natural consensus filters for second order infinite dimensional systems abstract this work proposes consensus filters for a class of second order infinite dimensional systems the proposed structure of the consensus filters is that of a local filter written in the natural setting of a second order formulation with the additional coupling that enforces consensus by minimizing the disagreement between all local filters an advantage of the second order formulation imposed on the local filters is the natural interpretation that they retain namely that the time derivative of the estimated position is equal to the estimated velocity stability analysis of the collective dynamics is achieved via the use of a parameter dependent lyapunov functional and which guarantees that asymptotically all filters agree with each other and that they all converge to the true state of the second order system

robust partial pole assignment problem for high order control systems in this paper we consider the partial pole assignment problem ppap for high order control systems it is shown that solving the ppap is essentially solving a pole assignment for a linear system of a much lower order and the robust ppap is then concerning the robust pole assignment problem for this linear system based on this theory a rather simple algorithm for solving the robust ppap is proposed and numerical examples show that this algorithm does lead to comparable results with earlier algorithms but at much lower computational cost

introducing a new kinetic model which admits an h theorem for simulating the nearly incompressible fluid flows we present a new kinetic model for simulating the nearly incompressible fluid flows the model uses constant speed particles which are free to move in all directions in the new model the maxwellian is replaced by a fractional form while the navier stokes and continuity equations are recovered it is known that the conventional lattice boltzmann model lbm with polynomial equilibrium distribution function cannot admit an h theorem wagner 1998 9 in the present work we show that the new model admits an h theorem and the numerical schemes which stem from the new model are more stable than the conventional lbm for the streaming stage two different approaches namely the lattice based and the discontinuous galerkin based schemes are introduced the former is more cost effective than the conventional lattice boltzmann models while it maintains their simplicity the latter is a higher order spectral element method using which one can employ non uniform triangular elements with high accuracy and geometrical flexibility unlike the conventional lbm the new model is derived from continuous relations hence it does not require a symmetric discrete velocity model the accuracy and stability of the model have been verified by simulating three benchmark problems the plane couette flow lid driven square cavity and flow around an impulsively started cylinder have been simulated the results of the present work are in excellent agreement with the exact solutions and with the results reported by others

variational formulation of interior cavity frequencies for spheroidal bodies this paper presents interior cavity frequencies for spheroidal bodies in cases of neumann and dirichlet homogenous boundary conditions the helmholtz wave equation is expressed in terms of prolate spheroidal coordinates from which a variational formulation is derived for the determination of the interior cavity frequencies the search of stationarity is performed by means of a rayleigh ritz type expansion of trial functions the trial functions are expressed as a double summation of basis functions in radial and angular coordinates a variable transformation is applied to the variational form in order to have homogenous boundary conditions which are essential for establishing a complete function space of the associated boundary conditions the present analysis is verified by comparisons of interior frequencies of a spherical body of prolate spheroidal bodies and of the interior characteristic functions with the radial and angular functions obtained from prolate spheroidal differential equations interior frequencies are tabulated for various aspect ratios of spheroidal bodies in accordance with harmonic orders in azimuthal directions for both neumann and dirichlet conditions

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii application to flow around a sphere at drag crisis the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness

output feedback stabilization of an unstable wave equation we consider the problem of stabilization of a one dimensional wave equation that contains instability at its free end and control on the opposite end in contrast to classical collocated boundary damper feedbacks for the neutrally stable wave equations with one end satisfying a homogeneous boundary condition the controllers and the associated observers designed in the paper are more complex due to the open loop instability of the plant the controller and observer gains are designed using the method of backstepping which results in explicit formulae for the gain functions we prove exponential stability and the existence and uniqueness of classical solutions for the closed loop system we also derive the explicit compensators in frequency domain the results are illustrated with simulations

optimisation and adaptation of synchronisation controllers for networked second order infinite dimensional systems abstractthe adaptation and optimisation of synchronisation control for networked second order distributed parameter systems are considered the objective is to design output feedback controllers guaranteeing agreement between the states of the n systems that individually track a reference model the controller structure involves feedback terms consisting of the pairwise difference of the measurements of the second order systems as well as coupling terms that enforce consensus placing the closed loop networked systems in aggregate form allows for further optimisation of the synchronisation gains using the aggregate systems closed loop energy as a suitable optimisation measure the search for the synchronisation gains reduces to the minimisation of the optimisation index which eventually is described by the trace of the solution to a parameterised lyapunov operator equation considering the adaptation of the synchronisation gains offers an alternative to optimisation the adaptation is based on lyapuno

acoustic analysis of a rectangular cavity with general impedance boundary conditions a fourier series method is proposed for the acoustic analysis of a rectangular cavity with impedance boundary conditions arbitrarily specified on any of the walls the sound pressure is expressed as the combination of a three dimensional fourier cosine series and six supplementary two dimensional expansions introduced to ensure accelerate the uniform and absolute convergence rate of the series representation in the cavity including the boundary surfaces the expansion coefficients are determined using the rayleigh ritz method since the pressure field is constructed adequately smooth throughout the entire solution domain the rayleigh ritz solution is mathematically equivalent to what is obtained from a strong formulation based on directly solving the governing equations and the boundary conditions to unify the treatments of arbitrary nonuniform impedance boundary conditions the impedance distribution function on each specified surface is invariantly expressed as a double fourier series expansion so that all the relevant integrals can be calculated analytically the modal parameters for the acoustic cavity can be simultaneously obtained from solving a standard matrix eigenvalue problem instead of iteratively solving a nonlinear transcendental equation as in the existing methods several numerical examples are presented to demonstrate the effectiveness and reliability of the current method for various impedance boundary conditions including nonuniform impedance distributions

controllability and observability criteria for multivariable linear second order models criteria are discussed for the determination of controllability stabilizability observability or detectability of linear second order multivariable models of for example large space structures an initial modal transformation is not required and the criteria are thus applicable to models with arbitrary damping coefficients moreover the criteria are modal in the sense that some or all of the modes may be tested for controllability or observability this aspect has advantages if not all the modes are known or easily computable the criteria are further illustrated for a number of important special cases in a series of corollaries

a solution adaptive lattice boltzmann method for two dimensional incompressible viscous flows a stencil adaptive lattice boltzmann method lbm is developed in this paper it incorporates the stencil adaptive algorithm developed by ding and shu 26 for the solution of navier stokes n s equations into the lbm calculation based on the uniform mesh the stencil adaptive algorithm refines the mesh by two types of 5 points symmetric stencils which are used in an alternating sequence for increased refinement levels the two types of symmetric stencils can be easily combined to form a 9 points symmetric structure using the one dimensional second order interpolation recently developed by wu and shu 27 along the straight line and the d2q9 model the adaptive lbm calculation can be effectively carried out note that the interpolation coefficients are only related to the lattice velocity and stencil size hence the simplicity of lbm is not broken down and the accuracy is maintained due to the use of adaptive technique much less mesh points are required in the simulation as compared to the standard lbm as a consequence the computational efficiency is greatly enhanced the numerical simulation of two dimensional lid driven cavity flows is carried out accurate results and improved efficiency are reached in addition the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries the obtained results compare well with data in the literature

lattice boltzmann method on quadtree grids for simulating fluid flow through porous media a new automatic algorithm abstract during the past two decades the lattice boltzmann lb method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations in this method instead of solving the navier stocks equation the boltzmann equation is solved to simulate the flow of a fluid this method was originally developed based on uniform grids however in order to model complex geometries such as porous media it can be very slow in comparison with other techniques such as finite differences and finite elements to eliminate this limitation a number of studies have aimed to formulate the lattice boltzmann on the unstructured grids this paper deals with simulating fluid flow through a synthetic porous medium using the lb method and on the quadtree grid structure to this end the lb method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media accuracy and efficiency of this algorithm is compared against the conventional lb method based on uniform grids while the decrease in computational time in the proposed lb method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images the same level of accuracy is obtained when compared with the conventional lb method on uniform grids

orthogonal basis selection method for robust partial eigenvalue assignment problem in second order control systems in this paper we study the robust partial eigenvalue assignment problem using state feedback control in second order control systems which means that the feedback control matrices not only assign specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations in the coefficient matrices some measures of robustness of the closed loop system are discussed and a numerical method is proposed such that it aims to minimize one measure of the conditioning of the closed loop system numerical examples show that the method is convergent and often leads to better conditioned closed loop system

an immersed boundary method for fluids using the xfem and the hydrodynamic boltzmann transport equation abstract this paper presents a stabilized finite element formulation of the hydrodynamic boltzmann transport equation hbte to predict nearly incompressible fluid flow the hbte is discretized with hermite polynomials in the velocity variable and a streamline upwind petrov galerkin formulation is used to discretize the spatial variable a nonlinear stabilization scheme is presented from which a simple linear stabilization scheme is constructed in contrast to the navier stokes ns equations the hbte is a first order equation and allows for conveniently enforcing dirichlet conditions along immersed boundaries a simple and efficient formulation for enforcing dirichlet boundary conditions is presented and its accuracy is studied for immersed boundaries captured by the extended finite element method xfem numerical experiments indicate that both the linear and non linear stabilization methods are sufficiently accurate and stable but the linear formulation reduces the computational cost significantly the accuracy of enforcing boundary conditions is satisfactory and shows second order convergence as the mesh is refined augmenting the boundary condition formulation with a penalty term increases the accuracy of enforcing the boundary condition constraints but may degrade the accuracy of the global solution comparisons with results of a single relaxation time lattice boltzmann method show that the proposed finite element method features greater robustness and lesser dependence of the computational costs on the level of mesh refinement

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

multiscale lattice boltzmann schemes with turbulence modeling abstract the viability of multiscale lattice boltzmann schemes for the numerical simulation of turbulent flows is discussed and numerically demonstrated for turboaxial machine applications the extension of boundary fitting formulas based on wall functions is proposed which enables the efficient computation of turbulent flows in complex curvilinear geometry using a simple cartesian grid examples of two dimensional turbulent flows in an axial compressor cascade are presented

applications of waveguide type base functions for the eigenproblems of two dimensional cavities an acoustic modal analysis technique useful for two dimensional cavities of general shapes is developed as an extension of the technique developed earlier by kim and kang j acoust soc am 99 2938 2946 1996 for the modal analysis of convex membranes both neumann and dirichlet problems can be solved with the present choice of cosinusoidally varying waveguide type functions instead of sinusoidally varying waveguide type functions adopted earlier j acoust soc am 99 2938 2946 1996 a cavity subdivision technique for general nonconvex cavities overcomes the limitation of the earlier technique useful only for convex cavities successful applications of the present technique are demonstrated in some practical two dimensional cavity problems the present technique is potentially a very efficient technique in handling higher eigenmodes

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

equivalent partial differential equations of a lattice boltzmann scheme we show that when we formulate the lattice boltzmann equation with a small time step dt and an associated space scale dx a taylor expansion joined with the so called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit we recover the euler equations of gas dynamics at the first order and the compressible navier stokes equations at the second order

second order observers for second order distributed parameter systems in r2 this note addresses observer design for second order distributed parameter systems in r2 particularly second order distributed parameter systems without distributed damping are studied based on finite number of measurements exponentially stable observer is designed the existence uniqueness and stability of solutions of the observers are based on semigroup theory

finite volume lattice boltzmann method we present a finite volume formulation for the lattice boltzmann method fvlbm based on standard bilinear quadrilateral elements in two dimensions the accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the navier stokes equations for time dependent rotating couette flow and taylor vortex flow to demonstrate the flexibility of the scheme we have also simulated a modified rotating couette flow where the inner cylinder has an elliptical shape the results agree with those obtained from the traditional marker and cell method the fvlbm scheme is applicable to arbitrarily shaped two dimensional regions and thus the range of applicability of the lattice boltzmann method has been significantly extended

infinite dimensional luenberger like observers for a rotating body beam system the paper proposes luenberger like observers for a rotating body beam system the latter is described by a partial differential equation and its dynamic is governed a unitary group the observers proposed in the paper are able to reconstitute the dynamic evolution of the beam profile by measuring the moment force on the boundary only meanwhile we propose a reliable numerical scheme based on a finite element method in order to simulate the observation system and the observers the efficiency of our proposed scheme and the performances of the observers are illustrated with numerical simulation results

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

power series expansions for mathieu functions with small arguments power series expansions for the even and odd angular mathieu functions se m h cos and so m h cos with small argument h are derived for general integer values of m the expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind

an optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures the partial quadratic eigenvalue assignment problem pqevap concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged the problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems the solution of this problem requires computations of a pair of feedback matrices for practical effectiveness these feedback matrices must be computed in such a way that their norms and the condition number of the closed loop eigenvector matrix are as small as possible these considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem mnpqevap and the robust partial quadratic eigenvalue assignment problem rpqevap respectively in this paper we propose new optimization based algorithms for solving these problems the problems are solved directly in a second order setting without resorting to a standard first order formulation so as to avoid the inversion of a possibly ill conditioned matrix and the loss of exploitable structures of the original model the algorithms require the knowledge of only the open loop eigenvalues to be replaced and their corresponding eigenvectors the remaining open loop eigenvalues and their corresponding eigenvectors are kept unchanged the invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result furthermore the gradient formulas needed to solve the problems by using the quasi newton optimization technique employed are computed in terms of the known quantities only above all the proposed methods do not require the reduction of the model order or the order of the controller even when the underlying finite element model has a very large degree of freedom these attractive features coupled with minimal computational requirements such as solutions of small diagonal sylvester equations make the proposed algorithms ideally suited for application to large real life structures numerical results show significant improvement in feedback norms and in the condition number of the closed loop system also the closed loop eigenvalues have acceptable accuracy

dissipative lqg control systems an indefinite lyapunov test matrix for closed loop dissipativeness using lqg linear quadratic gaussian design is presented the application of this test to relaxation systems lossless systems hamiltonian systems positive real systems and second order systems with collocated rate sensors and actuators is explored the lyapunov test also helps clarify the role of collocated sensors and actuators in lqg design a set of duality theorems based on the indefinite lyapunov test matrix is derived

derivation of a ritz series modeling technique for acoustic cavity structural systems based on a constrained hamilton s principle hamilton s principle for dynamic systems is adapted to describe the coupled response of a confined acoustic domain and an elastic structure that forms part or all of the boundary a key part of the modified principle is the treatment of the surface traction as a lagrange multiplier function that enforces continuity conditions at the fluid solid interface the structural displacement fluid velocity potential and traction are represented by ritz series where the usage of the velocity potential as the state variable for the fluid assures that the flow is irrotational designation of the coefficients of the potential function series as generalized velocities leads to corresponding series representations of the particle velocity displacement and pressure in the fluid which in turn leads to descriptions of the mechanical energies and virtual work application of the calculus of variations to hamilton s principle yields linear differential algebraic equations whose form is identical to those governing mech

natural second order observers for second order distributed parameter systems the aim of this manuscript is to present an alternative method for designing state observers for second order distributed parameter systems without resorting to a first order formulation this method has the advantage of utilizing the algebraic structure that second order systems enjoy with the obvious computational savings in observer gain calculations the proposed scheme ensures that the derivative of the estimated position is indeed the estimate of the velocity component and to achieve such a result a parameter dependent lyapunov function was utilized to ensure the asymptotic convergence of the state estimation error

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

large eddy simulation coupled with wall models for turbulent channel flows at high reynolds numbers with a lattice boltzmann method application to coriolis mass flowmeter abstract the numerical prediction of pressure drop within wall bounded flow domains at high reynolds numbers re using a large eddy simulation les approach is a challenging task for industrial applications because the fluid domain is usually underresolved a lattice boltzmann method lbm with bhatnagar gross and krook bgk collision operator coupled with the smagorinsky lilly turbulence model is used to model these wall bounded turbulent flows the near wall region is modelled using wall functions to decrease the required mesh resolution for high re the influence of different velocity boundary approaches and wall functions is investigated for the benchmark bi periodic fully developed turbulent channel flow for friction reynolds numbers re of 1000 2000 and 5200 this benchmark case is validated against direct numerical simulation dns results for turbulent statistics of 1st and 2nd order based on this validation the pressure drop of an industrial coriolis mass flowmeter is compared to experimental data for re up to 127 800 the error of the pressure drop calculation in underresolved grids is reduced by two orders of magnitude in comparison to a no slip approach for curved boundaries

investigation of the les wale turbulence model within the lattice boltzmann framework turbulence models which can perform the transition from laminar flow to fully developed turbulent flow are of key importance in industrial applications a promising approach is the les wale model which can be used without wall functions or global damping functions the model produces an efficient and fast scheme due to its algebraic character additionally its prediction of the transition from laminar to turbulent regimes has shown promising results in this work the les wale model is investigated within the lattice boltzmann framework for validation purposes various test cases are presented first a channel flow at a reynolds number of 6876 is investigated secondly the flow around a wall mounted cube at various reynolds numbers is determined the flow regime varies from laminar to transitional to fully turbulent conditions at a reynolds number of 40 000 with respect to the cube height

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

least squares finite element lattice boltzmann method a new numerical model of the lattice boltzmann method utilizing least squares finite element in space and crank nicolson method in time is presented the new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite element method s geometric flexibility and numerical stability while employing efficient and accurate least squares optimization for the pure advection equation on a uniform mesh the proposed method provides for fourth order accuracy in space and second order accuracy in time with unconditional stability in the time domain accurate numerical results are presented through two dimensional incompressible poiseuille flow and couette flow

acoustic eigenfrequencies in concentric spheroidal spherical cavities abstract the acoustic eigenfrequenciesfnsmin concentric spheroidal spherical cavities are determined for both dirichlet and neumann boundary conditions two types of cavities are examined one with spheroidal outer and spherical inner boundary and inversely for the other the pressure field is expressed in terms of both spherical and spheroidal wave functions connected with one another by well known expansion formulas when the solution is specialized to small values ofh d 2r2 wheredis the interfocal distance of the spheroidal boundary andr2the half length of its rotation axis exact closed form expressions are obtained for the coefficientsgnsm 2 andgnsm 4 in the resulting relationsfnsm h fns 0 1 gnsm 2 h2 gnsm 4 h4 o h6 numerical results are given for various values of the parameters

boundary output feedback of second order distributed parameter systems boundary output feedback of a class of second order distributed parameter systems is addressed in particular second order distributed parameter systems without distributed damping are studied first a uniformly exponentially stable observer is designed then exponentially stabilizing control laws are proposed the existence uniqueness and stability of solutions of the observer and the closed loop system are based on semigroup theory

filter matrix lattice boltzmann simulation of lid driven deep cavity flows part i steady flows this paper seeks to make a systematic study over a series of lid driven flow in various deep cavities using the filter matrix lattice boltzmann fmlb model a concise description of the fmlb model is presented in this paper and important numerical considerations for effective use of the fmlb model are also clearly elucidated in particular the selection of a free parameter employed to appropriately control the weight of the third order terms in the fmlb solution vector is carefully examined resulting in some general suggestions that may render the fmlb stability consistently secured for simulations of different cavity flow scenarios employing the fmlb and the lattice bhatnagar gross krook lbgk methods for comparison purpose the first series of test cases correspond to the lid driven cavity flows with a low reynolds number re 0 01 at a variety of aspect ratios the simulation results demonstrate that the fmlb model is superior to the lbgk method in terms of numerical stability and particularly the fmlb result can reach quite good agreement with the benchmark solution even if the aspect ratio goes up to 15 then the fmlb model is used to compute the steady flows for deep cavities with aspect ratios ranging from 1 5 to 7 and elevated reynolds numbers ranging from 100 to 5000 a number of features of steady flows such as the locations strengths and sizes of the vortices as well as the effects of reynolds number and aspect ratio on the vortex structure are all predicted by the fmlb model with an obviously improved accuracy when compared to some other available numerical results

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

power series expansions for spheroidal wave functions with small arguments power series expansions for the angular spheroidal wave functions of the first kind smn c with small arguments c are derived for general integer values of m and n the various evaluated expansion coefficients can also be used in the calculation of the corresponding angular functions of the second kind as well as for the radial functions of any kind only the prolate functions are considered explicitly but corresponding formulas for the oblate ones are obtained immediately

balancing and model reduction for second order form linear systems model reduction of second order form linear systems is considered where a second order form reduced model is desired the focus is on reduction methods that employ or mimic moore s balance and truncate 1981 first we examine second order form model reduction by conversion to first order form and obtain a complete solution for this problem then new gramians and input output i o invariants for second order systems are motivated and defined based on these direct second order balancing methods are developed this leads naturally to direct second order form analogs for the well known first order form balance and truncate model reduction method explicit algorithms are given throughout the paper

quantitative measures of modal controllability and observability in vibration control of defective and near defective systems in this paper we focus on the control problem of defective systems with repeated eigenvalues using the singular value decomposition of input matrix b and output matrix c in the modal subspace the quantitative measures of modal controllability and observability of defective systems are discussed for a near defective system with close eigenvalues we first transform it into a defective one and then apply the same method to deal with near defective systems numerical examples for a general damping system and an airfoil are given to illustrate the applications of the present method

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

a fully implicit method for lattice boltzmann equations existing approaches for solving the lattice boltzmann equations with finite difference methods are explicit and semi implicit both have certain stability constraints on the time step size in this work a fully implicit second order finite difference scheme is developed we focus on a parallel highly scalable newton krylov ras algorithm for the solution of a large sparse nonlinear system of equations arising at each time step here ras is a restricted additive schwarz preconditioner based on a first order spatial discretization we show numerically that by using the fully implicit method the time step size is no longer constrained by the cfl condition and the newton krylov ras algorithm is scalable on a supercomputer with more than ten thousand processors moreover to calculate the steady state solution we investigate an adaptive time stepping strategy the total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several t

a simplified finite volume lattice boltzmann method for simulations of fluid flows from laminar to turbulent regime part ii extension towards turbulent flow simulation abstract in this paper the original finite volume lattice boltzmann method fvlbm on an unstructured grid part i of these twin papers is extended to simulate turbulent flows to model the turbulent effect the k sst turbulence model is incorporated into the present fvlbm framework and is also solved by the finite volume method based on the eddy viscosity hypothesis the eddy viscosity is computed from the solution of the k sst model and the total viscosity is modified by adding this eddy viscosity to the laminar kinematic viscosity given in the bhatnagar gross krook collision term because of solving for the collision term with the explicit method in the original fvlbm scheme the computational efficiency is much lower for simulating high reynolds number flow this is due to the fact that the largest time step decided by the stability condition of the collision term which is less than twice the relaxation time is much smaller than that decided by the cfl condition in order to enhance the computational efficiency the three stage second order implicit explicit imex runge kutta method is used for temporal discretization and the time step can be one or two orders of magnitude larger as compared with the explicit euler forward scheme although the computational cost is increased the final computational efficiency is enhanced by about one order of magnitude and good results can also be obtained at a large time step through the test case of a lid driven cavity flow two turbulent flow cases are carried out to validate the present method including flow over a backward facing step and flow around a naca0012 airfoil the numerical results are found to be in agreement with experimental data and numerical solutions demonstrating the applicability of the present fvlbm coupled with the k sst model to accurately predict the incompressible turbulent flows

eigenmode analysis of arbitrarily shaped two dimensional cavities by the method of point matching in the proposed method as in the boundary element method bem a field problem is solved on its boundary along which nodes are distributed the distinct feature of the proposed method is related to the fact that no interpolation functions between the nodes are required so that the basic collocation method is employed to satisfy a given boundary condition this approach reduces a large amount of numerical calculation induced due to the interpolation functions unlike the method of auxiliary sources mas in the proposed method only the regular functions that have finite functional values everywhere including the origins are employed as basis functions as a result the proposed method does not need the auxiliary surface the construction of which is a troublesome work because its form dimension shifting etc strongly influence the accuracy of the mas the eigenvalues calculated by the proposed method rapidly converge to the exact values thanks to the simplicity of the method moreover the method gives mode shapes successfully without using the interpolation functions between the nodes the efficiency and accuracy of the method are verified through several applications

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

observability of linear discrete time systems of algebraic and difference equations abstractthe notion of observability for higher order discrete time systems of algebraic and difference equations is studied such systems are also known as polynomial matrix descriptions attention is first given to a special form of descriptor systems with a state lead in the output this system is transformed into its causal and noncausal subsystems and observability criteria are given in terms of the subsystem s matrices and the fundamental matrix sequence of the matrix pencil e a afterwards the higher order system is studied by transforming it into a first order descriptor system of the above form an observability criterion is provided for the higher order system in terms of the laurent expansion at infinity of the system s polynomial matrix in addition observability is connected with the coprimeness of the polynomial matrices of the higher order system and the coprimeness of the matrix pencils of the descriptor system

new explicit solutions in acoustics of closed spaces on the basis of divergent series a new approach to the acoustics of closed spaces is developed that involves solutions for polygonal shapes in explicit form it is shown that exact solutions can be constructed for polygonal geometries where all the interior angles are equal to n n is an integer it is stated that the set of such polygons consists of the rectangle known result and three types of triangles some new explicit formulas are obtained for the eigenfrequencies of the triangles it is demonstrated that the proposed technique also permits an exact representation of the impulse response function for the geometries described

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

acoustic eigenfrequencies in a spheroidal cavity with a concentric penetrable sphere the acoustic eigenfrequencies fnsm in a spheroidal cavity containing a concentric penetrable sphere are determined analytically for both dirichlet and neumann conditions in the spheroidal boundary two different methods are used for the evaluation in the first the pressure field is expressed in terms of both spherical and spheroidal wave functions connected with one another by well known expansion formulas in the second a shape perturbation method this field is expressed in terms of spherical wave functions only while the equation of the spheroidal boundary is given in spherical coordinates the analytical determination of the eigenfrequencies is possible when the solution is specialized to small values of h d 2r2 h 1 with d the interfocal distance of the spheroidal boundary and 2r2 the length of its rotation axis in this case exact closed form expressions are obtained for the expansion coefficients gnsm 2 and gnsm 4 in the resulting relation fnsm h fns 0 1 h2gnsm 2 h4gnsm 4 o h6

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

wall model for large eddy simulation based on the lattice boltzmann method an original wall model for lattice boltzmann based large eddy simulation is presented it relies on either an analytical profile for the velocity profile within the first off wall cell or the solution of turbulent boundary layer equations the latter are solved thanks to a meshless approach to obtain a user friendly method the proposed method is observed to be both robust and accurate yielding very satisfactory results in plane channel flow up to re email protected 000 on uniform grids with dx email protected email protected 1000 the computed maximum error on skin friction is about 4 in most investigated cases on the coarsest grids 10 grid points across the half channel height it lies within 1 2 on finer grids with 20 60 uniformly distributed grid points in the channel half height

optimal actuator sensor location for active noise regulator and tracking control problems in this paper we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity we offer two control strategies the first is based on linear quadratic tracking where the offending noise is tracked and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem the first method which is based on full state information is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators for both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and or the sensors numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors

a variational integrators approach to second order modeling and identification of linear mechanical systems the theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system preserving key properties of the continuous time flow the discrete time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures we discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete time identified model we test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous time parameters of second order mechanical systems starting from discrete measured data

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness we demonstrate that the cumulant lattice boltzmann model with optimized parameters captures the drag crisis for flows over a sphere no sub grid model and no wall function is required and the boundary layer is only marginally resolved it is observed that in the transition regime between the high and the low drag configuration the flow switches from one state to the other state

near wall treatment for the simulation of turbulent flow by the cumulant lattice boltzmann method abstract we present a new wall function implementation for the cumulant lattice boltzmann method that sets a partial slip velocity on the wall by computing a skin frictional coefficient our approach uses local information and is particularly appropriate for implementations on general purpose graphics processing units the validation of the model has been conducted by performing numerical simulations of the turbulent channel flow test case with different grid resolutions and for different reynolds numbers the results showed encouraging agreement with direct numerical simulation data for velocity profile reynolds shear and normal stresses

a nonlinearly preconditioned inexact newton algorithm for steady state lattice boltzmann equations most existing methods for calculating the steady state solution of the lattice boltzmann equations are based on pseudo time stepping which often requires a large number of time steps especially for high reynolds number problems to calculate the steady state solution directly without the time integration in this paper we propose and study a nonlinearly preconditioned inexact newton algorithm with a domain decomposition based linear solver for parallelization more precisely the proposed algorithmic framework involves an implicit second order discretization a two level inexact newton method and a nonlinear elimination preconditioner to accelerate the convergence of newton iteration a nonstandard pollution removing coarse space is introduced for the two level method numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm especially for problems at a high reynolds number a comparison is also included to show the superiority of the proposed approach over o

grid refinement for lattice bgk models lattice boltzmann models proposed at the end of the 1980s as the noise free version of lattice gas models are based on gas kinetic representation of fluid flow their recent modifications the lattice bgk models provide especially simple effective and stable algorithms for the solution of hydrodynamical problems a local second order grid refinement scheme for the lattice bgk model is proposed in this work the refinement scheme and a boundary fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel with small and moderate reynolds numbers

sampled data observers for 1 d parabolic pdes with non local outputs abstract the present work provides a systematic approach for the design of sampled data observers to a wide class of 1 d parabolic pdes with non local outputs the studied class of parabolic pdes allows the presence of globally lipschitz nonlinear and non local terms in the pde two different sampled data observers are presented one with an inter sample predictor for the unavailable continuous measurement signal and one without an inter sample predictor explicit conditions on the upper diameter of the uncertain sampling schedule for both designs are derived for exponential convergence of the observer error to zero in the absence of measurement noise and modeling errors moreover explicit estimates of the convergence rate can be deduced based on the knowledge of the upper diameter of the sampling schedule when measurement noise and or modeling errors are present input to output stability ios estimates of the observer error hold for both designs with respect to noise and modeling errors the main results are illustrated by two examples which show how the proposed methodology can be extended to other cases e g boundary point measurements

resonance modes in a one dimensional medium with two purely resistive boundaries calculation methods orthogonality and completeness studying the problem of wave propagation in media with resistive boundaries can be made by searching for resonance modes or free oscillations regimes in the present article a simple case is investigated which allows one to enlighten the respective interest of different classical methods some of them being rather delicate this case is the one dimensional propagation in a homogeneous medium having two purely resistive terminations the calculation of the green function being done without any approximation using three methods the first one is the straightforward use of the closed form solution in the frequency domain and the residue calculus then the method of separation of variables space and time leads to a solution depending on the initial conditions the question of the orthogonality and completeness of the complex valued resonance modes is investigated leading to the expression of a particular scalar product the last method is the expansion in biorthogonal modes in the frequency domain the modes having eigenfrequencies depending on the frequency results of the three methods generalize or and correct some results already existing in the literature and exhibit the particular difficulty of the treatment of the constant mode

a combined integro modal approach for predicting acoustic properties of irregular shaped cavities an integro modal approach is presented in this paper for computing the acoustic properties of irregular shaped cavities the method consists of discretizing the whole cavity into a series of subcavities whose acoustic pressure is decomposed either over a modal basis of regular subcavities or over that of the bounding cavities in the case of irregular shaped boundaries an integral formulation is then established to ensure continuity of both pressure and velocity between adjacent subcavities using a membrane with zero mass and stiffness to some extent the method provides a combined approach retaining the advantages of both the acoustoelastic method aem and the green s function method gfm numerical and experimental results are presented demonstrating the efficiency and accuracy of the suggested technique comparisons with other existing methods are also made it is shown that good accuracy on the computation of cavity modes can be obtained using a very limited number of subcavities

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

on implementation of boundary conditions in the application of finite volume lattice boltzmann method a new implementation of boundary condition based on the half covolume and bounce back rule for the non equilibrium distribution function for the finite volume lbm is proposed here the numerical simulation results for the expansion channel flow and driven cavity problem indicate that this method is workable for arbitrary meshes in addition the fourth order runge kutta scheme is found to be a practical way in the lbm to accelerate the calculation speed

acoustical cavity excitation a tutorial exposition is given of cavity excitations and it is shown that relatively simple analytical solutions for the excitation of acoustic fields in cavities with lossy walls can be obtained for a broad class of such cavities the standard analytic procedure whereby one expresses the acoustic field as a sum over the eigenmodes of the cavity is reviewed and its limitations are pointed out an alternate procedure is to seek to make use of green s functions depending on a single coordinate and to not express such green s functions as sums over eigenfunctions instead one expresses the green s function as a closed form function that has a discontinuous slope at the value of the coordinate corresponding to the source location although the class of cavities for which this approach is possible is limited it is sufficiently broad to be of intrinsic interest and the results may be helpful to those seeking benchmark solutions and analytic insight displayed examples are for cavities whose shapes are spheres and cylinders with interior monopole dipole line and distributed sources the formulation yields simple expressions for the total power absorbed by the cavity walls

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

decay of solutions of wave equations in a bounded region with boundary dissipation abstract an energy decay rate is obtained for solutions of wave type equations in a bounded region in rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface

on the extended luenberger type observer for semilinear distributed parameter systems the design of an extended luenberger observer is considered to solve the state observation problem for semilinear distributed parameter systems for this a backstepping based technique is proposed for the design of the output injection weights by making use of the extended linearization of the semilinear observer error system with respect to the observer state stability of both the linearized and the semilinear observer error dynamics is analyzed theoretically moreover an efficient sample and hold implementation is considered to improve the computational efficiency of the observer design simulation examples are provided for a bistable semilinear partial differential equation and the simplified model of a bioreactor with monod kinetics

a spectral element discontinuous galerkin lattice boltzmann method for nearly incompressible flows we present a spectral element discontinuous galerkin lattice boltzmann method for solving nearly incompressible flows decoupling the collision step from the streaming step offers numerical stability at high reynolds numbers in the streaming step we employ high order spectral element discontinuous galerkin discretizations using a tensor product basis of one dimensional lagrange interpolation polynomials based on gauss lobatto legendre grids our scheme is cost effective with a fully diagonal mass matrix advancing time integration with the fourth order runge kutta method we present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous galerkin approach we show convergence studies for couette flows and demonstrate two benchmark cases with lid driven cavity flows for re 400 5000 and flows around an impulsively started cylinder for re 550 9500 computational results are compared with those of other theoretical and computational work that used a multigrid method a vortex method and a spectral element model

controllability and observability at infinity of multivariable linear second order models in this note we give in the spirit of 4 numerically attractive tests of controllability and observability of linear multivariable second order systems in which the leading matrix is singular

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

finite volume versus streaming based lattice boltzmann algorithm for fluid dynamics simulations a one to one accuracy and performance study a finite volume fv discretization method for the lattice boltzmann lb equation which combines high accuracy with limited computational cost is presented in order to assess the performance of the fv method we carry out a systematic comparison focused on accuracy and computational performances with the standard streaming lattice boltzmann equation algorithm in particular we aim at clarifying whether and in which conditions the proposed algorithm and more generally any fv algorithm can be taken as the method of choice in fluid dynamics lb simulations for this reason the comparative analysis is further extended to the case of realistic flows in particular thermally driven flows in turbulent conditions we report the successful simulation of high rayleigh number convective flow performed by a lattice boltzmann fv based algorithm with wall grid refinement

design of interval observers and controls for pdes using finite element approximations synthesis of interval state estimators is investigated for the systems described by a class of parabolic partial differential equations pdes first a finite element approximation of a pde is constructed and the design of an interval observer for the derived ordinary differential equation is given second the interval inclusion of the state function of the pde is calculated using the error estimates of the finite element approximation finally the obtained interval estimates are used to design a dynamic output stabilizing control the results are illustrated by numerical experiments with an academic example and the black scholes model of financial market

non body fitted cartesian mesh simulation of highly turbulent flows using multi relaxation time lattice boltzmann method this paper presents a lattice boltzmann method lbm based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non body fitted cartesian meshes the approach features 1 combining the interpolated bounce back scheme with the lbm of multi relaxation time mrt type to enable the use of simple cartesian mesh for the flow cases even with complex geometries and 2 incorporating the spalart allmaras sa turbulence model into lbm in order to represent the turbulent flow effect the numerical experiments are performed corresponding to flows around an naca0012 airfoil at re 5x10 5 and around a flat plate at re 2x10 4 respectively the agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced lbm proposed in this paper for simulating simply on cartesian meshes complex flows that may involve bodies of curved boundary high reynolds number and large angle of attack

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder