a semi implicit numerical scheme for reacting flow an additive semi implicit projection scheme for the simulation of unsteady combustion in two dimensions is constructed the scheme relies on a zero mach number formulation of the compressible conservation equations with detailed chemistry the governing equations are discretized in space using second order differences and integrated in time using a semi implicit approach time integration of the evolution equations for species mass fraction thermodynamic pressure and density is performed using a semi implicit nonsplit scheme that combines a second order predictor corrector treatment of convection and diffusion terms and a stiff integrator for the reaction source terms meanwhile the momentum equations are integrated using a second order projection scheme the projection scheme is based on a predictor corrector approach that couples the evolution of the velocity and density fields in order to stabilize computations of reacting flows with large density variations a pressure poisson equation is inverted following both the predictor and corrector steps using a fast solver the advantages of the stiff integration of reaction source terms are analyzed by comparing the performance of the scheme to that of a predictor corrector scheme in which reaction and diffusion are integrated in a similar nonstiff fashion the comparison in based on both one dimensional 1d unsteady tests of a premixed methane air flame and unsteady two dimensional tests of the same flame interacting with a counterrotating vortex pair in both cases the grimech1 2 reaction mechanism with 32 species and 177 elementary reactions is used computed results show that the stiff reaction scheme enables selection of larger time steps and thus leads to substantial improvement in the performance of the computations for the present reaction mechanism and flame conditions speedup factors of about 10 are achieved in the 1d tests and about five in two dimensions possible extensions of the present scheme to further improve efficiency are also discussed

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

an algebraic variational multiscale multigrid method for large eddy simulation of turbulent variable density flow at low mach number an algebraic variational multiscale multigrid method is proposed for large eddy simulation of turbulent variable density flow at low mach number scale separating operators generated by level transfer operators from plain aggregation algebraic multigrid methods enable the application of modeling terms to selected scale groups here the smaller of the resolved scales in a purely algebraic way thus for scale separation no additional discretization besides the basic one is required in contrast to earlier approaches based on geometric multigrid methods the proposed method is thoroughly validated via three numerical test cases of increasing complexity a rayleigh taylor instability turbulent channel flow with a heated and a cooled wall and turbulent flow past a backward facing step with heating results obtained with the algebraic variational multiscale multigrid method are compared to results obtained with residual based variational multiscale methods as well as reference results from direct numerical simulation experiments and les published elsewhere particularly mean and various second order velocity and temperature results obtained for turbulent channel flow with a heated and a cooled wall indicate the higher prediction quality achievable when adding a small scale subgrid viscosity term within the algebraic multigrid framework instead of residual based terms accounting for the subgrid scale part of the non linear convective term

a new version of bishop frame and an application to spherical images abstract in this work we introduce a new version of bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as type 2 bishop frame thereafter by translating type 2 bishop frame vectors to the center of unit sphere of three dimensional euclidean space we introduce new spherical images and call them as type 2 bishop spherical images frenet serret apparatus of these new spherical images are obtained in terms of base curve s type 2 bishop invariants additionally we express some interesting relations and illustrate two examples of our main results

a numerical method for two phase flows of dense granular mixtures in this paper a novel algorithm for incompressible flows of two phase granular mixtures is proposed the algorithm constitutes a generalization of projection type methods to multi phase flows and employs a predictor corrector time marching scheme for the computation of the phasial pressures a poisson equation and a second order elliptic pde with variable coefficients are solved at both the prediction and the correction stage further the algorithm is combined with a regularization scheme for the numerical treatment of material interfaces which are a common characteristic of the flows of interest the efficiency and robustness of the proposed algorithm are illustrated via numerical simulations of unsteady two dimensional shear flows for a reference mixture of beach sand and water

semidefinite relaxations for quadratically constrained quadratic programming a review and comparisons at the intersection of nonlinear and combinatorial optimization quadratic programming has attracted significant interest over the past several decades a variety of relaxations for quadratically constrained quadratic programming qcqp can be formulated as semidefinite programs sdps the primary purpose of this paper is to present a systematic comparison of sdp relaxations for qcqp using theoretical analysis it is shown that the recently developed doubly nonnegative relaxation is equivalent to the shor relaxation when the latter is enhanced with a partial first order relaxation linearization technique these two relaxations are shown to theoretically dominate six other sdp relaxations a computational comparison reveals that the two dominant relaxations require three orders of magnitude more computational time than the weaker relaxations while providing relaxation gaps averaging 3 as opposed to gaps of up to 19 for weaker relaxations on 700 randomly generated problems with up to 60 variables an sdp relaxation derived from lagrangian relaxation after the addition of redundant nonlinear constraints to the primal achieves gaps averaging 13 in a few cpu seconds

time accurate calculation of variable density flows with strong temperature gradients and combustion a time accurate algorithm is proposed for low mach number variable density flows with or without chemical reactions the algorithm is based on a predictor corrector time integration scheme that employs a projection method for the momentum equation a constant coefficient poisson equation is solved for the pressure following both the predictor and corrector steps to fully satisfy the continuity equation at each time step spatial discretization is performed on a collocated grid system that offers computational simplicity and straightforward extension to curvilinear coordinate systems to avoid the pressure odd even decoupling that is typically encountered in such grids a flux interpolation technique is introduced for the equations governing variable density flows an important characteristic of the proposed algorithm is that it can be applied to flows in both open and closed domains its robustness and accuracy are illustrated with a series of numerical experiments in particular we present simulations of non isothermal turbulent channel flow as well as simulations of a premixed flame vortex interaction

a numerical method for large eddy simulation in complex geometries we discuss the development of a numerical algorithm and solver capable of performing large eddy simulation in the very complex geometries often encountered in industrial applications the algorithm is developed for unstructured hybrid grids is non dissipative yet robust at high reynolds numbers on highly skewed grids simulation results for a variety of flows are presented

alternating direction ghost fluid methods for solving the heat equation with interfaces abstract this work presents two new alternating direction implicit adi schemes for solving parabolic interface problems in two and three dimensions first the ghost fluid method gfm is adopted for the first time in the literature to treat interface jumps in the adi framework which results in symmetric and tridiagonal finite difference matrices in each adi step the proposed gfm adi scheme achieves a first order of accuracy in both space and time as confirmed by numerical experiments involving complex interface shapes and spatial temporal dependent jumps the gfm adi scheme also maintains the adi efficiency the computational complexity for each time step scales as o n for a total degree of freedom n in higher dimensions second a new matched interface and boundary mib scheme is constructed which downgrades the quadratic polynomial bases in the existing second order mib to linear ones interestingly the resulting mib adi or madi scheme produces the same finite difference matrices as the gfm adi scheme in all dimensions hence the madi scheme can be regarded as an improvement of the gfm because it calculates tangential jumps which are omitted in the gfm consequently the present madi scheme is constantly more accurate than the gfm adi in all numerical examples while keeping the same computational efficiency nevertheless the madi scheme is semi implicit due to tangential jump approximations while the gfm adi scheme is fully implicit without tangential corrections thus the gfm adi scheme could be more stable than the madi scheme when a huge contrast is presented in diffusion coefficients

rational rotation minimizing frames recent advances and open problems recent developments in the basic theory algorithms and applications for curves with rational rotation minimizing frames rrmf curves are reviewed and placed in the context of the current state of the art by highlighting the many significant open problems that remain the simplest non trivial rrmf curves are the quintics characterized by a scalar condition on the angular velocity of the euler rodrigues frame erf two different classes of rrmf quintics can be identified the first class of curves may be characterized by quadratic constraints on the quaternion coefficients of the generating polynomials by the root structure of those polynomials or by a certain polynomial divisibility condition the second class has a strictly algebraic characterization less well suited to geometrical construction algorithms the degree 7 rrmf curves offer more shape freedoms than the quintics but only one of the four possible classes of these curves has been satisfactorily described generalizations of the adapted rotation minimizing frames for which the angular velocity has no component along the tangent to directed and osculating frames with analogous properties relative to the polar and binormal vectors are also discussed finally a selection of applications for rotation minimizing frames are briefly reviewed including construction of swept surfaces rigid body motion planning 5 axis cnc machining and camera orientation control

indefinite trust region subproblems and nonsymmetric eigenvalue perturbations this paper extends the theory of trust region subproblems in two ways i it allows indefinite inner products in the quadratic constraint and ii it uses a two sided upper and lower bound quadratic constraint characterizations of optimality are presented that have no gap between necessity and sufficiency conditions for the existence of solutions are given in terms of the definiteness of a matrix pencil a simple dual program is introduced that involves the maximization of a strictly concave function on an interval this dual program simplifies the theory and algorithms for trust region subproblems it also illustrates that the trust region subproblems are implicit convex programming problems and thus explains why they are so tractable the duality theory also provides connections to eigenvalue perturbation theory trust region subproblems with zero linear term in the objective function correspond to eigenvalue problems and adding a linear term in the objective function is seen to correspond to a p

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

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

a robust colocated implicit algorithm for direct numerical simulation of compressible turbulent flows a non dissipative robust implicit algorithm is proposed for direct numerical and large eddy simulation of compressible turbulent flows the algorithm addresses the problems caused by low mach numbers and under resolved high reynolds numbers it colocates variables in space to allow easy extension to unstructured grids and discretely conserves mass momentum and total energy the navier stokes equations are non dimensionalized using an incompressible scaling for pressure and the energy equation is used to obtain an expression for the velocity divergence a pressure correction approach is used to solve the resulting equations such that the discrete divergence is constrained by the energy equation as a result the discrete equations analytically reduce to the incompressible equations at very low mach number i e the algorithm overcomes the acoustic time scale limit without preconditioning or solution of an implicit system of equations the algorithm discretely conserves kinetic energy in the incompressible inviscid limit and is robust for inviscid compressible turbulence on the convective time scale these properties make it well suited for dns les of compressible turbulent flows results are shown for acoustic propagation the incompressible taylor problem periodic shock tube problem and isotropic turbulence

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

a ghost fluid method for large eddy simulations of premixed combustion in complex geometries in this paper a new ghost fluid method for interfaces of finite thickness is described it allows to compute efficiently turbulent premixed flames with a finite thickness in low mach flows a level set algorithm is used to track accurately the flame and to define the overlapping region where the burned and unburned gases satisfy the jump conditions these algorithms are combined with a fractional step method to alleviate the acoustic cfl constraint the full algorithm is verified for simple flame vortex interactions and it is validated by computing a turbulent flame anchored by a triangular flame holder finally the algorithm is applied in the les of an industrial lean premixed swirl burner

back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function we propose a method that significantly improves the accuracy of the level set method and could be of value for numerical solutions of differential equations in general level set methods use a level set function usually an approximate signed distance function to represent the interface as the zero set of when is advanced to the next time level by an advection equation its new zero level set will represent the new interface position but the non zero curvature of the interface will result in uneven gradients of the level set function which induces extra numerical error instead of attempting to reduce this error directly we update the level set function forward in time and then backward to get another copy of the level set function say 1 1 and should have been equal if there were no numerical error therefore 1 provides us the information of error induced by uneven gradients and this information can be used to compensate before updating forward again in time

multivariate nonnegative quadratic mappings in this paper we study several issues related to the characterization of specific classes of multivariate quadratic mappings that are nonnegative over a given domain with nonnegativity defined by a prespecified conic order in particular we consider the set cone of nonnegative quadratic mappings defined with respect to the positive semidefinite matrix cone and study when it can be represented by linear matrix inequalities we also discuss the applications of the results in robust optimization especially the robust quadratic matrix inequalities and the robust linear programming models in the latter application the implementational errors of the solution are taken into account and the problem is formulated as a semidefinite program

a semidefinite framework for trust region subproblems with applications to large scale minimization primal dual pairs of semidefinite programs provide a general framework for the theory and algorithms for the trust region subproblem trs this latter problem consists in minimizing a general quadratic function subject to a convex quadratic constraint and therefore it is a generalization of the minimum eigenvalue problem the importance of trs is due to the fact that it provides the step in trust region minimization algorithms the semidefinite framework is studied as an interesting instance of semidefinite programming as well as a tool for viewing known algorithms and deriving new algorithms for trs in particular a dual simplex type method is studied that solves trs as a parametric eigenvalue problem this method uses the lanczos algorithm for the smallest eigenvalue as a black box therefore the essential cost of the algorithm is the matrix vector multiplication and thus sparsity can be exploited a primal simplex type method provides steps for the so called hard case extensive numerical tests for large sparse problems are discussed these tests show that the cost of the algorithm is 1 n times the cost of finding a minimum eigenvalue using the lanczos algorithm where 0 n 1 is a fraction which decreases as the dimension increases

on mass conservation and solvability of the discretized variable density zero mach navier stokes equations abstract this paper presents a study of a variable density zero mach navier stokes discretization and subtle difficulties associated with the pressure a consistent compatibility condition between the temperature and velocity is first derived it is shown that one can accurately and efficiently solve all primitive variables with the uniform order of accuracy of the specified discretization and time marching schemes it is shown that higher density ratios than those commonly reported are achievable and it is in part traced to the solvability of the pressure poisson equation numerical properties are assessed with the method of manufactured solutions and several classical testing cases are carried out to validate the code ranging from variable density mixing problems to premixed flames with forcing

a local anisotropic adaptive algorithm for the solution of low mach transient combustion problems a novel numerical algorithm for the simulation of transient combustion problems at low mach and moderately high reynolds numbers is presented these problems are often characterized by the existence of a large disparity of length and time scales resulting in the development of directional flow features such as slender jets boundary layers mixing layers or flame fronts this makes local anisotropic adaptive techniques quite advantageous computationally in this work we propose a local anisotropic refinement algorithm using for the spatial discretization unstructured triangular elements in a finite element framework for the time integration the problem is formulated in the context of semi lagrangian schemes introducing the semi lagrange galerkin slg technique as a better alternative to the classical semi lagrangian sl interpolation the good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem the flame vortex interaction first a premixed methane air flame vortex interaction with simplified transport and chemistry description test i is considered results are found to be in excellent agreement with those in the literature proving the superior performance of the slg scheme when compared with the classical sl technique and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement as a more realistic example we then conduct simulations of non premixed hydrogen air flame vortex interactions test ii using a more complex combustion model which involves state of the art transport and chemical kinetics in addition to the analysis of the numerical features this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature

direct numerical simulation of a turbulent reactive plume on a parallel computer a computational algorithm is described for direct numerical simulation dns of a reactive plume in spatially evolving grid turbulence the algorithm uses sixth order compact differencing in conjunction with a fifth order compact boundary scheme which has been developed and found to be stable a compact filtering method is discussed as a means of stabilizing calculations where the viscous diffusive terms are differenced in their conservative form this approach serves as an alternative to nonconservative differencing previously advocated as a means of damping the 2 waves in numerically solving the low mach number equations the time derivative of the density field in the pressure poisson equation was found to be the most destabilizing part of the calculation even ordered finite difference approximations to this derivative were found to be more stable allow for larger density gradients than odd ordered approximations turbulence at the inlet boundary is generated by scanning through an existing three dimensional field of fully developed turbulence in scanning through the inlet field it was found that a high order interpolation e g cubic spline interpolation is necessary in order to provide continuous velocity derivatives regarding pressure a neumann inlet condition combined with a dirichlet outlet condition was found to work well the chemistry follows the single step irreversible global reaction fuel r oxidizer 1 r product heat with parameters chosen to match experimental data as far as allowed by resolution constraints simulation results are presented for four different cases in order to examine the effects of heat release damkohler number and arrhenius kinetics on the flow physics statistical data from the dns are compared to theory and wind tunnel data and found in reasonable agreement with regard to growth of turbulent length scales decay of turbulent kinetic energy decay of centerline scalar concentration decrease in scalar rms and spread of plume profile reactive scalar statistics are consistent with expected behavior

a new lower bound via projection for the quadratic assignment problem new lower bounds for the quadratic assignment problem qap are presented these bounds are based on the orthogonal relaxation of qap the additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums the new bound is easy to implement and often provides high quality bounds under an acceptable computational effort

projection methods for two velocity two pressure models for flows of heterogeneous mixtures in this paper a numerical analysis of two velocity two pressure models for flows of solid particles and fluids is presented first a formal exploitation of the weak formulation of such models asserts that they are amenable to integration via projection methods the challenging issues in the algorithm development for these models are then documented and suitable numerical methodologies for their remedy are devised subsequently an algorithm for the integration of the models of interest is proposed this is a two phase projection method on collocated grids that utilizes a fractional step time marching scheme it is further endowed with an interface detection and treatment methodology to properly account for the stiffness induced by the presence of moving and deforming material interfaces the efficiency and robustness of the proposed numerical method are assessed in a series of numerical experiments that are delineated in the last part of this paper

the equilibrium limit of a constitutive model for two phase granular mixtures and its numerical approximation in this paper we analyze the equilibrium limit of the constitutive model for two phase granular mixtures introduced in papalexandris 2004 13 and develop an algorithm for its numerical approximation at equilibrium the constitutive model reduces to a strongly coupled overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase first we carry a perturbation analysis based on standard hydrostatic type scaling arguments which reduces the complexity of the coupling of the equations the perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator further based on the helmholtz decomposition and ladyzhenskaya s decomposition theorem we develop a projection type successive over relaxation numerical method this method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro structure we also prove that this method is both stable and consistent hence under standard assumptions convergent the paper concludes with the presentation of representative numerical results

a note on lack of strong duality for quadratic problems with orthogonal constraints abstract the general quadratically constrained quadratic program qqp is an important modelling tool for many diverse problems the qqp is in general np hard and numerically intractable lagrangian relaxations often provide good approximate solutions to these hard problems such relaxations are equivalent to semidefinite programming relaxations and can be solved efficiently for several special cases of qqp the lagrangian relaxation provides the exact optimal value this means that there is a zero duality gap and the problem is tractable it is important to know for which cases this is true since they can then be used as subproblems to improve lagrangian relaxation for intractable qqps in this paper we study the special qqp with orthogonal matrix constraints xx t i if c 0 the zero duality gap result holds if the redundant orthogonal constraints x t x i are added we show that this is not true in the general case however we show how to close the duality gap in the pure linear case by adding variables in addition to constraints

design of rational rotation minimizing rigid body motions by hermite interpolation the construction of space curves with rational rotation minimizing frames rrmf curves by the interpolation of g1 hermite data i e initial final points pi and pf and frames ti ui vi and tf uf vf is addressed noting that the rrmf quintics form a proper subset of the spatial pythagorean hodograph ph quintics characterized by a vector constraint on their quaternion coefficients and that c1 spatial ph quintic hermite interpolants possess two free scalar parameters sufficient degrees of freedom for satisfying the rrmf condition and interpolating the end points and frames can be obtained by relaxing the hermite data from c1 to g1 it is shown that after satisfaction of the rrmf condition interpolation of the end frames can always be achieved by solving a quadratic equation with a positive discriminant three scalar freedoms then remain for interpolation of the end point displacement pf pi and this can be reduced to computing the real roots of a degree 6 univariate polynomial the nonlinear dependence of the polynomial coefficients on the prescribed data precludes simple a priori guarantees for the existence of solutions in all cases although existence is demonstrated for the asymptotic case of densely sampled data from a smooth curve modulation of the hodograph by a scalar polynomial is proposed as a means of introducing additional degrees of freedom in cases where solutions to the end point interpolation problem are not found the methods proposed herein are expected to find important applications in exactly specifying rigid body motions along curved paths with minimized rotation for animation robotics spatial path planning and geometric sweeping operations

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined