valuable but indecipherable qubit the algorithm proceeds by repeatedly pairing two unfavorable qubits to make a new qubit in a more favorable representation of d n once the algorithm obtains certain target representations direct measurements reveal the hidden subgroup

short note on high order finite difference metric discretizations satisfying gcl on moving and deforming grids in this note we generalize our previous treatment of the discretizations of geometric conservation laws on steady grids vinokur and yee 2000 to general time dependent grids the commutative property of mixed difference operators is generalized to apply to time metrics and jacobians our treatment uses half the number of terms as those used in a recent paper by abe et al 2012 we also derive the proper temporal discretizations of both runge kutta and linear multistep methods to satisfy the commutativity property for higher than first order

high order compact finite difference methods on general overset grids this work investigates the coupling of a very high order finite difference algorithm for the solution of conservation laws on general curvilinear meshes with overset grid techniques originally developed to address complex geometric configurations the solver portion of the algorithm is based on pade type compact finite differences of up to sixth order with up to 10th order filters employed to remove spurious waves generated by grid non uniformities boundary conditions and flow non linearities the overset grid approach is utilized as both a domain decomposition paradigm for implementation of the algorithm on massively parallel machines and as a means for handling geometric complexity in the computational domain two key features have been implemented in the current work the ability of the high order algorithm to accommodate holes cut in grids by the overset grid approach and the use of high order interpolation at non coincident grid overlaps several high order high accuracy interpolation methods were considered and a high order explicit non optimized lagrangian method was found to be the most accurate and robust for this application several two dimensional benchmark problems were examined to validate the interpolation methods and the overall algorithm these included grid to grid interpolation of analytic test functions the inviscid convection of a vortex laminar flow over single and double cylinder configurations and the scattering of acoustic waves from one and three cylinder configurations the employment of the overset grid techniques coupled with high order interpolation at overset boundaries was found to be an effective way of employing the high order algorithm for more complex geometries than was previously possible

prediction of high lift flows using turbulent closure models the flow over two different multi element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model a subset of recently measured transition locations using hot film on a mcdonnell douglas configuration is presented and the effect of transition location on the computed solutions is explored deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element and not necessarily inadequate turbulence modeling in the wake using measured transition locations for the main element improves the prediction of its boundary layer thickness skin friction and wake profile shape however using measured transition locations on the slat still yields poor slat wake predictions the computation of the slat flow field represents a key roadblock to successful predictions of multi element flows in general the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models

central values of fuzzy numbers defuzzification abstract axioms for defining a central value of a fuzzy set are developed various proposed central values are examined implications for defuzzification are discussed

generation of curvilinear coordinates on multiply connected regions with boundary singularities a new algorithm to generate smooth two dimensional boundary conforming coordinates with grid lines control on multiply connected regions including boundary singularities is devised the technique fits into the category of elliptic grid generators since it is based on the numerical solution of poisson equations the physical domain d is transformed into a topologically equivalent connected rectangular domain d by defining a branch cut inside d control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut and on other boundary curves simple and computationally convenient expressions for the control functions present in the poisson system are obtained from this initial distribution of points thus a natural link between clustering properties and the control functions is created fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points an iterative smoothing process relocating the branch cut is described as a result smooth grids are obtained grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well known commercial software the algorithm is successfully tested over a variety of multiply connected domains the computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes

a spectral fc solver for the compressible navier stokes equations in general domains i explicit time stepping we present a fourier continuation fc algorithm for the solution of the fully nonlinear compressible navier stokes equations in general spatial domains the new scheme is based on the recently introduced accelerated fc method which enables use of highly accurate fourier expansions as the main building block of general domain pde solvers previous fc based pde solvers are restricted to linear scalar equations with constant coefficients the fc methodology presented in this text thus constitutes a significant generalization of the previous fc schemes as it yields general domain fc solvers for nonlinear systems of pdes while not restricted to periodic boundary conditions and therefore applicable to general boundary value problems on arbitrary domains the proposed algorithm inherits many of the highly desirable properties arising from rapidly convergent fourier expansions including high order convergence essentially spectrally accurate dispersion relations and much milder cfl constraints than those imposed by polynomial based spectral methods since for example the spectral radius of the fc first derivative grows linearly with the number of spatial discretization points we demonstrate the accuracy and optimal parallel efficiency of the algorithm in a variety of scientific and engineering contexts relevant to fluid dynamics and nonlinear acoustics

a new compact scheme for parallel computing using domain decomposition direct numerical simulation dns of complex flows require solving the problem on parallel machines using high accuracy schemes compact schemes provide very high spectral resolution while satisfying the physical dispersion relation numerically however as shown here compact schemes also display bias in the direction of convection often producing numerical instability near the inflow and severely damping the solution always near the outflow this does not allow its use for parallel computing using domain decomposition and solving the problem in parallel in different sub domains to avoid this in all reported parallel computations with compact schemes the full domain is treated integrally while using parallel thomas algorithm pta or parallel diagonal dominant pdd algorithm in different processors with resultant latencies and inefficiencies for domain decomposition methods using compact scheme in each sub domain independently a new class of compact schemes is proposed and specific strategies are developed to remove remaining problems of parallel computing this is calibrated here for parallel computing by solving one dimensional wave equation by domain decomposition method we also provide the error norm with respect to the wavelength of the propagated wave packet next the advantage of the new compact scheme on a parallel framework has been shown by solving three dimensional unsteady navier stokes equations for flow past a cone cylinder configuration at a mach number of 4 additionally a test case is conducted on the advection of a vortex for a subsonic case to provide an estimate for the error and parallel efficiency of the method using the proposed compact scheme in multiple processors

geometric interpretations and spatial symmetry property of metrics in the conservative form for high order finite difference schemes on moving and deforming grids the role of a geometric conservation law gcl on a finite difference scheme is revisited for conservation laws and the conservative forms of coordinate transformation metrics are introduced in general dimensions the sufficient condition of a linear high order finite difference scheme is arranged in detail for which the discretized conservative coordinate transformation metrics and jacobian satisfy the gcl identities on three dimensional moving and deforming grids subsequently the geometric interpretation of the metrics and jacobian discretized by a linear high order finite difference scheme is discussed and only the symmetric conservative forms of the discretized metrics and jacobian are shown to have the appropriate geometric structures the symmetric and asymmetric conservative forms of the metrics and jacobian are examined by the computation of an inviscid compressible fluid on highly skewed stationary and deforming grids using sixth order compact and fourth order explicit central difference schemes respectively the resolution of the isentropic vortex and the robustness of the computation are improved by employing symmetric conservative forms on the coordinate transformation metrics and jacobian that have an appropriate geometry background an integrated conservation of conservative quantities is also attained on the deforming grid when symmetric conservative forms are adopted to the time metrics and jacobian

boundary states at reflective moving boundaries we derive and evaluate boundary states for maxwell s equations the linear and the nonlinear euler gas dynamics equations to compute wave reflection from moving boundaries in this study we use a discontinuous galerkin spectral element method dgsem with arbitrary lagrangian eulerian ale mapping for the spatial approximation but the boundary states can be used with other methods like finite volume schemes we present four studies using maxwell s equations one for the linear euler equations and one more for the nonlinear euler equations these are reflection of light from a plane mirror moving at constant velocity reflection of light from a moving cylinder reflection of light from a vibrating mirror reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow the studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity

high order numerical simulation of turbulent flow over a wall mounted hump the development of a high order spatial discretization for a k e turbulence model and its application to flow over a wall mounted hump is described the high order implementation is validated for a flat plate and subsequently applied to the more complex wall mounted hump for conditions with and without flow control results for the hump flow are compared to experimental data the turbulence model is incorporated in an implicit parallel flow solver that is based on an approximately factored time integration method coupled with spatially fourth and sixth order compact difference formulations and a high order filtering strategy both second order and high order discretizations of the k e turbulence equations were included in the compact solver validation using flow over a flat plate demonstrated that use of a second order scheme for the k turbulence equations dominates the solution even when high order compact differencing is used for the flow equations this validation also demonstrated that significant computational savings are possible because less mesh resolution is required when using a high order discretization of the k e turbulence equations comparison of the high order and second order solutions was also performed for the wall mounted hump qualitative agreement was achieved with experimental data for both high and low order schemes high order solutions on a coarse grid agreed very well with second order solutions on a considerably finer grid

an efficient implementation of fourth order compact finite difference scheme for poisson equation with dirichlet boundary conditions fourth order compact finite difference scheme has been proposed for solving the poisson equation with dirichlet boundary conditions for some time an efficient implementation of such numerical scheme is often desired for practical usage in this paper based on fast discrete sine transform we design an efficient algorithm to implement this scheme to do this poisson equation is first discretized by fourth order compact finite difference method the subsequent discretized system is not solved by the usual method matrix inversion instead it is solved with the fast discrete sine transform by doing this way the computational cost of proposed algorithm for such scheme with large grid numbers can be greatly reduced detailed numerical algorithm of this fast solver for one dimensional two dimensional and three dimensional poisson equation has been presented numerical results in one dimension two dimensions three dimensions and four dimensions have shown that the applied compact finite difference scheme has fourth order accuracy and can be efficiently implemented

compressible large eddy simulation of separation control on a wall mounted hump compressible large eddy simulations of turbulent flow over a wall mounted hump with active flow control are performed and compared with previous experiments the flow is characterized by the unsteady separation before the steep trailing edge which naturally reattaches downstream of the hump to form an unsteady turbulent separation bubble the low mach number large eddy simulation demonstrated a good prediction of surface pressure coefficient separation bubble length and velocity profiles compared with experiments the effect of compressibility on the baseline flow is documented and analyzed and is found to increase the separation bubble size due to a reduced growth rate control is applied just before the natural separation point via steady suction and zero net mass flux oscillatory forcing and steady suction is shown to be more effective in decreasing the size of the separation bubble and pressure drag for the control parameters investigated controlled flow at a compressible subsonic mach number is applied and found to be slightly less effective than the same control parameters at low mach numbers

stabilized non dissipative approximations of euler equations in generalized curvilinear coordinates we discuss stabilization strategies for finite difference approximations of the compressible euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables our approach rather relies on a skew symmetric like splitting of the convective derivatives that guarantees preservation of kinetic energy in the semi discrete low mach number limit a locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers the validity of the approach is tested for benchmark flow cases including the propagation of a cylindrical vortex and the head on collision of two vortex dipoles the tests support high accuracy and superior stability over conventional central discretization of the convective derivatives the potential use for dns les of turbulent compressible flows in complex geometries is discussed

modelling atmospheric flows with adaptive moving meshes an anelastic atmospheric flow solver has been developed that combines semi implicit non oscillatory forward in time numerics with a solution adaptive mesh capability a key feature of the solver is the unification of a mesh adaptation apparatus based on moving mesh partial differential equations pdes with the rigorous formulation of the governing anelastic pdes in generalised time dependent curvilinear coordinates the solver development includes an enhancement of the flux form multidimensional positive definite advection transport algorithm mpdata employed in the integration of the underlying anelastic pdes that ensures full compatibility with mass continuity under moving meshes in addition to satisfy the geometric conservation law gcl tensor identity under general moving meshes a diagnostic approach is proposed based on the treatment of the gcl as an elliptic problem the benefits of the solution adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated the developed solver is verified for two idealised flow problems with distinct levels of complexity passive scalar advection in a prescribed deformational flow and the life cycle of a large scale atmospheric baroclinic wave instability showing fine scale phenomena of fronts and internal gravity waves

on the use of higher order finite difference schemes on curvilinear and deforming meshes this study enables the use of very high order finite difference schemes for the solution of conservation laws on stretched curvilinear and deforming meshes to illustrate these procedures we focus on up to 6th order pade type spatial discretizations coupled with up to 10th order low pass filters these are combined with explicit and implicit time integration methods to examine wave propagation and wall bounded flows described by the navier stokes equations it is shown that without the incorporation of the filter application of the high order compact scheme to nonsmooth meshes results in spurious oscillations which inhibit their applicability inclusion of the discriminating low pass high order filter restores the advantages of high order approach even in the presence of large grid discontinuities when three dimensional curvilinear meshes are employed the use of standard metric evaluation procedures significantly degrades accuracy since freestream preservation is violated to overcome this problem a simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes for dynamically deforming grids an effective numerical treatment is described to evaluate expressions containing the time varying transformation metrics with these techniques metric cancellation is guaranteed regardless of the manner in which grid speeds are defined the efficacy of the new procedures is demonstrated by solving several model problems as well as by application to flow past a rapidly pitching airfoil and past a flexible panel

direct numerical simulation of turbulent flow separation from a wall mounted hump a high order accurate numerical method for solving the incompressible navier stokes equations in general orthogonal coordinates is presented the method is applied to a test case of the nasa langley computational fluid dynamics validation workshop 2004 a turbulent flow over a wall mounted hump geometry results of direct numerical simulations dns for the unforced flow as well as for a case with steady suction are presented and compared to the available experimental data the dns predictions are shown to agree well with the experiments except in the vicinity of the experimental reattachment locations the simulations predict slightly longer recirculation regions for both the unforced and the controlled case the results presented in this work suggest that with the rapidly increasing computational resources of modern supercomputers such as the cray x1 dns is becoming a viable alternative to the use of turbulence models for investigating complex turbulent flows at moderately high reynolds numbers

an efficient time splitting compact finite difference method for gross pitaevskii equation abstract we propose an efficient time splitting compact finite difference method for gross pitaevskii equation gpe in our method we solve the gpe in time with time splitting technique and in space by the compact finite difference method to find the numerical solution of the resulting discretized system in one dimension 1d two dimensions 2d and three dimensions 3d we apply the fast discrete sine transform in 1d 2d and 3d respectively and get an efficient solver for the discretized system in 1d 2d and 3d respectively our numerical algorithm at every time step does not need linear algebraic equations solver whose computation cost will be much higher when the spatial dimension increases the method also has the merit that it is unconditionally stable and conservative moreover the method can achieve spectral like accuracy in space when high order compact finite difference method is applied extensive numerical tests for the gpe in 1d 2d and 3d are presented to demonstrate the power and accuracy of the proposed numerical method

three dimensional boundary conditions for numerical simulations of reactive compressible flows with complex thermochemistry the navier stokes characteristic boundary conditions nscbc is a very efficient numerical strategy to treat boundary conditions in fully compressible solvers the present work is an extension of the 3d nscbc method proposed by yoo et al and lodato et al in order to account for multi component reactive flows with detailed chemistry and complex transport a new approach is proposed for the outflow boundary conditions which enables clean exit of non normal flows and the specific treatment of all kinds of edges and corners is carefully addressed the proposed methodology is successfully validated on various challenging multi component reactive flow configurations

on the issue of defuzzification and selection based on a fuzzy set abstract we are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set a problem which manifests itself in the defuzzification step in fuzzy logic controllers we provide a unifying approach to this selection process among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework we show that this selection can be viewed as a three step operation transformation of the decision fuzzy set normalization to probability distribution selection based on the probability distribution a number of different procedures for selection are discussed

experimental investigation of separation control part 2 zero mass flux oscillatory blowing the control of a separated flow over a wall mounted hump by means of two dimensional zero mass flux perturbations was studied experimentally to generate a data set for the development and evaluation of computational methods the companion paper part 1 considered details of the baseline uncontrolled case and a steady suction control case the data set for a specific zero mass flux control case comprised static surface pressures together with phase averaged unsteady surface pressures and particle image velocimetry flowfield measurements additional surface pressures were acquired for a variety of control frequencies control amplitudes and reynolds numbers due consideration was given to characterizing the flow in the vicinity of the control slot with and without external flow and to perturbation two dimensionality triple decomposition of the fluctuating velocity and pressure fields was employed for presenting and analyzing the experimental data this facilitated an assessment of the mechanism of separation control and the quantification of the coherent and turbulent surface pressures reynolds stresses and energy fluxes spanwise surface pressures and phase averaged stereoscopic particle image velocimetry data revealed an effectively two dimensional flowfield despite highly three dimensional instantaneous flow structures

application of compact finite difference schemes to simulations of stably stratified fluid flows abstract this paper presents a comparison of the results of numerical simulations obtained by two different numerical methods for one specific case of stably stratified incompressible flow the focus in this paper is on the numerical results obtained using some of the compact finite difference discretizations introduced in the paper 1 the numerical scheme itself follows the principle of semi discretisation with high order compact discretisation in space while the time integration is carried out by the strong stability preserving runge kutta scheme results are compared against the reference solution obtained by the ausm finite volume method the test case used to demonstrate the capabilities of selected numerical methods represents the flow of stably stratified fluid over low smooth hill like wall mounted obstacle

fourier continuation methods for high fidelity simulation of nonlinear acoustic beams on the basis of recently developed fourier continuation fc methods and associated efficient parallelization techniques this text introduces numerical algorithms that due to very low dispersive errors can accurately and efficiently solve the types of nonlinear partial differential equation pde models of nonlinear acoustics in hundred wavelength domains as arise in the simulation of focused medical ultrasound as demonstrated in the examples presented in this text the fc approach can be used to produce solutions to nonlinear acoustics pdes models with significantly reduced discretization requirements over those associated with finite difference finite element and finite volume methods especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths in these examples the fc methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches a variety of one and two dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology including an example containing a number of scattering centers and nonlinear multiple scattering events

the symmetric group defies strong fourier sampling the dramatic exponential speedups of quantum algorithms over their best existing classical counterparts were ushered in by the technique of fourier sampling introduced by bernstein and vazirani and developed by simon and shor into an approach to the hidden subgroup problem this approach has proved successful for abelian groups leading to efficient algorithms for factoring extracting discrete logarithms and other number theoretic problems we show however that this method cannot resolve the hidden subgroup problem in the symmetric groups even in the weakest information theoretic sense in particular we show that the graph isomorphism problem cannot be solved by this approach our work implies that any quantum approach based upon the measurement of coset states must depart from the original framework by using entangled measurements on multiple coset states

a 2d compact fourth order projection decomposition method a 2d fourth order compact direct scheme projection decomposition method for solving incompressible viscous flows in multi connected rectangular domains is devised in each subdomain the governing navier stokes equations are discretized by using fourth order compact schemes in space and second order scheme in time the coupling between subdomains is based on a direct non overlapping multidomain method it allows to solve each helmholtz poisson problem resulting of a projection method in complex geometries the major difficulty of the poisson neumann problem solvability is addressed and correctly treated the present numerical method is checked through some classical numerical experiments first the second order accuracy in time and the fourth order accuracy in space are shown by matching with the analytical solution of the taylor problem the method is also tested by simulating the flow in a 2d lid driven cavity the utility of the compact scheme projection decomposition method approach is further illustrated by two other benchmark problems viz the flow over a backward facing step and the laminar flow past a square prism the present results are in good agreement with the experimental data and other numerical solutions available in the literature

an adaptive approach to defuzzification based on level sets abstract we look at the process of defuzzification used in fuzzy logic controllers we provide a parametrized formulation for this procedure based upon the use of level sets which we call generalized level set defuzzification we show that the commonly used defuzzification procedures mean of maxima and center of area are special cases of this general procedure and are simply distinguished by the choice of the parameter we provide a simple algorithm for adaptive choice of the best defuzzification procedure