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

interactive group decision making procedure under incomplete information this paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers multiple criteria group decision making mcgdm are involved usually decision makers dms are willing or able to provide only incomplete information because of time pressure lack of knowledge or data and their limited expertise related with problem domain there have been just a few studies considering incomplete information in group settings this incompletely specified information constructs region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings hence to handle this difficulty we suggest a method utilizing individual decision results to form group consensus final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings using individual decision results under group members possibly different weight constraints

grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

consistency measures for hesitant fuzzy linguistic preference relations hesitant fuzzy linguistic term sets hfltss are used to deal with situations in which the decision makers dms think of several possible linguistic values or richer expressions than a single term for an indicator alternative variable etc compared with fuzzy linguistic approaches they are more convenient and flexible to reflect the dms preferences in decision making for further applications of hfltss to decision making we develop a concept of hesitant fuzzy linguistic preference relations hflprs as a tool to collect and present the dms preferences due to the importance of the consistency measures using preference relations in decision making we develop some consistency measures for hflprs to ensure that the dms are being neither random nor illogical a consistency index is defined to establish the consistency thresholds of hflprs to measure whether an hflpr is of acceptable consistency for hflprs with unacceptable consistency we develop two optimization methods to improve the consistency until they are acceptable several illustrative examples are given to validate the consistency measures and the optimization methods

operators and comparisons of hesitant fuzzy linguistic term sets the theory of hesitant fuzzy linguistic term sets hfltss is very useful in objectively dealing with situations in which people are hesitant in providing linguistic assessments the purpose of this paper is to develop comparison methods and study the aggregation theory for hfltss we first define operations on hfltss and give possibility degree formulas for comparing hfltss we then define two aggregation operators for hfltss a hesitant fuzzy lwa operator and a hesitant fuzzy lowa operator in actual application we use these operators and the comparison methods to deal with multicriteria decision making problems with different situations in which importance weights of criteria or experts are known or unknown

hopf bifurcation calculations for a symmetric airfoil in transonic flow the application of a sparse matrix solver for the direct calculation of hopf bifurcation points arising for an airfoil moving in pitch and plunge in a transonic flow is considered the iteration scheme for solving the hopf equations is based on a modified newton s method direct solution of the linear system for the updates has previously been restrictive for application of the method and the sparse solver overcomes this limitation results of experiments with the approximation to the jacobian matrix driving the iteration to convergence are presented finally it is shown that an entire flutter boundary for the naca0012 airfoil can be traced out in a time comparable to that required for a small number of time response calculations i introduction c omputational fluid dynamics cfd has matured to the point where it is being applied to complex problems in external aerodynamics aeroelastic analysis relies on high fidelity predictions of aerodynamics particularly for phenomena associated with shock motions or separation these two observations have motivated the development of cfd based aeroelastic simulation a field now being called computational aeroelasticity developments in computational aeroelasticity have mainly been focused on time marching calculations where the temporal response of a system to an initial perturbation is calculated to determine growth or decay and from this to infer stability this type of simulation has developed significantly in the past decade with efforts concentrating on mesh movement load and displacement transfer between the aerodynamic and structural grids 1 and sequencing of solutions 2 3 recent and impressive example calculations have been made for complete aircraft configurations 4 5 the time marching method will remain a powerful tool in computational aeroelasticity because of its generality however the cost of these calculations motivates attempts to find quicker ways of evaluating stability while still retaining the detailed aerodynamic predictions given by cfd one way of doing this is to boil down the cfd into a reduced order model that still retains the essence of the aerodynamics various approaches have been proposed with an expansion of the flowfield in a truncated series of modes derived from proper orthogonal decomposition currently receiving much attention 6 a second approach proposed by morton and beran from the u s air force is to use dynamic systems theory to characterize the nature of the aeroelastic instability and then to use this additional information to concentrate the use of the cfd aeroelastic instabilities that are commonly termed flutter are of the hopf type where an eigenvalue of the system jacobian matrix crosses the imaginary axis at the flutter point a model problem was used to evaluate the approach 7 in which the main difficulties associated with the method calculation of the jacobian matrix solution of the augmented system by newton s method solution of a large sparse linear system were considered the method was applied to an aeroelastic system consisting of an airfoil moving in pitch and plunge in ref 8 the

multi staging of jacobi relaxation to improve smoothing properties of multigrid methods for steady euler equations abstract multi stage versions of jacobi relaxation are studied for use in multigrid methods for steady euler equations it is shown that these multi stage versions allow much more general and much more efficient multigrid methods than possible with classic relaxation methods

supervised aggregated feature learning for multiple instance classification this paper introduces a novel algorithm called supervised aggregated feature learning or safe which combines both local instance level and global bag level information in a joint framework to address the multiple instance classification task in this realm the collective assumption is used to express the relationship between the instance labels and the bag labels by means of taking the sum as aggregation rule the proposed model is formulated within a least squares support vector machine setting where an unsupervised core model either kernel pca or kernel spectral clustering at the instance level is combined with a classification loss function at the bag level the corresponding dual problem consists of solving a linear system and the bag classifier is obtained by aggregating the instance scores synthetic experiments suggest that safe is advantageous when the instances from both positive and negative bags can be naturally grouped in the same cluster moreover real life experiments indicate that safe is competitive with the best state of the art methods

a new stream function formulation for the steady euler equations a new stream function formulation is presented for the solution of euler equations in the transonic flow region in this method the stream function and the density are the dependent variables the governing equations for adiabatic flow are then the momentum equations which are solved in the strong conservation law form the method differs from the recent formulation of hafez and lovell which is based on crocco s equation in that it does not require knowledge of the vorticity to study arbitrary geometries the algorithm is combined with the automatic grid solver grape of steger and sorenson results are presented for an naca 0012 airfoil at various mach numbers angles of attack and cylinders comparisons with other solutions of the euler equations show good agreement

a parallel well balanced finite volume method for shallow water equations with topography on the cubed sphere a finite volume scheme for the global shallow water model on the cubed sphere mesh is proposed and studied in this paper the new cell centered scheme is based on osher s riemann solver together with a high order spatial reconstruction on each patch interface of the cubed sphere only one layer of ghost cells is needed in the scheme and the numerical flux is calculated symmetrically across the interface to ensure the numerical conservation of total mass the discretization of the topographic term in the equation is properly modified in a well balanced manner to suppress spurious oscillations when the bottom topography is non smooth numerical results for several test cases including a steady state nonlinear geostrophic flow and a zonal flow over an isolated mountain are provided to show the flexibility of the scheme some parallel implementation details as well as some performance results on a parallel supercomputer with more than one thousand processor cores are also provided

a shock adaptive godunov scheme based on the generalised lagrangian formulation application of the godunov scheme to the euler equations of gas dynamics based on the eulerian formulation of flow smears discontinuities sliplines especially over several computational cells while the accuracy in the smooth flow region is of the order 0 h where h is the cell width based on the generalised lagrangian formulation glf of hui et al the godunov scheme yields superior accuracy by the use of coordinate streamlines in the glf the slip line itself a streamline is resolved crisply infinite shock resolution is achieved through the splitting of shock cells an improved entropy conservation formulation of the governing equations is also proposed for computations in smooth flow regions finally the use of the glf substantially simplifies the programming logic resulting in a very robust accurate and efficient scheme 15 refs 6 figs

novel basic operational laws for linguistic terms hesitant fuzzy linguistic term sets and probabilistic linguistic term sets in the process of decision making people sometimes may feel more comfortable to express their preferences by linguistic terms instead of the quantitative form however as the basic premise of operations the existing operational laws of linguistic terms and the extended linguistic term sets are very unreasonable in order to overcome this issue in this paper we redefine some more logical operational laws for linguistic terms hesitant fuzzy linguistic elements hfles and probabilistic linguistic term sets pltss based on two equivalent transformation functions these novel operational laws can not only avoid the operation values exceeding the bounds of ltss but also keep the operation results more reasonable in decision making with linguistic information furthermore the operational laws can keep the probability information complete when computing with pltss additionally lots of properties of the operational laws are discussed and some three dimensional figures are drawn to show the regions of different operational laws of linguistic terms more vividly

general procedure for riemann solver to eliminate carbuncle and shock instability a novel procedure for the riemann solver flux calculation is proposed in this paper with this simple normal velocity reconstruction procedure all of the commonly used flux solvers such as goduno

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

multigrid acceleration of a flux difference splitting method for steady euler equations abstract a flux difference splitting based on the polynomial character of the flux vectors is introduced for steady euler equations this splitting is applied to finite volumes centered around the vertices of the computational grid a discrete set of equations is obtained which is both conservative and positive the flux difference splitting is done in an algebraically exact way as a consequence shocks are represented as sharp discontinuities without wiggles due to the positivity the set of equations can be solved by collective relaxation methods a full multigrid method based on symmetric successive relaxation full weighting bilinear interpolation and w cycle is presented typical full multigrid efficiency is achieved for the gamm transonic bump test case since after the starting cycle and one multigrid cycle the solution cannot be distinguished anymore from the fully converged solution

a new version of 2 tuple fuzzy linguistic representation model for computing with words in this paper we provide a new proportional 2 tuple fuzzy linguistic representation model for computing with words cw which is based on the concept of symbolic proportion this concept motivates us to represent the linguistic information by means of 2 tuples which are composed by two proportional linguistic terms for clarity and generality we first study proportional 2 tuples under ordinal contexts then under linguistic contexts and based on canonical characteristic values ccvs of linguistic labels we define many aggregation operators to handle proportional 2 tuple linguistic information in a computational stage for cw without any loss of information our approach for this proportional 2 tuple fuzzy linguistic representation model deals with linguistic labels which do not have to be symmetrically distributed around a medium label and without the traditional requirement of having equal distance between them moreover this new model not only provides a space to allow a continuous interpolation of a sequence of ordered linguistic labels but also provides an opportunity to describe the initial linguistic information by members of a continuous linguistic scale domain which does not necessarily require the ordered linguistic terms of a linguistic variable being equidistant meanwhile under the assumption of equally informative which is defined by a condition based on the concept of ccv we show that our model reduces to herrera and mart spl inodot spl acute nez s translational 2 tuple fuzzy linguistic representation model

a unified coordinate system for solving the three dimensional euler equations it is well known that the use of eulerian coordinates for shock capturing methods results in badly smeared slip lines and that lagrangian coordinates while capable of producing sharp slip line resolution may result in severe grid deformation causing inaccuracy and even breakdown of computation a unified coordinate system is introduced in which the flow variables are considered to be functions of time and of some permanent identification of pseudo particles which move with velocity hq q being the velocity of fluid particles it includes the eulerian coordinates as a special case when h 0 and the lagrangian when h 1 for two dimensional inviscid flow the free function h is chosen so as to preserve the grid angles this results in a coordinate system which avoids excessive numerical diffusion across slip lines in the eulerian coordinates and avoids severe grid deformation in the lagrangian coordinates yet it retains sharp resolution of slip lines especially for steady flow furthermore the two dimensional unsteady euler equations of gasdynamics in the unified coordinates are found to be hyperbolic for all values of h except when h 1 i e lagrangian in the latter case the euler equations are only weakly hyperbolic lacking one eigenvector although all eigenvalues are real the consequences of this deficiency of the lagrangian coordinates are pointed out in connection with numerical computation

a support vector machine formulation to pca analysis and its kernel version in this paper we present a simple and straightforward primal dual support vector machine formulation to the problem of principal component analysis pca in dual variables by considering a mapping to a high dimensional feature space and application of the kernel trick mercer theorem kernel pca is obtained as introduced by scholkopf et al 2002 while least squares support vector machine classifiers have a natural link with the kernel fisher discriminant analysis minimizing the within class scatter around targets 1 and 1 for pca analysis one can take the interpretation of a one class modeling problem with zero target value around which one maximizes the variance the score variables are interpreted as error variables within the problem formulation in this way primal dual constrained optimization problem interpretations to the linear and kernel pca analysis are obtained in a similar style as for least square support vector machine classifiers

a high order streamline godunov scheme for steady supersonic flow computation abstract a space marching godunov method using control volumes consisted of streamlines and the coordinate lines in the marching direction is described for the computation of two dimensional and axisymmetric steady supersonic flows these streamline meshes are solution generated they follow the fluid particles closely and also simplify the implementation of the godunov method a second order extension to the godunov scheme using essentially nonoscillatory interpolation is also presented computations of various supersonic and hypersonic flow problems indicate that the method accurately represents smooth flow and crisply resolves all flow discontinuities such as shocks and slip lines even at high mach numbers

very sparse lssvm reductions for large scale data least squares support vector machines lssvms have been widely applied for classification and regression with comparable performance with svms the lssvm model lacks sparsity and is unable to handle large scale data due to computational and memory constraints a primal fixed size lssvm pfs lssvm introduce sparsity using nystrom approximation with a set of prototype vectors pvs the pfs lssvm model solves an overdetermined system of linear equations in the primal however this solution is not the sparsest we investigate the sparsity error tradeoff by introducing a second level of sparsity this is done by means of l 0 norm based reductions by iteratively sparsifying lssvm and pfs lssvm models the exact choice of the cardinality for the initial pv set is not important then as the final model is highly sparse the proposed method overcomes the problem of memory constraints and high computational costs resulting in highly sparse reductions to lssvm models the approximations of the two models allow to scale the models to large scale datasets experiments on real world classification and regression data sets from the uci repository illustrate that these approaches achieve sparse models without a significant tradeoff in errors

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

efficient additive kernels via explicit feature maps large scale nonlinear support vector machines svms can be approximated by linear ones using a suitable feature map the linear svms are in general much faster to learn and evaluate test than the original nonlinear svms this work introduces explicit feature maps for the additive class of kernels such as the intersection hellinger s and 2 kernels commonly used in computer vision and enables their use in large scale problems in particular we 1 provide explicit feature maps for all additive homogeneous kernels along with closed form expression for all common kernels 2 derive corresponding approximate finite dimensional feature maps based on a spectral analysis and 3 quantify the error of the approximation showing that the error is independent of the data dimension and decays exponentially fast with the approximation order for selected kernels such as 2 we demonstrate that the approximations have indistinguishable performance from the full kernels yet greatly reduce the train test times of svms we also compare with two other approximation methods nystrom s approximation of perronnin et al 1 which is data dependent and the explicit map of maji and berg 2 for the intersection kernel which as in the case of our approximations is data independent the approximations are evaluated on a number of standard data sets including caltech 101 3 daimler chrysler pedestrians 4 and inria pedestrians 5

fast prediction of transonic aeroelastic stability and limit cycles the exploitation of computational fluid dynamics for aeroelastic simulations is mainly based on time domain simulations there is an intense research effort to overcome the computational cost of this approach significant aeroelasticeffectsdrivenbynonlinearaerodynamicsincludethetransonic flutterdipandlimit cycleoscillations the paper describes the use of hopf bifurcation and center manifold theory to compute flutter speeds and limit cycle responses of wings in transonic flow when the aerodynamics are modeled by the euler equations the cost of the calculations is comparable to steady state calculations based on computational fluid dynamics the paper describes twomethodsfor findingstabilityboundariesandthenanapproachtoreducingthefull ordersystemtotwodegreesof freedom in the critical mode details of the three methods are given including the calculation of first second and thirdjacobiansandthesolutionofsparselinearsystems resultsfortheagardwing asupercriticaltransporttype of wing and the limit cycle response of the goland wing are given nomenclature a jacobian matrix of r with respect to w b c second and third jacobian operators h scalar increment for finite differences f quadratic and higher terms in r g taylor coefficients of the residual restricted to the critical eigenspace h taylor coefficients of the residual restricted to the noncritical eigenspace f convective flux discretization kij coefficients in center manifold expansion of y p right eigenvector of a p1 ip2 q left eigenvector of a q1 iq2 qs constant scaling vector for the augmented system r residual vector v vector for the matrix free product w vector of unknowns y part of w in the noncritical eigenspace z part of w in the critical eigenspace t time step i sequence of eigenvalues in the inverse power method bifurcation parameter dynamic pressure frequency of critical eigenvalue or shift for the inverse power method subscripts

transonic aeroelastic stability analysis using a kriging based schur complement formulation a method is described to allow searches for transonic aeroelastic instability of realistically sized aircraft models in multidimensional parameter spaces when computational fluid dynamics are used to model the aerodynamics aeroelastic instability is predicted from a small nonlinear eigenvalue problem the approximation of the computationally expensive interaction term modeling the fluid response is formulated to allow the automated and blind search for aeroelastic instability the approximation uses a kriging interpolation of exact numerical samples covering the parameter space the approach demonstrated for the goland wing and the multidisciplinary optimization transport wing results in stability analyses over whole flight envelopes at an equivalent cost of several steady state simulations

a linear programming method for multiple criteria decision making with probabilistic linguistic information abstract the hesitant fuzzy linguistic term set hflts is applicable in expressing people s hesitant qualitative preference information however it may lose preference information as all the terms in the hflts are assigned the same weight the probabilistic linguistic term set plts can avoid this drawback by allowing the decision makers dms to give the weight of each linguistic term as a probability due to the flexibility of the plts the multiple criteria decision making mcdm with probabilistic linguistic information is now becoming a hot research topic the aim of this paper is to propose a linear programming method to solve the mcdm problems in which the dms preferences over the alternatives with respect to the given criteria are expressed as the pltss we first give the weighted deviation square measure for the normalized probabilistic linguistic positive ideal solution and each normalized probabilistic linguistic evaluation vector of each alternative then we define the inconsistency index and the consistency index according to the objective and subjective evaluations given by the dms based on which a linear programming model is then built to derive the weight of each criterion furthermore a linear programming method is developed to solve the mcdm problems with probabilistic linguistic information and a case study about the evaluation of hospitals is conducted to illustrate the proposed method finally some comparative analyses with the aggregation operator based method and the probabilistic linguistic preference ranking organization method for enrichment evaluation pl promethee method are made to show the advantages of the proposed method

a fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making decision making is a process common to human beings the uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision the recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguistic terms to provide their assessments the use of linguistic intervals whose results lose their initial fuzzy representation was introduced to facilitate the computing processes in which such expressions are used the aim of this paper is to present a new representation of the hesitant fuzzy linguistic term sets by means of a fuzzy envelope to carry out the computing with words processes this new fuzzy envelope can be directly applied to fuzzy multicriteria decision making models an illustrative example of its application to a supplier selection problem through the use of fuzzy topsis is presented

multiway spectral clustering with out of sample extensions through weighted kernel pca a new formulation for multiway spectral clustering is proposed this method corresponds to a weighted kernel principal component analysis pca approach based on primal dual least squares support vector machine ls svm formulations the formulation allows the extension to out of sample points in this way the proposed clustering model can be trained validated and tested the clustering information is contained on the eigendecomposition of a modified similarity matrix derived from the data this eigenvalue problem corresponds to the dual solution of a primal optimization problem formulated in a high dimensional feature space a model selection criterion called the balanced line fit blf is also proposed this criterion is based on the out of sample extension and exploits the structure of the eigenvectors and the corresponding projections when the clusters are well formed the blf criterion can be used to obtain clustering parameters in a learning framework experimental results with difficult toy problems and image segmentation show improved performance in terms of generalization to new samples and computation times

a rational consensus model in group decision making using linguistic assessments abstract a new consensus model for the consensus reaching process in a linguistic framework is presented in heterogeneous group decision making problems called rational consensus model it is guided by some linguistic consensus and linguistic consistency meaures all the measures are calculated from a set of linguistic preference relations used to provide experts opinions this consensus model allows more rational consensus solutions to be obtained and thus more human consistency to be incorporated in decision support systems

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 two dimensional mesh moving technique for time dependent partial differential equations abstract we discuss an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial boundary value problems for systems of partial differential equations in two space dimensions and time the mesh moving technique is based on an algebraic node movement function determined from the geometry and propagation of regions having significant discretization error indicators our procedure is designed to be flexible so that it can be used with many existing finite difference and finite element methods to test the mesh moving algorithm we implemented it in a system code with an initial mesh generator and a maccormack finite difference scheme on quadrilateral cells for hyperbolic vector systems of conservation laws results are presented for several computational examples the moving mesch scheme reduces dispersive errors near shocks and wave fronts and thereby reduces grid requirements necessary to compute accurate solutions while increasing computational efficiency

probabilistic linguistic term sets in multi attribute group decision making when expressing preferences in qualitative setting several possible linguistic terms with different weights represented by probabilities may be considered at the same time the probabilistic distribution is usually hard to be provided completely and ignorance may exist in this paper we first propose a novel concept called probabilistic linguistic term set plts to serve as an extension of the existing tools then we put forward some basic operational laws and aggregation operators for pltss after that we develop an extended topsis method and an aggregation based method respectively for multi attribute group decision making magdm with probabilistic linguistic information and apply them to a practical case concerning strategy initiatives finally the strengths and weaknesses of our methods are clarified by comparing them with some similar techniques

parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed sphere high resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate in this paper we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second order well balanced finite volume method on the cubed sphere with the fully implicit approach the time step size is no longer limited by the stability condition and with the multilevel preconditioners good scalabilities are obtained on computers with a large number of processors the investigation focuses on the use of semismooth inexact newton method for the case with nonsmooth topography and the use of two and three level overlapping schwarz methods with different order of discretizations for the preconditioning of the jacobian systems we test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors

a fully implicit domain decomposition algorithm for shallow water equations on the cubed sphere popular approaches for solving shallow water equations swes for climate modeling are explicit and semiimplicit methods and both have certain constraints on the time step size in this paper we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step the focus of the paper is a parallel fully coupled newton krylov ras algorithm with a jacobian matrix explicitly calculated on a weakly nonmatching cubed sphere mesh here ras is a restricted additive schwarz method we show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the cfl condition and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions

multigrid formulation of polynomial flux difference splitting for steady euler equations a flux difference splitting method based on the polynomial character of the flux vectors is applied to steady euler equations the discretization is done with a vertex centered finite volume method in first order form a discrete set of equations is obtained which is both conservative and positive the flux difference splitting is done in an algebraically exact way so that shocks are represented without wiggles due to the positivity the set of equations can be solved by collective relaxation methods a full multigrid method based on symmetric successive relaxation full weighting bilinear interpolation and w cycle is presented in firstorder form typical full multigrid efficiency is achieved this is demonstrated on the gamm transonic bump test case the second order formulation is based on the roe chakravarthy minmod limiter the discrete system is solved using a multigrid defect correction formulation the second order formulation is demonstrated on harten s shock reflection problem

mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information abstract regression analysis is widely used in evaluation and prediction and fuzzy least absolute regression is preferred when data is fat tailed or out linear given that the probabilistic linguistic term set is a powerful tool in expressing evaluators complex linguistic perceptions this paper incorporates the probabilistic linguistic term set to the fuzzy least absolute regression and builds a fuzzy regression model with mixed types of inputs to achieve this goal this paper introduces the concept of double cut set of the probabilistic linguistic term set then new operations of probabilistic linguistic term sets based on the double cut sets are investigated a mixed fuzzy least absolute regression model is proposed and a linear programming is introduced to work out the fuzzy regression parameters a numerical example concerning the house lease price evaluation under the shared economy is provided to validate the applicability of the proposed model the study ends with some concluding remarks

spatial discretization of the shallow water equations in spherical geometry using osher s scheme abstract the shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models since the seventies these models have often been solved with spectral methods increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods in this paper we study the use of osher s finite volume scheme for the spatial discretization of the shallow water equations on the rotating sphere this finite volume scheme of upwind type is well suited for solving a hyperbolic system of equations special attention is paid to the pole problem to that end osher s scheme is applied on the common reduced latitude longitude grid and on a stereographic grid the latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist the latitude longitude grid is preferred on lower latitudes therefore across the sphere we apply osher s scheme on a combined grid connecting the two grids at high latitude we will show that this provides an attractive spatial discretization for explicit integration methods as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude longitude grid only when time step limitation plays no significant role the standard reduced latitude longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles

validation of the steady state hover formulation for accurate performance predictions this paper shows accurate predictions for hover performance regardless of planform geometry blade tip mach number or disk loading to prove this statement sensitivity analyses were performed along with performance predictions for four rotor designs planform effects were also studied such as the blade anhedral showing the strong sensitivity of the rotor blade performance due to geometric features the steady state solution methodology with imposed froude boundary conditions is shown to give accurate results for relatively coarse grid sizes this approach leads to reduced computational costs as compared to time dependent simulations it is also recognized that given the current accuracy of the available experimental data the use of more advanced computational fluid dynamics methods may not be fully justified to advance the accuracy of modern computational fluid dynamics methods a comprehensive experimental dataset is required

upwind formulations for the euler equations in steady supersonic flows the euler equations that describe the steady supersonic flow can be reformulated in order to emphasize the role of propagating signals from such formulations upwind criteria are derived for the approximation of derivatives by finite differences formulations based on the quasilinear form and the divergence form of the governing equations are considered a numerical procedure based on these formulations is used as a tool for understanding the inviscid physics of the flow about a pointed cone at incidence the generation and development of embedded crossflow shocks and related spiral entropy singularities are investigated

modification of the osher upwind scheme for use in three dimensions the pertinent formulas are given by eq 24 for the variation of c kleb with the modified clauser pressure gradient parameter by eq 14 for the variation of ccp with ckleb and by eq 26 for the variation of the clauser factor k with low reynolds number as presented here the relations for the baldwin lomax factors have an indirect experimental validity by being derived from the experimentally confirmed velocity similarity laws finally it should be apparent that for boundary layers in pressure gradients constant values for the baldwin lomax factors are unsatisfactory in satisfying the velocity similarity laws to approach the same accuracy as the parent cebeci smith method the baldwinlomax factors should be varied as indicated

a flux difference splitting method for steady euler equations abstract the polynomial flux difference splitting method is applied to steady euler equations a discrete set of equations which is both conservative and positive is obtained the set of equations is solved by the relaxation technique

energy conservation under incompatibility for fluid structure interaction problems concurrent numerical methods for fluid structure interaction problems are typically based on partitioned solution procedures however such partitioned methods are inherently non conservative in the present work we investigate the conservation properties of monolithic discretisations for fluid structure interaction problems we consider a prototypical fluid structure interaction problem viz the piston problem a variational formulation allows us to establish precisely the conservation properties of the continuum problem and its discretisation by the finite element method we show that the conservation of energy by monolithic discretisations is only trivially maintained under restrictive compatibility conditions on the approximation spaces in the fluid and the structure moreover we introduce a new discretisation based on coincidence conditions which ensures energy conservation under incompatibility numerical results which illustrate the effectiveness of the new discretisation are presented

compact higher order characteristic based euler solver for unstructured grids two new methods are presented for solving the euler equations using a compact higher order polynomial reconstruction technique on unstructured grids the methods use a characteristic based approach with a cell centered finite volume method for transonic ringleb flow computations are performed for first order to fourth order accuracy and are compared with the hodograph solution results for a 10 deg ramp case are also presented an analysis is performed that demonstrates that the higher order method is an order of magnitude more efficient than the lower order method in modeling the flow for moderate to fine error tolerances accuracy speed and memory requirements are evaluated in the efficiency study compact higher order polynomial reconstruction technique is developed that allows for higher order char acteristic based numerical solutions to the euler equations on unstructured grids this reconstruction requires an extended set of euler equations that includes as dependent variables not only mass momentum and energy but also their spatial derivatives these additional dependent variables are used in a compact polynomial reconstruction process within a finite volume framework the development presented follows some of the ideas in the computational fluid dynamics cfd litera ture using continuous and discontinuous piecewise polynomial approximations continuous piecewise linear polynomials have been used in several finite volume and finite element unstructured grid methods jameson and mavriplis 1 lohner et al 2 and others have developed continuous piecewise linear elements using an added artificial dissipation and or flux corrected transport terms more recently oden3 has extended the linear elements by the use of higher order elements oden s work represents a compact higher order approximation of the continuous ele ment type discontinuous piecewise linear polynomials have similarly been used on unstructured grids with a characteristic based approach thareja et al 4 batina 5 frink 6 and others have developed discontinuous piecewise linear schemes with ap proximate riemann solvers on unstructured grids earth and frederickson7 developed a technique where polynomials of degree k are reconstructed for each cell by maintaining aver age dependent variable properties over a neighboring set of cells in a least squares formulation these polynomials are reconstructed using a large number of neighboring cells there fore the representation is not compact this paper describes two methods that compactly reconstruct higher order polyno mials over each cell in a discontinuous piecewise polynomial procedure two methods are presented for extending the euler equa tion set the first method solves the spatial derivatives of the governing integral equations the second method follows the work of allmaras 8 where the spatial moments of the govern ing equations are solved allmaras developed an approach

hyperbolicity and optimal coordinates for the three dimensional supersonic euler equations the two dimensional 2 d steady euler equations for supersonic flow in cartesian coordinates x y is hyperbolic except on the singular line u a where a is the speed of sound and u is the x component of velocity however the cauchy problem for x x circ with initial data prescribed at x x circ is well posed only when u a for the 2 d case the optimal coordinates have been found w h hui and d l chu comput fluid dynamics 4 1996 pp 403 426 to be the orthogonal system consisting of streamlines and their orthogonal lines this gives the most robust and accurate computation for supersonic flow it is commonly thought e g c y loh and m s liou j comput phys 113 1994 pp 224 248 that the system of three dimensional 3 d steady euler equations for supersonic flow is hyperbolic the present paper shows that it is hyperbolic only when the velocity in the marching direction is supersonic in which case it also simultaneously guarantees the well posedness of the cau

solving the multiple instance problem with axis parallel rectangles the multiple instance problem arises in tasks where the training examples are ambiguous a single example object may have many alternative feature vectors instances that describe it and yet only one of those feature vectors may be responsible for the observed classification of the object this paper describes and compares three kinds of algorithms that learn axis parallel rectangles to solve the multiple instance problem algorithms that ignore the multiple instance problem perform very poorly an algorithm that directly confronts the multiple instance problem by attempting to identify which feature vectors are responsible for the observed classifications performs best giving 89 correct predictions on a musk odor prediction task the paper also illustrates the use of artificial data to debug and compare these algorithms

upwind schemes and boundary conditions with applications to euler equations in general geometries abstract a unified treatment of several upwind shock capturing algorithms is presented each algorithm has a riemann initial value problem as its basis the treatment of boundaries involves solving the associated riemann initial boundary value problem the first author s algorithm applied to multidimensional euler equations in general geometries is then presented its worth is verified by various calculations which include mach 8 supersonic flow past a circular cylinder

liquid and liquid gas flows at all speeds all speed flows and in particular low mach number flow algorithms are addressed for the numerical approximation of the kapila et al 1 multiphase flow model this model is valid for fluid mixtures evolving in mechanical equilibrium but out of temperature equilibrium and is efficient for material interfaces computation separating miscible and non miscible fluids in this context the interface is considered as a numerically diffused zone captured as well as all present waves shocks expansion waves the same flow model can be used to solve cavitating and boiling flows 2 many applications occurring with liquid gas interfaces and cavitating flows involve a very wide range of mach number from 10 3 to supersonic and even hypersonic conditions with respect to the mixture sound speed it is thus important to address numerical methods free of restrictions regarding the mach number to do this a preconditioned riemann solver is built and embedded into the godunov explicit scheme it is shown that this method converges to exact solutions but needs too small time steps to be efficient an implicit version is then derived first in one dimension and second in the frame of 2d unstructured meshes two phase flow preconditioning is then addressed in the frame of the saurel et al 3 algorithm modifications of the preconditioned riemann solver are needed and detailed convergence of both single phase and two phase numerical solutions are demonstrated with the help of single phase and two phase steady nozzle flow solutions last the method is illustrated by the computation of real cavitating flows in venturi nozzles vapour pocket size and instability frequencies are reproduced by the model and method without using any adjustable parameter

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

computing the numerical scale of the linguistic term set for the 2 tuple fuzzy linguistic representation model when using linguistic approaches to solve decision problems we need the techniques for computing with words cw together with the 2 tuple fuzzy linguistic representation models i e the herrera and martinez model and the wang and hao model some computational techniques for cw are also developed in this paper we define the concept of numerical scale and extend the 2 tuple fuzzy linguistic representation models under the numerical scale we find that the key of computational techniques based on linguistic 2 tuples is to set suitable numerical scale with the purpose of making transformations between linguistic 2 tuples and numerical values by defining the concept of the transitive calibration matrix and its consistent index this paper develops an optimization model to compute the numerical scale of the linguistic term set the desired properties of the optimization model are also presented furthermore we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations the results in this paper are pretty helpful to complete the fuzzy 2 tuple representation models for cw

a consensus process for group decision making with probabilistic linguistic preference relations abstract in group decision making gdm process consensus is a fundamental problem the information provided by the experts in a gdm problem is usually expressed as preferences and the linguistic preference relation lpr is one of the most frequently used structures to model the experts preferences as a new type of lpr the probabilistic linguistic preference relation plpr not only allows the experts to provide more than one linguistic term about linguistic variables but also reflects different importance degrees of the possible preference values this paper focuses on the consensus reaching process for gdm with plprs an index for measuring the consensus degree is defined first then as for the expert group with unacceptable consensus degree a consensus improving method is introduced based on the consistency and consensus criteria moreover the whole gdm process is introduced based on the aggregation operators for the probabilistic linguistic term sets pltss finally an application case about medical information presented on search engine is discussed

transonic aeroelastic instability searches using sampling and aerodynamic model hierarchy doi 10 2514 1 j050509 a hierarchy of flow models is exploited for transonic aeroelastic stability analysis using the kriging interpolation technique applied within the schur complement eigenvalue framework in the schur framework a modified structural eigenvalue problem describes the coupled aeroelastic system with a precomputed interaction term depending on the response frequency the interaction term representing the influence of the high dimensional computational fluid dynamics system is approximated by reconstruction based on samples that can be computed using a frequency or time domain solver the computationally cheap approximation model is developed and discussed in this paper for two degree of freedom aerofoil cases the approximation model is used for both the parametric blind search of aeroelastic instability and for updating predictions based on aerodynamic models of different fidelities

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

a new lagrangian method for three dimensional steady supersonic flows in this paper the new lagrangian method introduced by loh and hui is extended for 3d steady supersonic flow computation we present the derivation of the conservation form and the solution of the local riemann solver using the godunov and the high resolution tvd schemes the new approach is accurate and robust capable of handling complicated geometry and interactions between discontinuous waves as shown in the test problems the current lagrangian method retains all the advantages claimed in the 2d method e g crisp resolution of a slip surface contact discontinuity and automatic grid generation in this paper we also suggest a novel 3d riemann problem in which interesting and intricate flow features are present

a multigrid method for the cauchy riemann equations based on flux difference splitting and its extension to the steady euler equations abstract flux vector splitting and flux difference splitting techniques are applied to the cauchy riemann equations it is shown that the discrete equations obtained by both techniques can be solved by relaxation methods which can be used in the multigrid technique the flux difference splitting technique is applied to the steady one dimensional euler equations and the resulting set of discrete equations is solved by a relaxation algorithm the solution for transonic flow is free of transition points in the shock region by analogy with the cauchy riemann equations it is concluded that this technique is extendable to two dimensions and that it can be used in the multigrid method

a finite volume scheme with shock fitting for the steady euler equations abstract analysis of two alternative finite volume formulations in respect of accuracy on non uniform meshes and number of spurious modes leads to a preference for the more compact cell vertex scheme over the cell centre scheme the resulting equations are solved iteratively by using a lax wendroff procedure as a smoother for a multigrid algorithm then application of boundary conditions in a natural way leads rapidly to all individual residuals being driven close to zero except at shocks at shocks the residuals should not be zero and a shock fitting procedure is introduced to avoid this inconsistency sharp accurate solutions on a relatively coarse mesh are obtained for a channel low problem in which the zierep singularity is displayed and for the naca 0012 aerofoil

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented

minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making in some real world decision processes decision makers may prefer to provide their opinions using linguistic expressions instead of a single linguistic term particularly they may hesitate between several linguistic terms in this paper we deal with the consensus issue in the hesitant linguistic group decision making gdm problem firstly a novel distance based consensus measure is proposed then using this consensus measure we develop an optimization based consensus model in the hesitant linguistic gdm which minimizes the number of adjusted simple terms in the consensus building furthermore a two stage model is displayed to further optimize the solutions to the proposed consensus model through which we obtain the unique optimal adjustment suggestion to support the consensus reaching process in the hesitant linguistic gdm finally several desirable properties are proposed to justify the proposal and two examples are used to demonstrate the validity of the models