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

control of the vorticity mode in the linearized euler equations for hybrid aeroacoustic prediction the issue of vorticity mode perturbation in linearized euler equations lee is addressed in this paper we chose to tackle this question by the point of view of source term formulation it is numerically shown that the use of a rotational free acoustic source term significantly reduces the development of the hydrodynamic mode in accordance with the theory the proposed source term lead to a quasi total absence of vorticity mode in a spatially uniform mean flow and a strong reduction in a sheared mean flow

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

on twistor spaces of anti self dual hermitian surfaces we consider a complex surface m with anti self dual hermitian metric h and study the holomorphic properties of its twistor space z we show that the naturally defined divisor line bundle x is isomorphic to the 1 2 power of the canonical bundle of z if and only if there is a kahler metric of zero scalar curvature in the conformal class of h this has strong consequences on the geometry of m which were also found by c boyer 3 using completely different methods we also prove the existence of a very close relation between holomorphic vector fields on m and z in the case that m is compact and kahler

a third order boundary value problem with jumping nonlinearities abstract a third order boundary value problem with jumping nonlinearities is studied some results obtained for second order boundary value problems with jumping nonlinearities are shown to hold also for the third order case

le nombre de solutions de certains problemes semi lineaires elliptiques abstract in this paper we compute the exact number of solutions for certain semi linear elliptic problems in the first part we derive some complementary results to a theorem of ambrosetti and prodi the global behaviour of bifurcating branches is then studied for some classes of problems in the context of a concave or a convex nonlinearity in the second part we consider the branch of positive solutions lastly in the third part in dimension one for an autonomous equation we obtain a precise description of all the solutions to these problems the proofs rely on simple eigenvalue comparison arguments

the influence of boundary data on the number of solutions of boundary value problems with jumping nonlinearities this paper contains results concerning the number of solutions as a function of the boundary data for boundary value problems with jumping nonlinearities an example seems to indicate that boundary data has a different influence on this number than does forcing data through approximating techniques this example leads to lower bounds on solution numbers for the more general case

singular hyperbolic monopoles we study the twistor theory of singular hyperbolic su 2 monopoles following the approach taken by kronheimer 9 in the euclidean case we use our results to show that the moduli space of charge 1 monopoles possesses a natural 2 sphere of scalar flat kahler metrics in the zero mass limit the metrics reduce to a class of metrics first studied by lebrun in 10

generalized ambrosetti prodi conditions for nonlinear two point boundary value problems 1 under the assumptions that g is of class c2 strictly convex and such that o lim g u l lim g u l 2 u ro it 0 where 1 a2 are the first two eigenvalues of the dirichlet problem on 52 for a they proved that the holder space c a was split into two open sets 0 and o2 by a c manifold m such that i if k e oo 1 has no solution ii if 12 e m 1 has exactly one solution iii if h e 02 1 has exactly two solutions 422

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

computation of flow noise using source terms in linearized euler s equations an acoustic analogy using linearized euler s equations lee forced with aerodynamic source terms is investigated to computetheacousticfare eld thishybridmethod isappliedto threemodelproblemssimulatedby solving navier stokes equations in this way its validity is estimated by comparing the predicted acoustic e eld with the reference solution given directly by the navier stokes equations the noise radiated by two corotating vortices is studied e rst in a medium at rest and second in a mean sheared e ow with no convection velocity then the sound e eld generated by vortex pairings in a subsonic mixing layer is investigated in this case a simplie ed formulation of lee is proposed to prevent the exponential growth of instability waves the acoustic e elds obtained by solving lee are in good agreement with the reference solution this study shows that the source terms introduced into the lee are appropriate for free sheared e ows and that acoustic mean e ow interactions are properly taken into account in the wave operator nomenclature b half width of the monopolar source c sound velocity e f h vectors in linearized euler s equations lee f frequency f0 fundamental frequency of the mixing layer k complex wave number kr ciki m mach number p pressure re reynolds number rc vortex core radius r0 initial half distance between the two vortices s sound source vector in lee si source terms in the momentum equations t period tij lighthill s tensor t time u unknown vector in lee u1 slow stream velocity of the mixing layer u2 rapid stream velocity of the mixing layer u velocity vector u1 u2 v initial tangential velocity of vortices

multiple solutions for a dirichlet problem with jumping nonlinearities ii on considere l existence des solutions pour le probleme x t g x t p t c t 0 1 x 0 x 1 0 ou p t est une fonction continue et c est une constante on suppose que g est de classe c 1 et que g est positive et strictement croissante sur 0

multiplicity results for ode s with nonlinearities crossing all but a finite number of eigenvalues on considere des equations differentielles du type suivant u x u x p u x te 1 x x 0 u 0 u 0 ou p 1 u max u 0 r et e 1 x sinx est la fonction propre correspondant a 1 ou 0 1 2 3 k denotent les valeurs propres de l operateur d 2 dx 2 a conditions aux limites nulles

a second order projection method for variable density flows this paper describes a second order projection method for variabledensity incompressible flows the method is suitable for both finite amplitude density variations and for fluids that are modeled using a boussinesq approximation it is based on a second order fractional step scheme in which diffusion convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergencefree vector fields the nonlinear convection terms are treated using a godunov type procedure that is second order for smooth flow and remain stable and non oscillatory for nonsmooth flows with low fluid viscosities the method is described for finite amplitude density variation and the simplifications for a boussinesq approximation are sketched numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems

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

an analysis of the fractional step method the fractional step method for solving the incompressible navier stokes equations in primitive variables is analyzed as a block lu decomposition in this formulation the issues involving boundary conditions for the intermediate velocity variables and the pressure are clearly resolved in addition it is shown that poor temporal accuracy first order is not due to boundary conditions but due to the method itself a generalized block lu decomposition that overcomes this difficulty is presented allowing arbitrarily high temporal order of accuracy the generalized decomposition is shown to be useful for a wide range of problems including steady problems technical issues such as stability and the appropriate pressure update scheme are also addressed numerical simulations of the steady incompressible navier stokes equations in a square domain confirm the theoretical results 18 refs 4 figs

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

on the number of solutions of two classes of sturm liouville boundary value problems abstract we employ global bifurcation theory of p h rabinowitz together with sturm comparison theorem to establish multiplicity results for some classes of sturm liouville boundary value problems

a fast pressure correction method for incompressible two fluid flows we have developed a new pressure correction method for simulating incompressible two fluid flows with large density and viscosity ratios the method s main advantage is that the variable coefficient poisson equation that arises in solving the incompressible navier stokes equations for two fluid flows is reduced to a constant coefficient equation which can be solved with an fft based fast poisson solver this reduction is achieved by splitting the variable density pressure gradient term in the governing equations the validity of this splitting is demonstrated from our numerical tests and it is explained from a physical viewpoint in this paper the new pressure correction method is coupled with a mass conserving volume of fluid method to capture the motion of the interface between the two fluids but in general it could be coupled with other interface advection methods such as level set phase field or front tracking first we verified the new pressure correction method using the capillary wave test case up to density and viscosity ratios of 10 000 then we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value next the method is shown to be second order accurate in space and time independent of the vof method and it conserves mass momentum and kinetic energy in the inviscid limit also we show that for solving the two fluid navier stokes equations the method is 10 40 times faster than the standard pressure correction method which uses multigrid to solve the variable coefficient poisson equation finally we show that the method is capable of performing fully resolved direct numerical simulation dns of droplet laden isotropic turbulence with thousands of droplets using a computational mesh of 1024 3 points

nonautonomous boundary value problems with jumping nonlinearities soit f 0 1 r r une fonction continue continument differentiable par rapport au second argument sous l hypothese que les limites lim s f x s s x lim s f x s x x existent et sont uniformes sur 0 1 on etudie le probleme aux valeurs limites u f x u th u 0 u 1 0 ou t est un nombre reel et h une fonction continue pour f fixee on etudie le nombre de solutions

the exact number of solutions for a class of ordinary differential equations through morse index computation we consider a class of second order ordinary differential equations with jumping nonlinearities that cross the first k eigenvalues under zero boundary conditions and by means of a morse index computation show the existence of exactly 2 k solutions

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

magnetic monopoles on three manifolds on etudie des monopoles magnetiques sur une 3 variete de riemann complete orientee m on associe a m une collection d espaces de modules de solutions des equations des monopoles pourvu que m soit non compacte et que la metrique de riemann sur m soit bonne pres de l infini

monopoles and geodesics using the holomorphic geometry of the space of straight lines in euclidean 3 space it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the atiyah ward ansatz a k

numerical appraisal of three low mach number algorithms for radiative convective flows in enclosures abstract the present study investigates three different algorithms for the numerical simulation of non boussinesq convection with thermal radiative heat transfer based on a low mach number formulation the solution methodology employs a fractional step approach based on the finite volume method on arbitrary polyhedral meshes the three algorithms compute the coupled governing equations in a segregated manner using the conservative form of momentum equations in conjunction with a variable coefficient pressure poisson equation the first algorithm algorithm a uses conservation of mass and energy equation to compute density and temperature the other two algorithms algorithm b and algorithm c calculates temperature and density from the equation of state respectively and solves a conservative form of the continuity and energy equation to obtain density and temperature respectively the energy and mass conservation errors arising due to the use of algorithms b and c are derived concerning various non dimensional parameters governing the flow and heat transfer the significance of these errors is highlighted by performing investigations over a range of rayleigh prandtl and planck numbers for various two and three dimensional natural convection problems with radiative heat transfer finally the role of balancing of the pressure and buoyancy terms is emphasized for robust calculations of large temperature difference thermo buoyant convection with radiative heat transfer

instantons on mathbf cp _2 on decrit et on classe les instantons sur cp 2 pour les groupes de lie simples compacts unitaires et classiques

some characterizations of dirac type singularity of monopoles we study singular monopoles on open subsets in the 3 dimensional euclidean space we give two characterizations of dirac type singularities one is given in terms of the growth order of the norms of sections which are invariant by the scattering map the other is given in terms of the growth order of the norms of the higgs fields

hamiltonian systems admitting a runge lenz vector and an optimal extension of bertrand s theorem to curved manifolds bertrand s theorem asserts that any spherically symmetric natural hamiltonian system in euclidean 3 space which possesses stable circular orbits and whose bounded trajectories are all periodic is either a harmonic oscillator or a kepler system in this paper we extend this classical result to curved spaces by proving that any hamiltonian on a spherically symmetric riemannian 3 manifold which satisfies the same conditions as in bertrand s theorem is superintegrable and given by an intrinsic oscillator or kepler system as a byproduct we obtain a wide panoply of new superintegrable hamiltonian systems the demonstration relies on perlick s classification of bertrand spacetimes and on the construction of a suitable globally defined generalization of the runge lenz vector