accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

exponential stabilisation of a simple tree shaped network of timoshenko beams system the stabilisation problem of a forked triple system of timoshenko beams which is a simple tree shaped network is considered in this article suppose that the root of the fork is clamped at the interior node of the fork the displacement and rotational angle of the beams are continuous the shearing force and bending moments of the beams satisfy the transmission conditions the feedback controllers are designed at the exterior tips to stabilise this system then the closed loop system is proved to be well posed by the eigenfrequency analysis together with the asymptotic technique the system is shown to satisfy the spectrum determined growth condition finally this closed loop system is proved to be exponentially stable furthermore a simulation is given to support these results

a sufficient condition on riesz basis with parentheses of non self adjoint operator and application to a serially connected string system under joint feedbacks this paper gives an abstract sufficient condition on riesz basis with parentheses property for the generators of c0 groups in hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account the condition is then applied to the closed loop system of a serially connected string system under joint damping feedbacks to show that there is a family of generalized eigenfunctions that form a riesz basis with parentheses in the state space the spectrum determined growth condition is concluded as a consequence

fine level set structure of flat isometric immersions a result by pogorelov asserts that c 1 isometric immersions u of a bounded domain s subset mathbb r 2 into mathbb r 3 whose normal takes values in a set of zero area enjoy the following regularity property the gradient f nabla u is developable in the sense that the nondegenerate level sets of f consist of straight line segments intersecting the boundary of s at both endpoints motivated by applications in nonlinear elasticity we study the level set structure of such f when s is an arbitrary bounded lipschitz domain we show that f can be approximated by uniformly bounded maps with a simplified level set structure we also show that the domain s can be decomposed up to a controlled remainder into finitely many subdomains each of which admits a global line of curvature parametrization

approximation of flat w2 2 isometric immersions by smooth ones let s subset mathbb r 2 be a bounded lipschitz domain and denote by w 2 2 text iso s mathbb r 3 the set of mappings u in w 2 2 s mathbb r 3 which satisfy nabla u t nabla u id almost everywhere under an additional regularity condition on the boundary partial s which is satisfied if partial s is piecewise continuously differentiable we prove that the strong w2 2 closure of w 2 2 text iso s mathbb r 3 cap c infty overline s mathbb r 3 agrees with w 2 2 text iso s mathbb r 3

the expansion of a semigroup and a riesz basis criterion problems on the expansion of a semigroup and a criterion for being a riesz basis are discussed in the present paper suppose that a is the generator of a c0 semigroup on a hilbert space and a 1 a 2 a with 2 a is consisted of isolated eigenvalues distributed in a vertical strip it is proved that if 2 a is separated and for each 2 a the dimension of its root subspace is uniformly bounded then the generalized eigenvectors associated with 2 a form an l basis under different conditions on the riesz projection the expansion of a semigroup is studied in particular a simple criterion for the generalized eigenvectors forming a riesz basis is given as an application a heat exchanger problem with boundary feedback is investigated it is proved that the heat exchanger system is a riesz system in a suitable state hilbert space

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

stochastic homogenization of the bending plate model abstract we use the notion of stochastic two scale convergence introduced in 32 to solve the problem of stochastic homogenization of the elastic plate in the bending regime

a cache aware algorithm for pdes on hierarchical data structures based on space filling curves competitive numerical algorithms for solving partial differential equations have to work with the most efficient numerical methods like multigrid and adaptive grid refinement and thus with hierarchical data structures unfortunately in most implementations hierarchical data typically stored in trees cause a nonnegligible overhead in data access to overcome this quandary numerical efficiency versus efficient implementation our algorithm uses space filling curves to build up data structures which are processed linearly in fact the only kind of data structure used in our implementation is stacks thus data access becomes very fast even faster than the common access to nonhierarchical data stored in matrices and in particular cache misses are reduced considerably furthermore the implementation of multigrid cycles and or higher order discretizations as well as the parallelization of the whole algorithm become very easy and straightforward on these data structures

approximate projection methods part i inviscid analysis the use of approximate projection methods for modeling low mach number flows avoids many of the numerical complications associated with exact projection methods but introduces additional design choices in developing a robust algorithm in this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples we then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations as part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

control of a network of euler bernoulli beams abstract the aim is to study the boundary controllability of a system modeling the vibrations of a network of n euler bernoulli beams connected by n vibrating point masses using the classical hilbert uniqueness method the control problem is reduced to the obtention of an observability inequality the solution is then expressed in terms of fourier series so that it is also enough to show that the distance between two consecutive large eigenvalues of the spatial operator involved in this evolution problem is superior to a minimal fixed value this property called spectral gap holds as soon as the roots of a function denoted by f and giving the asymptotic behaviour of the eigenvalues are all simple for a network of n 2 different beams this assumption on the multiplicity of the roots of f denoted by a is proved to be satisfied and controllability follows for higher values of n a numerical approach allows one to prove a in many situations and no counterexample has been found but the problem of giving a general proof of controllability remains open

krylov subspace methods for solving large unsymmetric linear systems some algorithms based upon a projection process onto the krylov subspace k sub m span r sub 0 ar sub 0 a sup m 1 r sub 0 are developed generalizing the method of conjugate gradients to unsymmetric systems these methods are extensions of arnoldi s algorithm for solving eigenvalue problems the convergence is analyzed in terms of the distance of the solution to the subspace k sub m and some error bounds are established showing in particular a similarity with the conjugate gradient method for symmetric matrices when the eigenvalues are real several numerical experiments are described and discussed

stochastic homogenization of nonconvex unbounded integral functionals with convex growth we consider the well trodden ground of the problem of the homogenization of random integral functionals when the integrand has standard growth conditions the qualitative theory is well understood when it comes to unbounded functionals that is when the domain of the integrand is not the whole space and may depend on the space variable there is no satisfactory theory in this contribution we develop a complete qualitative stochastic homogenization theory for nonconvex unbounded functionals with convex growth we first prove that if the integrand is convex and has p growth from below with p d the dimension then it admits homogenization regardless of growth conditions from above this result that crucially relies on the existence and sublinearity at infinity of correctors is also new in the periodic case in the case of nonconvex integrands we prove that a similar homogenization result holds provided that the nonconvex integrand admits a two sided estimate by a convex integrand the domain of which may depend on the space variable that itself admits homogenization this result is of interest to the rigorous derivation of rubber elasticity from polymer physics which involves the stochastic homogenization of such unbounded functionals

a numerical method for the incompressible navier stokes equations based on an approximate projection in this method we present a fractional step discretization of the time dependent incompressible navier stokes equations the method is based on a projection formulation in which we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields our treatment of the diffusion convection step uses a specialized second order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high reynolds number in contrast to conventional projection type discretizations that impose a discrete form of the divergence free constraint we only approximately impose the constraint i e the velocity field we compute is not exactly divergence free the approximate projection is computed using a conventional discretization of the laplacian and the resulting linear system is solved using conventional multigrid methods numerical examples are presented to validate the second order convergence of the method for euler finite reynolds number and stokes flow a second example illustrating the behavior of the algorithm on an unstable shear layer is also presented

exponential stability analysis of xa long chain of coupled vibrating strings with dissipative linkage consider a long chain of coupled vibrating strings where a stabilizer is installed at each internal node and perhaps also at a boundary point the exponential stability of the stabilizers arrangement for this large dynamic structure will be determined through a careful transformation of the coupled wave equations for this structure into an equivalent hyperbolic system and analysis of the eigendeterminant it will be proven that the energy of the system decays uniformly exponentially if there is a stabilizer installed at a boundary point if the stabilizers are installed only at internal nodes it will be proven that the energy may decay either uniformly exponentially or nonuniformly or may not decay at all depending on the different wave speeds and the stabilizers arrangement all possible outcomes have been classified

convergence of equilibria of three dimensional thin elastic beams a convergence result is proved for the equilibrium configurations of a three dimensional thin elastic beam as the diameter h of the cross section goes to zero more precisely we show that stationary points of the nonlinear elastic functional e whose energies per unit cross section are bounded by ch converge to stationary points of the limit of e h this corresponds to a nonlinear one dimensional model for inextensible rods describing bending and torsion effects the proof is based on the rigidity estimate for low energy deformations by friesecke james and muller 4 and on a compensated compactness argument in a singular geometry in addition possible concentration effects of the strain are controlled by a careful truncation argument

nonlinear stochastic homogenization and ergodic theory on etudie l homogeneisation stochastique non lineaire d une classe de fonctionnelles integrales on relie le probleme a la theorie ergodique

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

on the sobolev space of isometric immersions we prove that every w 2 2 isometric immersion from a convex regular domain of r 2 into r3 can be approximated in w 2 2 norm by smooth isometric immersions from the same domain into r3

a numerical scheme for the green naghdi model abstract in this paper a hybrid numerical method using a godunov type scheme is proposed to solve the green naghdi model describing dispersive shallow water waves the corresponding equations are rewritten in terms of new variables adapted for numerical studies in particular the numerical scheme preserves the dynamics of solitary waves some numerical results are shown and compared to exact and or experimental ones in different and significant configurations a dam break problem and an impact problem where a liquid cylinder is falling to a rigid wall are solved numerically this last configuration is also compared with experiments leading to a good qualitative agreement

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

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 cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

spectrum of a network of euler bernoulli beams abstract a network of n flexible beams connected by n vibrating point masses is considered the spectrum of the spatial operator involved in this evolution problem is studied if 2 is any real number outside a discrete set of values s and if is an eigenvalue then it satisfies a characteristic equation which is given the associated eigenvectors are also characterized if 2 lies in s and if the n beams are identical same mechanical properties another characteristic equation is available it is not the case for different beams no general result can be stated some numerical examples and counterexamples are given to illustrate the impossibility of such a generalization at last the asymptotic behaviour of the eigenvalues is investigated by proving the so called weyl s formula

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

a gpu based multi level algorithm for boundary value problems abstract a novel geometric single grid multi level gsgml algorithm is presented for the numerical solution of boundary value problems bvps the algorithm is specifically designed for parallel scalability with high occupancy of streaming processors inside many core architectures like the graphics processing unit gpu the algorithm consists of iterative superposed operations on a single grid and is composed of two full grid routines a restriction and a coarsened interpolation relaxation the restriction is a local average of scalar or vector fields and the interpolation relaxation is a simultaneous application of coarsened finite difference operators and interpolations in complementary subsets of the grid the routines are scheduled in a saw like refining cycle convergence to machine precision is achieved repeating the full cycle using residuals and superposition the algorithm is attractive for its computational simplicity and provides a competitive gpu based fast solver for elliptic partial differential equations like the poisson helmholtz equation applications shown in this work include the deformation of two dimensional grids the computation of three dimensional streamlines for a singular trifoil knot vortex and the calculation of three dimensional electric potentials in heterogeneous dielectric media

an adaptive mesh projection method for viscous incompressible flow many fluid flow problems of practical interest particularly at high reynolds number are characterized by small regions of complex and rapidly varying fluid motion surrounded by larger regions of relatively smooth flow efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed we present in this paper a fractional step version of chorin s projection method for incompressible flow with adaptive mesh refinement which is second order accurate in both space and time convection terms are handled by a high resolution upwind method which provides excellent resolution of small scale features of the flow while a multilevel iterative scheme efficiently solves the parabolic and elliptic equations associated with viscosity and the projection numerical examples demonstrate the performance of the method on two dimensional problems involving vortex spindown with viscosity and inviscid vortex merger

output feedback stabilisation of a tree shaped network of vibrating strings with non collocated observation in this article the authors consider the simple tree shaped network of strings with non collocated observation suppose that the network consists of three strings and the displacements of these strings are continuous at the common vertex the sensors and actuators are required to be set at different vertices we propose an observer based output feedback controller to stabilise this network the exponential stability of the closed loop network is obtained based on the riesz basis approach together with estimates of the spectral distribution finally a numerical simulation is given to support these results

a cell centered adaptive projection method for the incompressible euler equations we present an algorithm to compute adaptive solutions for incompressible flows using block structured local refinement in both space and time this method uses a projection formulation based on a cell centered approximate projection which allows the use of a single set of cell centered solvers because of refinement in time additional steps are taken to accurately discretize the advection and projection operators at grid refinement boundaries using composite operators which span the coarse and refined grids this ensures that the method is approximately freestream preserving and satisfies an appropriate form of the divergence constraint

a splitting approach for the fully nonlinear and weakly dispersive green naghdi model the fully nonlinear and weakly dispersive green naghdi model for shallow water waves of large amplitude is studied the original model is first recast under a new formulation more suitable for numerical resolution an hybrid finite volume and finite difference splitting approach is then proposed which could be adapted to many physical models that are dispersive corrections of hyperbolic systems the hyperbolic part of the equations is handled with a high order finite volume scheme allowing for breaking waves and dry areas the dispersive part is treated with a classical finite difference approach extensive numerical validations are then performed in one horizontal dimension relying both on analytical solutions and experimental data the results show that our approach gives a good account of all the processes of wave transformation in coastal areas shoaling wave breaking and run up

a quadtree adaptive multigrid solver for the serre green naghdi equations the serre green naghdi sgn equations also known as the fully nonlinear boussinesq wave equations accurately describe the behaviour of dispersive shoaling water waves this article presents and validates a novel combination of methods for the numerical approximation of solutions to the sgn equations the approach preserves the robustness of the original finite volume saint venant solver in particular for the treatment of wetting drying and equilibrium states the linear system of coupled vector equations governing the dispersive sgn momentum sources is solved simply and efficiently using a generic multigrid solver this approach generalises automatically to adaptive quadtree meshes adaptive mesh refinement is shown to provide orders of magnitude gains in speed and memory when applied to the dispersive propagation of waves during the tohoku tsunami the source code test cases and examples are freely available

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows in this paper we further investigate the use of a fully discontinuous finite element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dis persive flow regime we consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non hydrostatic effects this source term can be computed through the resolution of elliptic second order linear sub problems which only involve second order partial derivatives in space we then introduce an associated symmetric weighted internal penalty discrete bilinear form allowing to deal with the discontinuous nature of the elliptic problem s coefficients in a stable and consistant way similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dis persive models these formulations are validated again several benchmarks involving h convergence p convergence and comparisons with experimental data showing optimal convergence properties

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

abstract second order hyperbolic system and applications to controlled network of strings in this paper we study an abstract second order hyperbolic system valued in mathbb c n with appropriate boundary conditions we prove that the system is well posed and associates with a c 0 semigroup in a hilbert state space under certain conditions we show that the spectra of the system operator are located in the vertical strip and that there is a sequence of eigenvectors and generalized eigenvectors that forms a riesz basis with parentheses for the hilbert state space and hence that the system satisfies the spectrum determined growth assumption as applications we investigate the exponential stability of a controlled tree shaped network of 7 strings and a network of n connected strings

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

high order well balanced cdg fe methods for shallow water waves by a green naghdi model in this paper we consider a one dimensional fully nonlinear weakly dispersive green naghdi model for shallow water waves over variable bottom topographies such model describes a large spectrum of shallow water waves and it is thus of great importance to design accurate and robust numerical methods for solving it the governing equations contain mixed spatial and temporal derivatives of the unknowns they also have still water stationary solutions which should be preserved in stable numerical simulations in our numerical approach we first reformulate the green naghdi equations into balance laws coupled with an elliptic equation we then propose a family of high order numerical methods which discretize the balance laws with well balanced central discontinuous galerkin methods and the elliptic part with continuous finite element methods linear dispersion analysis for both the reformulated green naghdi system and versions of the proposed numerical scheme is performed when the bottom topography is flat numerical tests are presented to illustrate the accuracy and stability of the proposed schemes as well as the capability of the green naghdi model to describe a wide range of shallow water wave phenomena

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

a projection method for locally refined grids a numerical method for the solution of the two dimensional euler equatons for incompressible flow on locally refined grids is presented the method is a second order godunov projection method adapted from bell colella and glaz second order accuracy of the numerical method in time and space is established through numerical experiments the main contributions of this work concern the formulation and implementation of a projection for refined grids a discussion of the adjointness relation between gradient and divergence operators for a refined grid mac projection is presented and a refined grid approximate projection is developed an efficient multigrid method which exactly solves the projection is developed and a method for casting certain approximate projections as mac projections on refined grids is presented

the two scale convergence method applied to generalized besicovitch spaces the twoscale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems in the present paper we develop this theory to generalized besicovitch spaces

combined hybridizable discontinuous galerkin hdg and runge kutta discontinuous galerkin rk dg formulations for green naghdi equations on unstructured meshes abstract in this paper we introduce some new high order discrete formulations on general unstructured meshes especially designed for the study of irrotational free surface flows based on partial differential equations belonging to the family of fully nonlinear and weakly dispersive shallow water equations working with a recent family of optimized asymptotically equivalent equations we benefit from the simplified analytical structure of the linear dispersive operators to conveniently reformulate the models as the classical nonlinear shallow water equations supplemented with several algebraic source terms which globally account for the non hydrostatic effects through the introduction of auxiliary coupling variables high order discrete approximations of the main flow variables are obtained with a rk dg method while the trace of the auxiliary variables are approximated on the mesh skeleton through the resolution of second order linear elliptic sub problems with high order hdg formulations the combined use of hybrid unknowns and local post processing significantly helps to reduce the number of globally coupled unknowns in comparison with previous approaches the proposed formulation is then extended to a more complex family of three parameters enhanced green naghdi equations the resulting numerical models are validated through several benchmarks involving nonlinear waves transformations and propagation over varying topographies showing good convergence properties and very good agreements with several sets of experimental data

regular article generation of short and long range temporal correlated noises we present the implementation of an algorithm to generate gaussian random noises with prescribed time correlations that can be either long or short ranged examples of langevin dynamics with short and long range noises are presented and discussed