extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach numberm

an innovative eigenvalue problem solver for free vibration of euler bernoulli beam by using the adomian decomposition method this paper deals with free vibration problems of euler bernoulli beam under various supporting conditions the technique we have used is based on applying the adomian decomposition method adm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis

a splitting method for incompressible flows with variable density based on a pressure poisson equation a new fractional time stepping technique for solving incompressible flows with variable density is proposed the main feature of this method is that as opposed to other known algorithms the pressure is determined by just solving one poisson equation per time step which greatly reduces the computational cost the stability of the method is proved and the performance of the method is numerically illustrated

an innovative eigenvalue problem solver for free vibration of uniform timoshenko beams by using the adomian modified decomposition method this paper deals with free vibration problems of uniform timoshenko beams under various supporting boundary conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis

mixed stabilized finite element methods based on backward difference adams bashforth scheme for the time dependent variable density incompressible flows in this paper we consider a second order mixed stabilized finite element method based on pressure projection method for variable density incompressible flows the originality of the proposed approach is to use a stabilized method based on the difference between a consistent and an under integrated mass matrix of the pressure for variable density incompressible flows approximated by the lowest equal order finite element pairs a second order backward difference bdf for the temporal term and a second order adams bashforth ab for the explicit treatment of the nonlinear term lead to the presented second order bdf ab scheme the stability of the method was proved and the performance of the method is numerically illustrated finally comparison with some established methods a series of numerical experiments are given to show that this method has better stability and accuracy

iterative solutions for a beam equation with nonlinear boundary conditions of third order a fourth order differential equation with nonlinear boundary conditions modeling beams on elastic foundations is considered iterative solutions are proved through the contraction principle some numerical simulations are also provided

an hybrid finite volume finite element method for variable density incompressible flows this paper is devoted to the numerical simulation of variable density incompressible flows modeled by the navier stokes system we introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint the breakthrough relies on the definition of a suitable footbridge between the two methods through the design of compatibility condition in turn the method is very flexible and allows to deal with unstructured meshes several numerical tests are performed to show the scheme capabilities in particular the viscous rayleigh taylor instability evolution is carefully investigated

monotone positive solutions for a fourth order equation with nonlinear boundary conditions abstract this work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions the results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions numerical simulations are also presented

the method of lower and upper solutions for fourth order two point boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u iv f x u x u x u 0 u 1 u 0 u 1 0 where f 0 1 r r r is continuous

fourth order problems with nonlinear boundary conditions we develop a new method of lower and upper solutions for a fourth order nonlinear boundary value problem where the differential equation has dependence on all lower order derivatives our boundary conditions are nonlinear we will assume the functions that define the nonlinear boundary conditions are either monotone or nonmonotone as a result we obtain existence principles which improve recent results in the literature

the forced vibration and boundary control of pretwisted timoshenko beams with general time dependent elastic boundary conditions abstract the governing differential equations and the general time dependent elastic boundary conditions for the coupled bending bending forced vibration of a pretwisted non uniform timoshenko beam are derived by hamilton s principle by introducing a general change of dependent variable with shifting functions the original system is transformed into a system composed of four non homogeneous governing differential equations and eight homogeneous boundary conditions the transformed system is proved to be self adjoint consequently the method of separation of variables can be used to solve the transformed problem the physical meanings of these shifting functions are explored the orthogonality condition for the eigenfunctions of a pretwisted non uniform beam with elastic boundary conditions is also derived the relation between the shifting functions and the stiffness matrix is derived the boundary control of a pretwist timoshenko beam is studied the effects of the total pretwist angle the position of loading and the boundary spring constants on the energy required to control the performance of a pretwisted beam are investigated

a note on vibrations of generally restrained beams exact frequency and normal mode shape expressions are derived in this note for generally restrained bernoulli euler beams with unsymmetrical translations and rotations at either end the eigenfrequencies and mode shape parameters are presented for a wide range of restraint parameters several degenerate cases have been studied and some of these have been compared with those available in the published literature it is believed that the results presented in this paper will be of use in design of beams shafts and piping under dynamic considerations

a new stabilized finite element method for the transient navier stokes equations abstract this paper is concerned with the development and analysis of a new stabilized finite element method based on two local gauss integrations for the two dimensional transient navier stokes equations by using the lowest equal order pair of finite elements this new stabilized finite element method has some prominent features parameter free avoiding higher order derivatives or edge based data structures and stabilization being completely local at the element level an optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the galerkin finite element method under certain regularity assumptions on the solution compared with other stabilized methods using the same pair of mixed finite elements for the two dimensional transient navier stokes equations through a series of numerical experiments it is shown that this new stabilized method has better stability and accuracy results

bifurcation from interval and positive solutions of a nonlinear fourth order boundary value problem abstract we study the existence of positive solutions of the nonlinear boundary value problem u 4 t f t u t u t t 0 1 u 0 u 1 u 0 u 1 0 which is not necessarily linearizable our approaches are based on krein rutman theorem topological degree theory and global bifurcation techniques

reduced order modeling of time dependent incompressible navier stokes equation with variable density based on a local radial basis functions finite difference lrbf fd technique and the pod deim method abstract the main propose of this investigation is to introduce a rapid and impressive numerical procedure to simulate the time dependent incompressible navier stokes equation with variable density the developed formulation is constructed by using the meshfree rbf fd technique also to improve the numerical results an extra diffusion term has been added to the density equation with a small coefficient on the other hand a reduced order technique e g proper orthogonal decomposition pod has been employed to get a fast numerical method and to decrease the elapsed cpu time on the other hand since the considered problem is fully nonlinear thus in the reduced order model based on the pod idea there are some nonlinear terms that they take more computational time hence we employ the discrete empirical interpolation method deim to overcome the nonlinear terms four test problems have been proposed to show the ability of the numerical simulations

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

an extended residual based variational multiscale method for two phase flow including surface tension abstract in this study an extended residual based variational multiscale method is proposed for two phase flow including surface tension the extended residual based variational multiscale method combines a residual based form of the variational multiscale method and the extended finite element method xfem by extending the solution spaces it is possible to reproduce discontinuities of the solution fields inside elements intersected by the interface in particular we propose a quasi static enrichment to reproduce time dependent discontinuities kink enrichments of both velocity and pressure as well as kink enrichments of velocity combined with jump enrichments of pressure are considered here to capture the interface between the phases on a fixed grid a level set approach is used a residual based variational multiscale method is employed for computing both flow and interface motion the presented method is tested for various two phase flow examples exhibiting small and large density and viscosity ratios with and without surface tension a two phase couette flow a rayleigh taylor instability a sloshing tank and a three dimensional rising bubble to the best of our knowledge these are the first simulation results for representative time dependent three dimensional two phase flow problems using an extended finite element method stable and accurate results are obtained for all test examples

ordered probability spaces abstract let c be an open cone in a banach space equipped with the thompson metric with closure a normal cone the main result gives sufficient conditions for borel probability measures on c with finite first moment for which in the stochastic order induced by the cone to be order approximated by sequences n n of uniform finitely supported measures in the sense that n n for each n and n n in the wasserstein metric this result is the crucial tool in developing a pathway for extending various inequalities on operator and matrix means which include the harmonic geometric and arithmetic operator means on the cone of positive elements of a c algebra to the space p 1 c of borel measures of finite first moment on c as an illustrative and important particular application we obtain the monotonicity of the karcher geometric mean on p 1 a for the positive cone a of a c algebra a

existence multiplicity and infinite solvability of positive solutions to a nonlinear fourth order periodic boundary value problem abstract the existence of n and infinitely many positive solutions is proved for the nonlinear fourth order periodic boundary value problem u 4 t u t u t f t u t 0 t 1 u i 0 u i 1 i 0 1 2 3 where n is an arbitrary natural number and 2 2 0 1 2 2 2 2 4 2 1 0 this kind of fourth order boundary value problems usually describes the equilibrium state of an elastic beam with periodic boundary condition the main results show that the problem may have n or infinitely many positive solutions provided the growth rates of nonlinear term f t l are appropriate on some bounded subsets of its domain

gauge uzawa methods for incompressible flows with variable density two new gauge uzawa schemes are constructed for incompressible flows with variable density one is in the conserved form while the other is in the convective form it is shown that the first order versions of both schemes in their semi discretized form are unconditionally stable numerical experiments indicate that the first order resp second order versions of the two schemes lead to first order resp second order convergence rate for all variables and that these schemes are suitable for handling problems with large density ratios such as in the situation of air bubble rising in water

existence and uniqueness of the karcher mean on unital c algebras abstract the karcher mean on the cone of invertible positive elements of the c algebra b e of bounded operators on a hilbert space e has recently been extended to a contractive barycentric map on the space of l 1 probability measures on in this paper we first show that the barycenter satisfies the karcher equation and then establish the uniqueness of the solution next we establish that the karcher mean is real analytic in each of its coordinates and use this fact to show that both the karcher mean and karcher barycenter map exist and are unique on any unital c algebra the proof depends crucially on a recent result of the author giving a converse of the inverse function theorem

static analysis of frame structures by the differential quadrature element method in this paper a new version of differential quadrature method dqm is proposed and then extended to analyse frame structures the new method called the differential quadrature element method dqem retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original dqm the proposed method is however different from the quadrature element method qem proposed earlier by striz et al the methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method 1997 by john wiley sons ltd

error analysis of a fractional time stepping technique for incompressible flows with variable density in this paper we analyze the convergence properties of a new fractional time stepping technique for the solution of the variable density incompressible navier stokes equations the main feature of this method is that contrary to other existing algorithms the pressure is determined by just solving one poisson equation per time step first order error estimates are proved and stability of a formally second order variant of the method is established

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

a general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear time dependent internal boundary conditions abstract the subject of this paper is the development of a general solution procedure for the vibrations primary resonance and nonlinear natural frequency of systems with cubic nonlinearities subjected to nonlinear and time dependent internal boundary conditions this is a commonly occurring situation in the vibration analysis of continuous systems with intermediate elements the equations of motion form a set of nonlinear partial differential equations with nonlinear time dependent and coupled internal boundary conditions the method of multiple timescales an approximate analytical method is applied directly to each partial differential equation of motion as well as coupled boundary conditions i e on each sub domain and the corresponding internal boundary conditions for a continuous system with intermediate elements which ultimately leads to approximate analytical expressions for the frequency response relation and nonlinear natural frequencies of the system these closed form solutions provide direct insight into the relationship between the system parameters and vibration characteristics of the system moreover the suggested solution procedure is applied to a sample problem which is discussed in detail

regular article extension of finite volume compressible flow solvers to multi dimensional variable density zero mach number flows when attempting to compute unsteady variable density flows at very small or zero mach number using a standard finite volume compressible flow solver one faces at least the following difficulties i spatial pressure variations vanish as the mach number m 0 but they do affect the velocity field at leading order ii the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux iii violations of this constraint crucially affect the transport of mass preventing a code to properly advect even a constant density distribution we overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi dimensional finite volume methods in conservation form the construction of numerical fluxes involves 1 an explicit upwind step yielding predictions for the nonlinear convective flux components 2 a first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint this step requires the solution of a first poisson type equation 3 a second projection step which provides the yet unknown non convective pressure contribution to the total flux of momentum this second projection requires the solution of another poisson type equation and yields the cell centered velocity field at the new time this velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit step 1 can be done by any standard finite volume compressible flow solver the input to steps 2 and 3 involves solely the fluxes from step 1 and is independent of how these were obtained thus our approach allows any such solver to be extended to compute variable density incompressible flows

beam vibrations with time dependent boundary conditions abstract a procedure is outlined for the solution of the vibration problem of a bernoulli euler beam with time dependent boundary conditions the solution is greatly simplified if the dependent variable in the original partial differential equation can be changed to produce homogeneous boundary conditions and at the same time maintain a homogeneous differential equation a method for making such a change is given and illustrated by solving a cantilever beam problem with a time dependent tip displacement

influences of harmonic coupling on bifurcations in duffing oscillator with bounded potential well abstract the dynamics of bifurcations in a dufhng oscillator with a bounded potential well is investigated special attention is paid to the prominent phenomena of repeated sets of symmetry and reverse symmetry breaking the harmonic balance method and floquet theory are employed to account for this peculiar phenomena

a fixed point operator for a nonlinear boundary value problem we study a semilinear second order equation with a nonlinear boundary condition for the axial deformation of a nonlinear elastic beam in the presence of friction under appropriate conditions we define a fixed point operator in order to obtain solutions for this equation

a stabilized finite element method based on two local gauss integrations for the stokes equations this paper considers a stabilized method based on the difference between a consistent and an under integrated mass matrix of the pressure for the stokes equations approximated by the lowest equal order finite element pairs i e the p 1 p 1 and q 1 q 1 pairs this method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf sup condition optimal error estimates are obtained by applying the standard galerkin technique finally the numerical illustrations agree completely with the theoretical expectations

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

vibration of beams with generally restrained boundary conditions using fourier series this work presents a method to find accurate vibration frequencies of beams with generally restrained boundary conditions using fourier series the suggested method is very convenient to find an accurate frequency parameter for beams with not only classical boundary conditions but also non classical boundary conditions restrained by rotational and translational springs numerical results for various degenerate cases are compared with existing results for natural frequency obtained by conventional analysis the results indicate that the present method can be used very effectively in the design of beams with various supporting conditions

a generalization of the method of harmonic balance a procedure is provided for generalizing the method of harmonic balance to obtain higher order approximations to the periodic solutions of differential equations for two systems one a conservative system and the other nonconservative the procedure is currently being applied to investigate the possible solution behaviors of singular nonlinear oscillators where the usual perturbation methods do not work

operator means of probability measures and generalized karcher equations abstract in this article we consider means of positive bounded linear operators on a hilbert space we present a complete theory that provides a framework which extends the theory of the karcher mean its approximating matrix power means and a large part of kubo ando theory to arbitrary many variables in fact to the case of probability measures with bounded support on the cone of positive definite operators this framework characterizes each operator mean extrinsically as unique solutions of generalized karcher equations which are obtained by exchanging the matrix logarithm function in the karcher equation to arbitrary operator monotone functions over the positive real half line if the underlying hilbert space is finite dimensional then these generalized karcher equations are riemannian gradients of convex combinations of strictly geodesically convex log determinant divergence functions hence these new means are their global minimizers in analogy to the case of the karcher mean as pointed out our framework is based on fundamental contraction results with respect to the thompson metric which provides us nonlinear contraction semigroups in the cone of positive definite operators that form a decreasing net approximating these operator means in the strong topology from above

a high order projection method for tracking fluid interfaces in variable density incompressible flows we present a numerical method for computing solutions of the incompressible euler or navier stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties the method is based on a second order projection method for variable density flows using an approximate projection formulation the boundary between the fluids is tracked with a second order volume of fluid interface tracking algorithm we present results for viscious rayleigh taylor problems at early time with equal and unequal viscosities to demonstrate the convergence of the algorithm we also present computational results for the rayleigh taylor instability in air helium and for bubbles and drops in an air water system without surface tension to demonstrate the behavior of the algorithm on problems with large density and viscosity contrasts

an approximate method for one dimensional structures with strong nonlinear and nonhomogenous boundary conditions abstract there is a lack of analytic methods for vibration analysis of structures with strong nonlinear and non homogenous boundary conditions this paper proposes such a method a distinct feature of the method is to introduce the generalized coordinates for nonlinear and nonhomogeneous boundary conditions the total solution of the structure consists of a sum of a spatial particular solution for the boundary conditions and a field solution satisfying linear and homogeneous boundary conditions the field solution can be obtained in terms of the modal expansion the modal coefficients together with the generalized coordinates for the boundary conditions satisfy a set of nonlinear ordinary differential equations which are solved with the harmonic balance method two examples are presented to study the convergence and accuracy of the solution the first example is the longitudinal vibration of a bar subject to a base excitation on the left and restrained by a damper on the right the wave method and the differential quadrature method dqm are compared with the proposed method and are found in good agreement the second example is a beam with nonlinear torsional boundary absorbers the method shows a good accuracy to deal with the complex boundary conditions as compared with the differential quadrature element method dqem the proposed method is also compared with the multi scale method msm and shows an advantage to deal with strong nonlinearities the proposed method is highly promising for vibration analysis of complex structures with nonlinear and nonhomogeneous boundary conditions

existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions this paper is concerned with the existence and uniqueness of monotone positive solutions for an elastic beam equation with nonlinear boundary conditions the proof of our main results is based upon a new fixed point theorem of generalized concave operators

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

pretwisted nonuniform beams with time dependent elastic boundary conditions the governing differential equations with the nonhomogeneous time dependent elastic boundary conditions for the coupled bending bending vibration of a pretwisted nonuniform beam are derived by hamilton s principle by taking a general change of dependent variable with shifting functions the original system is transformed to be a system composed of two nonhomogeneous governing differential equations and eight homogeneous boundary conditions consequently the method of separation ofvariables can beused to solvethetransformed problem the physical meanings of these shifting functions are explored the orthogonality condition for the eigenfunctions of a pretwistednonuniformbeamwithelasticboundaryconditionsisalsoderived thestiffnessmatrixforanonuniform beam with arbitrary pretwist is derived as the coefe cients of the matrix can be integrated analytically the exact stiffness matrix is therefore obtained the relation between the shifting functions and the stiffness matrix is derived the ine uence of the pretwist angle on the dynamic response of the beam is studied the vibration control of a pretwist beam with boundary inputs is investigated

stabilization of low order mixed finite elements for the stokes equations we present a new family of stabilized methods for the stokes problem the focus of the paper is on the lowest order velocity pressure pairs while not lbb compliant their simplicity and attractive computational properties make these pairs a popular choice in engineering practice our stabilization approach is motivated by terms that characterize the lbb deficiency of the unstable spaces the stabilized methods are defined by using these terms to modify the saddle point lagrangian associated with the stokes equations the new stabilized methods offer a number of attractive computational properties in contrast to other stabilization procedures they are parameter free do not require calculation of higher order derivatives or edge based data structures and always lead to symmetric linear systems furthermore the new methods are unconditionally stable achieve optimal accuracy with respect to solution regularity and have simple and straightforward implementations we present numerical results in two and three dimensions that showcase the excellent stability and accuracy of the new methods

free vibration of non uniform euler bernoulli beams with general elastically end constraints using adomian modified decomposition method abstract this paper deals with free vibration problems of non uniform euler bernoulli beam under various supporting conditions the technique we have used is based on applying the adomian modified decomposition method amdm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literatures these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis

dynamic analysis of generally supported beams using fourier series the applicability of fourier series to the dynamic analysis of beams having arbitrary boundary conditions is explored for the simplicity of presenting the analysis procedure beams having zero end displacement are used in the discussion numerical results for free vibration and dynamic response based on the present analysis procedure are compared with existing results for natural frequencies and dynamic behavior obtained by the conventional modal analysis these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is seemingly simpler and more straightforward than the conventional modal analysis

the stochastic order of probability measures on ordered metric spaces abstract the general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first motivated by recent work on barycentric maps on spaces of probability measures on ordered banach spaces we introduce and study a stochastic order on the space of probability measures p x where x is a metric space equipped with a closed partial order and derive several useful equivalent versions of the definition we establish the antisymmetry and closedness of the stochastic order and hence that it is a closed partial order for the case of a partial order on a banach space induced by a closed normal cone with interior we also consider order completeness of the stochastic order for a cone of a finite dimensional banach space and derive a version of the arithmetic geometric harmonic mean inequalities in the setting of the associated probability space on positive invertible operators on a hilbert space