sufficient conditions for pseudo lipschitz property in convex semi infinite vector optimization problems abstract this paper is devoted to the study of the pseudo lipschitz property of the efficient pareto solution map for the perturbed convex semi infinite vector optimization problem csvo we establish sufficient conditions for the pseudo lipschitz property of the efficient solution map of csvo under continuous perturbations of the right hand side of the constraints and functional perturbations of the objective function examples are given to illustrate the obtained results

clarke coderivatives of efficient point multifunctions in parametric vector optimization abstract the paper is devoted to the study of the clarke circatangent coderivatives of the efficient point multifunction of parametric vector optimization problems in banach spaces we provide inner outer estimates for evaluating the clarke circatangent coderivative of this multifunction in a broad class of conventional vector optimization problems in the presence of geometrical operator and finite and infinite functional constraints examples are given for analyzing and illustrating the obtained results

asymptotic behavior of solutions of second order differential equations with integrable coefficients the differential equation x a t f x 0 t 0 is considered under the condition that lim x fl a s ds exists and is finite and necessary and or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions cl c2t

a new higher order finite volume method based on moving least squares for the resolution of the incompressible navier stokes equations on unstructured grids in this work a new higher order 2 accurate finite volume method for the resolution of the incompressible navier stokes equations on unstructured grids is presented the formulation is based on the use of moving least squares mls approximants third and fourth order accurate discretizations of the convective and viscous fluxes are obtained on collocated meshes in addition mls is employed to design a new momentum interpolation method that allows interpolations better than linear on any kind of mesh the accuracy and performance of the proposed method is demonstrated by solving different steady and unsteady benchmark problems on unstructured grids

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

semi infinite programming theory methods and applications starting from a number of motivating and abundant applications in 2 including control of robots eigenvalue computations mechanical stress of materials and statistical design the authors describe a class of optimization problems which are referred to as semi infinite because their constraints bound functions of a finite number of variables on a whole region in 3 5 first and second order optimality conditions are derived for general nonlinear problems as well as a procedure for reducing the problem locally to one with only finitely many constraints another main effort for achieving simplification is through duality in 6 there algebraic properties of finite linear programming are brought to bear on duality theory in semi infinite programming section 7 treats numerical methods based on either discretization or local reduction with the emphasis on the design of superlinearly convergent sqp type methods taking this differentiable point of view this paper can be considered to be complementar

kuratowski convergence of the efficient sets in the parametric linear vector semi infinite optimization abstract in the space of whole linear vector semi infinite optimization problems we consider the mappings putting into correspondence to each problem the set of efficient and weakly efficient points respectively we endow the image space with kuratowski convergence and by means of the lower and upper semi continuity of these mappings we prove generic well posedness of the vector optimization problems the connection between the continuity and some properties of the efficient sets is also discussed

stability and well posedness in linear semi infinite programming this paper presents an approach to the stability and the hadamard well posedness of the linear semi infinite programming problem lsip no standard hypothesis is required in relation to the set indexing of the constraints and consequently the functional dependence between the linear constraints and their associated indices has no special property we consider as parameter space the set of all lsip problems whose constraint systems have the same index set and we define in it an extended metric to measure the size of the perturbations throughout the paper the behavior of the optimal value function and of the optimal set mapping are analyzed moreover a certain type of hadamard well posedness which does not require the boundedness of the optimal set is characterized the main results provided in the paper allow us to point out that the lower semicontinuity of the feasible set mapping entails high stability of the whole problem mainly when this property occurs simultaneously with the boundedness of the optimal set in this case all the stability properties hold with the only exception being the lower semicontinuity of the optimal set mapping

on optimal node spacing for immersed boundary lattice boltzmann method in 2d and 3d abstract a computational study on optimal spacing of lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2d and 3d is presented in order to show how the density of the lagrangian points affects the numerical results of the immersed boundary lattice boltzmann method ib lbm the study is based on the implicit velocity correction based ib lbm proposed by wu and shu 2009 2010 that allows computing the fluid body interaction force however the original method fails for densely spaced lagrangian points due to ill conditioned or even singular linear systems that arise from the derivation of the method we propose a modification that improves the solvability of the linear systems and compare the performance of both methods using several benchmark problems the results show how the spacing of the lagrangian points affects the numerical results mainly the permeability of the discretized body boundary in applications to fluid flows over rigid obstacles and blood flows in arteries in 2d and 3d

lower semi continuity of the pareto solution map in quasiconvex semi infinite vector optimization abstract this paper is concerned with the lower semi continuity of the efficient pareto solution map for the perturbed quasiconvex semi infinite vector optimization problem qcsvo we establish sufficient conditions for the lower semi continuous property of the efficient solution map of qcsvo under functional perturbations of both the objective function and the constraints examples are designed to analyze the obtained results

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a three dimensional incompressible navier stokes flow solver using primitive variables an implicit finite difference computer code has been developed to solve the incompressible navier stokes equations in a three dimensional curvilinear coordinate system the pressure field solution is based on the pseudocompressibility approach in which a time derivative pressure term is introduced into the mass conservation equation the solution procedure employs an implicit approximate factorization scheme the reynolds stresses which are uncoupled from the implicit scheme are lagged by one time step to facilitate implementing various levels of the turbulence model test problems for external and internal flows are computer and the results are compared with existing experimental data the application of this technique for general three dimensional problems is then demonstrated

sufficient conditions for total ill posedness in linear semi infinite optimization abstract this paper deals with the so called total ill posedness of linear optimization problems with an arbitrary possibly infinite number of constraints we say that the nominal problem is totally ill posed if it exhibits the highest unstability in the sense that arbitrarily small perturbations of the problem s coefficients may provide both consistent with feasible solutions and inconsistent problems as well as bounded with finite optimal value and unbounded problems and also solvable with optimal solutions and unsolvable problems in this paper we provide sufficient conditions for the total ill posedness property exclusively in terms of the coefficients of the nominal problem

sensitivity analysis in linear semi infinite programming perturbing cost and right hand side coefficients this paper analyzes the effect on the optimal value of a given linear semi infinite programming problem of the kind of perturbations which more frequently arise in practical applications those which affect the objective function and the right hand side coefficients of the constraints in particular we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation

assessment and applications of point interpolation methods for computational mechanics two meshfree point interpolation methods pims which are based on the polynomial and the radial basis functions have been proposed recently in addition to the earlier work with the moving least squares mls approximation for the field function approximation however it is found that pims cannot automatically ensure the compatibility of the solution when they are used together with the energy principles in this paper issues related to the compatibility of pims are studied a technique of background cell based nodal selections and a penalty method are proposed to enforce the compatibility of the solution of pims the patch test is studied in great detail the convergences and performances are investigated for both conforming and non conforming pims it is found that those methods of the pim family are very easy to implement and are very efficient in obtaining numerical solutions for problems of computational mechanics copyright 2004 john wiley sons ltd

resolution of computational aeroacoustics problems on unstructured grids with a higher order finite volume scheme computational fluid dynamics cfd has become increasingly used in the industry for the simulation of flows nevertheless the complex configurations of real engineering problems make the application of very accurate methods that only work on structured grids difficult from this point of view the development of higher order methods for unstructured grids is desirable the finite volume method can be used with unstructured grids but unfortunately it is difficult to achieve an order of accuracy higher than two and the common approach is a simple extension of the one dimensional case the increase of the order of accuracy in finite volume methods on general unstructured grids has been limited due to the difficulty in the evaluation of field derivatives this problem is overcome with the application of the moving least squares mls technique on a finite volume framework in this work we present the application of this method fv mls to the solution of aeroacoustic problems

lipschitz like property of an implicit multifunction and its applications abstract the aim of this work is twofold first we use the advanced tools of modern variational analysis and generalized differentiation to study the lipschitz like property of an implicit multifunction more explicitly new sufficient conditions in terms of the frechet coderivative and the normal mordukhovich coderivative of parametric multifunctions for this implicit multifunction to have the lipschitz like property at a given point are established then we derive sufficient conditions ensuring the lipschitz like property of an efficient solution map in parametric vector optimization problems by employing the above implicit multifunction results

a fourth order accurate finite volume compact method for the incompressible navier stokes solutions abstract this paper presents a finite volume fourth order accurate compact scheme for discretization of the incompressible navier stokes equations in primitive variable formulation the numerical method of integrating the navier stokes equations comprises a compact finite volume formulation of the average convective and diffusive fluxes the pressure velocity coupling is achieved via the coupled solution of the resulting system of equations the solution of the coupled set of equations is performed with an implicit newton krylov matrix free method for stationary problems for simulation of unsteady flows a standard fourth order runge kutta method was used for temporal discretization and the velocity pressure coupling was ensured at each stage also using the matrix free method several incompressible viscous steady and unsteady flow problems have been computed to assess the robustness and accuracy of the proposed method

high order compact schemes for incompressible flows a simple and efficient method with quasi spectral accuracy in this paper a finite difference code for direct and large eddy simulation dns les of incompressible flows is presented this code is an intermediate tool between fully spectral navier stokes solvers limited to academic geometry through fourier or chebyshev representation and more versatile codes based on standard numerical schemes typically only second order accurate the interest of high order schemes is discussed in terms of implementation easiness computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations the equivalence rules between operations in physical and spectral spaces are efficiently used to solve the poisson equation introduced by the projection method it is shown that for the pressure treatment an accurate fourier representation can be used for more flexible boundary conditions than periodicity or free slip using the concept of the modified wave number the incompressibility can be enforced up to the machine accuracy the benefit offered by this alternative method is found to be very satisfactory even when a formal second order error is introduced locally by boundary conditions that are neither periodic nor symmetric the usefulness of high order schemes combined with an immersed boundary method ibm is also demonstrated despite the second order accuracy introduced by this wall modelling strategy in particular the interest of a partially staggered mesh is exhibited in this specific context three dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high order schemes to reduce the computational cost for a given accuracy the main conclusion of this paper is that finite difference schemes with quasi spectral accuracy can be very efficient for dns les of incompressible flows while allowing flexibility for the boundary conditions and easiness in the code development therefore this compromise fits particularly well for very high resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments

generalized formulations for the rhie chow interpolation in this paper generalized formulations for the rhie chow interpolation for co located grid discretizations are derived these generalized formulations eliminate the major known defects in the standard rhie chow interpolation including the following dependence of the converged solution on the value of the under relaxation factor saw tooth pressure oscillations in transient problems with small time steps and incorrect or non converged solutions for problems with discontinuities the generalized formulations are also shown to be applicable to a wider range of flow conditions than the standard rhie chow interpolation the derivation of the rhie chow interpolation is first recalled and its numerical errors are analyzed then the generalized formulations are presented and explained and the way in which they eliminate or counter some of the known defects of the standard rhie chow interpolation are outlined the generalized formulations are then verified and validated with numerical experiments including experiments with flow in porous media and in a packed bed it is then concluded that the generalized formulations presented in this work represent an advance over the standard rhie chow interpolation with a negligible increase in computational cost

pseudo lipschitz property of linear semi infinite vector optimization problems this paper is devoted to the study of the pseudo lipschitz property of pareto solution map for the parametric linear semi infinite vector optimization problem lsvo we establish new sufficient conditions for the pseudo lipschitz property of the pareto solution map of lsvo under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function examples are given to illustrate the results obtained

metric regularity in convex semi infinite optimization under canonical perturbations this paper is concerned with the lipschitzian behavior of the optimal set of convex semi infinite optimization problems under continuous perturbations of the right hand side of the constraints and linear perturbations of the objective function in this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping this condition consists of the slater constraint qualification together with a certain additional requirement in the karush kuhn tucker conditions for linear problems this sufficient condition turns out to be also necessary for the metric regularity and it is equivalent to some well known stability concepts

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

a staggered grid high order accurate method for the incompressible navier stokes equations a high order accurate finite difference method for the numerical solution of the incompressible navier stokes equations is presented fourth order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite difference formulas high order accuracy in time is obtained by marching the solution with runge kutta methods the incompressibility constraint is enforced for each runge kutta stage iteratively either by local pressure correction or by a poisson equation based global pressure correction method local pressure correction is carried out on cell by cell basis using a local fourth order accurate discrete analog of the continuity equation the global pressure correction is based on the numerical solution of a poisson type equation which is discretized to fourth order accuracy and solved using gmres in both cases the updated pressure is used to recompute the velocities in order to satisfy the incompressibility constraint to fourth order accuracy the accuracy and efficiency of the proposed method is demonstrated in test problems

a time adaptive finite volume method for the cahn hilliard and kuramoto sivashinsky equations this paper presents a complete finite volume method for the cahn hilliard and kuramoto sivashinsky type of equations the spatial discretization is high order accurate and suitable for general unstructured grids the time integration is addressed by means of implicit an implicit explicit fourth order runge kutta schemes with error control and adaptive time stepping the outcome is a practical accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations the use of adaptive time stepping is of paramount importance in problems governed by the cahn hilliard model an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps in addition to driving the simulations efficiently the time adaptive procedure provides a quantitative not just qualitative characterization of the rich temporal scales present in phase separation processes governed by the cahn hilliard phase field model

stability of semi infinite vector optimization problems without compact constraints this paper is devoted to the continuity of solution maps for perturbation semi infinite vector optimization problems without compact constraint sets the sufficient conditions for lower semicontinuity and upper semicontinuity of solution maps under functional perturbations of both objective functions and constraint sets are established some examples are given to analyze the assumptions in the main result

a collocated method for the incompressible navier stokes equations inspired by the box scheme we present a new finite difference numerical method to solve the incompressible navier stokes equations using a collocated discretization in space on a logically cartesian grid the method shares some common aspects with and it was inspired by the box scheme it uses centered second order accurate finite difference approximations for the spatial derivatives combined with semi implicit time integration the proposed method is constructed to ensure discrete conservation of mass and momentum by discretizing the primitive velocity pressure form of the equations the continuity equation is enforced exactly to machine accuracy at the collocated locations whereas the momentum equations are evaluated in a staggered manner this formulation preempts the appearance of spurious pressure modes in the embedded elliptic problem associated with the pressure the method shows uniform order of accuracy both in space and time for velocity and pressure in addition the skew symmetric form of the non linear advection term of the navier stokes equations improves discrete conservation of kinetic energy in the inviscid limit to within the order of the truncation error of the time integrator the method has been formulated to accommodate different types of boundary conditions fully periodic periodic channel inflow outflow and lid driven cavity always ensuring global mass conservation a novel aspect of this finite difference formulation is the derivation of the discretization near boundaries using the weak form of the equations as in the finite element method the method of manufactured solutions is utilized to perform accuracy analysis and verification of the solver to assess the applicability of the new method presented in this paper four realistic flow problems have been simulated and results are compared with those in the literature these cases include a lid driven cavity backward facing step kovasznay flow and fully developed turbulent channel