stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

advances in multi domain lattice boltzmann grid refinement grid refinement has been addressed by different authors in the lattice boltzmann method community the information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view while a decimation is performed when going from the fine to the coarse grid a reconstruction must performed to pass form the coarse to the fine grid in this context we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation we show this operation to be extremely important because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high reynolds numbers then we demonstrate that to reconstruct the information a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice boltzmann method these two fundamental extra steps are validated on two classical 2d benchmarks the 2d circular cylinder and the 2d dipole wall collision the latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high reynolds number of 5000 a very good agreement is found between the single grid and the refined grid cases the proposed grid refinement strategy has been implemented in the parallel open source library palabos

optimal low dispersion low dissipation lbm schemes for computational aeroacoustics lattice boltmzann methods lbm have been proved to be very effective methods for computational aeroacoustics caa which have been used to capture the dynamics of weak acoustic fluctuations in this paper we propose a strategy to reduce the dispersive and disspative errors of the two dimensional 2d multi relaxation time lattice boltzmann method mrt lbm by presenting an effective algorithm we obtain a uniform form of the linearized navier stokes equations corresponding to the mrt lbm in wave number space using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods we propose a class of minimization problems to optimize the free parameters in the mrt lbm we obtain this way a dispersion relation preserving lbm drp lbm to circumvent the minimized dispersion error of the mrt lbm the dissipation relation precision is also improved and the stability of the mrt lbm with the small bulk viscosity is guaranteed von neuman analysis of the linearized mrt lbm is performed to validate the optimized dispersion dissipation relations considering monochromatic wave solutions meanwhile dispersion and dissipation errors of the optimized mrt lbm are quantitatively compared with the original mrt lbm finally some numerical simulations are carried out to assess the new optimized mrt lbm schemes

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

stabilization of the lattice boltzmann method using the ehrenfests coarse graining idea the lattice boltzmann method lbm and its variants have emerged as promising computationally efficient and increasingly popular numerical methods for modeling complex fluid flow however it is acknowledged that the method can demonstrate numerical instabilities e g in the vicinity of shocks we propose a simple technique to stabilize the lbm by monitoring the difference between microscopic and macroscopic entropy populations are returned to their equilibrium states if a threshold value is exceeded we coin the name ehrenfests steps for this procedure in homage to the vehicle that we use to introduce the procedure namely the ehrenfests coarse graining idea

high order low dispersive and low dissipative explicit schemes for multiple scale and boundary problems explicit high order numerical schemes are proposed for the accurate computation of multiple scale problems and for the implementation of boundary conditions specific high order node centered finite differences and selective filters removing grid to grid oscillations are first designed for the discretization of the buffer region between a x grid domain and 2 x grid domain the coefficients of these matching schemes are chosen so that the maximum order of accuracy is reached non centered finite differences and selective filters are then developed with the aim of accurately computing boundary conditions they are constructed by minimizing the dispersion and the dissipation errors in the wave number space for waves down to four points per wavelength the dispersion and dissipation properties of the matching and the boundary schemes are described in detail and their accuracy limits are determined to show that these schemes calculate accurately waves with at least five points per wavelength test problems including linear convection wall reflection and acoustic scattering around a cylinder are finally solved to illustrate the accuracy of the schemes

lattice boltzmann method with selective viscosity filter for high reynolds number flows the lattice boltzmann method suffers from numerical instabilities that can induce local blowup of the computation the von neumann stability analysis applied to the lbe bgk and lbe mrt models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes as it is done in the lbe mrt model an increase of the bulk viscosity is an efficient way of damping spurious oscillations however this stabilization method induces an over damping of acoustic waves some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes three different lattice boltzmann algorithms based on filtering step are proposed the fully filtered lbe the lbe with filtered macroscopic quantities and the lbe with filtered collision operator the behavior of several explicit filter stencils is studied in the fourier space for a given filter stencil the filtered collision operator approach leads to the highest cut off wavenumber in this case the theoretical wavenumber dependent viscosity is n k c s 2 t email protected k 1 2 where f k is the filter shape and s the filter strength under resolved simulations high reynolds number are performed on the case of the doubly periodic shear layers the performance of the three filtered lbe is found to be the same as the mrt model for stability control propagation of acoustic plane waves is also simulated with the three filtering algorithms the measured dissipation of acoustic wave compares well with the theoretical results

comparison between lattice boltzmann method and navier stokes high order schemes for computational aeroacoustics computational aeroacoustic caa simulation requires accurate schemes to capture the dynamics of acoustic fluctuations which are weak compared with aerodynamic ones in this paper two kinds of schemes are studied and compared the classical approach based on high order schemes for navier stokes like equations and the lattice boltzmann method the reference macroscopic equations are the 3d isothermal and compressible navier stokes equations a von neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions three physical modes are recovered and the corresponding theoretical dispersion relations are obtained then the same analysis is made on the space and time discretization of the navier stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions different orders of discretization are considered with and without a uniform mean flow three different lattice boltzmann models are then presented and studied with the von neumann analysis the theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied it is shown that the dispersion error in the lattice boltzmann models is only due to the space and time discretization and that the continuous discrete velocity boltzmann equation yield the same exact dispersion as the navier stokes equations finally dispersion and dissipation errors of the different kind of schemes are quantitatively compared it is found that the lattice boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3 step runge kutta scheme in time the number of floating point operations at a given error level associated with these two kinds of schemes are then compared

hybrid system stability and robustness verification using linear matrix inequalities this paper addresses issues concerning exponential stability and robustness of hybrid systems stability conditions using lyapunov techniques are given the search for the lyapunov functions is formulated as a linear matrix inequality lmi problem for hybrid systems with affine as well as non linear vector fields it is shown how the lyapunov approach most advantageously also can be used to guarantee stability despite the presence of model uncertainties several examples are given to illustrate the theory

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

discontinuous piecewise quadratic lyapunov functions for planar piecewise affine systems abstract for planar piecewise affine systems this paper proposes sufficient stability conditions based on discontinuous lyapunov functions the monotonicity condition for discontinuous functions at switching instants is presented based on the behavior of state trajectories on the switching surfaces first the stability conditions are derived for a typical multiple lyapunov function and then these conditions are formulated as a set of linear matrix inequalities for piecewise quadratic lyapunov functions the implementation of the proposed method is illustrated by an example

global asymptotic stability of a pid control system with coulomb friction for a point mass subject to coulomb friction in feedback with a pid controller we consider a model based on a differential inclusion comprising all the possible magnitudes of static friction during the stick phase and having unique solutions we study the set of all equilibria and we establish its global asymptotic stability using a discontinuous lyapunov like function and a suitable lasalle s invariance principle the well posedness of the proposed model allows to establish useful robustness results including an iss property from a suitable input in a perturbed context simulation results are also given to illustrate our statements

half range completeness for the fokker planck equation half range completeness theorems are proved for eigenfunctions associated to the one dimensional fokker planck equation in a semi infinite medium existence and uniqueness results for perfectly absorbing partially absorbing and purely specularly reflecting boundary conditions are deduced for the stationary and time dependent problems similar results are obtained for a slab geometry

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

entropy function approach to the lattice boltzmann method in this paper we present the construction of the lattice boltzmann method equipped with the h theorem based on entropy functions whose local equilibria are suitable to recover the navier stokes equations in the framework of the lattice boltzmann method we derive a collision integral which enables simple identification of transport coefficients and which circumvents construction of the equilibrium we discuss performance of this approach as compared to the standard realizations

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

asymptotic stability of piecewise affine systems with filippov solutions via discontinuous piecewise lyapunov functions asymptotic stability of continuous time piecewise affine systems defined over a polyhedral partition of the state space with possible discontinuous vector field on the boundaries is considered in the first part of the paper the feasible filippov solution concept is introduced by characterizing single mode caratheodory sliding mode and forward zeno behaviors then a global asymptotic stability result through a possibly discontinuous piecewise lyapunov function is presented the sufficient conditions are based on pointwise classifications of the trajectories which allow the identification of crossing unreachable and caratheodory boundaries it is shown that the sign and jump conditions of the stability theorem can be expressed in terms of linear matrix inequalities by particularizing to piecewise quadratic lyapunov functions and using the cone copositivity approach several examples illustrate the theoretical arguments and the effectiveness of the stability result

cone copositive piecewise quadratic lyapunov functions for conewise linear systems in this technical note cone copositive piecewise quadratic lyapunov functions pwq lfs for the stability analysis of conewise linear systems are proposed the existence of a pwq lf is formulated as the feasibility of a cone copositive programming problem which is represented in terms of linear matrix inequalities a constructive procedure for its solution is provided examples show the effectiveness of the approach also in the case of uncertain conewise linear systems

on the search of more stable second order lattice boltzmann schemes in confined flows the von neumann linear analysis restricted by a heuristic selection of wave number vectors was applied to the search of explicit lattice boltzmann schemes which exhibit more stability than existing methods the relative stability of the family members of quasi incompressible collision kernels for the navier stokes equations in confined flows was analyzed the linear stability analysis was simplified by assuming a uniform velocity level over the whole domain where only the wave numbers of the first harmonic normal to the flow direction were permitted a singular equilibrium function that maximizes the critical velocity level was identified which was afterwards tested in particular cases of confined flows of interest validating the resulting procedure

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

brief paper a unified dissipativity approach for stability analysis of piecewise smooth systems the main objective of this paper is to present a unified dissipativity approach for stability analysis of piecewise smooth pws systems with continuous and discontinuous vector fields the filippov definition is considered for the solution of these systems using the concept of generalized gradients for nonsmooth functions sufficient conditions for the stability of a pws system are formulated based on lyapunov theory the importance of the proposed approach is that it does not need any a priori information about attractive sliding modes on switching surfaces which is in general difficult to obtain a section on application of the main results to piecewise affine pwa systems followed by a section with extensive examples clearly show the usefulness of the proposed unified methodology in particular we present an example with a stable sliding mode where the proposed method works and previously suggested methods fail

trajectory tracking control of bimodal piecewise affine systems this paper deals with a trajectory tracking problem for a class of bimodal piecewise affine systems which is inherently difficult because of the discontinuous changes of their vector fields first we introduce an error variable and an error system as a generalization of the tracking error and its system as an error variable a function switched by the mode of a piecewise affine system is adopted to overcome the inherent difficulty in trajectory tracking control of piecewise affine systems next we design a tracking controller which stabilizes the error system using a lyapunov like function which can be applied to systems including state jumps furthermore the feasibility condition of tracking for siso piecewise linear systems is simplified finally a numerical example is given to illustrate the effectiveness of the proposed method

a filtered cumulant lattice boltzmann method for violent two phase flows abstract the lattice boltzmann method lbm has been successfully applied to simulate various two phase flow problems such as rayleigh taylor instability rising bubble and droplet dynamics however the method known as two phase lbm faces difficulty in simulating violent two phase flow problems such as dam breaking and liquid jet breakup where the density ratio and reynolds number are high and there are rapid and complex topological changes in this paper we address the problem by using a filtered cumulant lbm the incompressible two phase flow equations are solved by using a velocity based formulation of two phase lbm with a cumulant collision model to stably simulate problems with high density ratio and reynolds number there is no pressure iteration in this formulation and we can keep the simplicity of the cumulant model to further enhance the stability in violent flows a second order filter is applied on the velocity field which can be turned off for non violent flows for interface capturing a conservative phase field lbm which guarantees the mass conservation is employed the proposed method is first validated using five non violent flow problems and the results are in good agreements with experimental and computational references the proposed method is then employed to solve three violent flow problems and the results are in qualitatively good agreements with experimental and computational references the proposed method is more diffusive than the unfiltered model but is stable for all problems simulated in this paper these results can be used as a preliminary study on violent two phase flow simulation using two phase lbm

input to state stability and interconnections of discontinuous dynamical systems in this paper we will extend the input to state stability iss framework to continuous time discontinuous dynamical systems dds adopting piecewise smooth iss lyapunov functions the main motivation for investigating piecewise smooth iss lyapunov functions is the success of piecewise smooth lyapunov functions in the stability analysis of hybrid systems this paper proposes an extension of the well known filippov s solution concept that is appropriate for open systems so as to allow interconnections of dds it is proven that the existence of a piecewise smooth iss lyapunov function for a dds implies iss in addition a small gain iss interconnection theorem is derived for two dds that both admit a piecewise smooth iss lyapunov function this result is constructive in the sense that an explicit iss lyapunov function for the interconnected system is given it is shown how these results can be applied to construct piecewise quadratic iss lyapunov functions for piecewise linear systems including sliding motions via linear matrix inequalities

a general class of commutative filters for les in complex geometries a class of filters for large eddy simulations of turbulent inhomogeneous flows is presented a general set of rules for constructing discrete filters in complex geometry is given and examples of such filters are presented with these filters the commutation error between numerical differentiation and filtering can be made arbitrarily small allowing for derivation of a consistent set of equations for the large scale field the application of such filters for explicit filtering in large eddy simulations and the issue of boundary conditions for the filtered field are also discussed

investigation of stability and hydrodynamics of different lattice boltzmann models stability and hydrodynamic behaviors of different lattice boltzmann models including the lattice boltzmann equation lbe the differential lattice boltzmann equation dlbe the interpolation supplemented lattice boltzmann method islbm and the taylor series expansion and least square based lattice boltzmann method tllbm are studied in detail our work is based on the von neumann linearized stability analysis under a uniform flow condition the local stability and hydrodynamic dissipation behaviors are studied by solving the evolution operator of the linearized lattice boltzmann equations numerically our investigation shows that the lbe schemes with interpolations such as dlbe islbm and tllbm improve the numerical stability by increasing hyper viscosities at large wave numbers small scales it was found that these interpolated lbe schemes with the upwind interpolations are more stable than those with central interpolations because of much larger hyper viscosities

on convergence properties of piecewise affine systems in this paper convergence properties of piecewise affine pwa systems are studied in general a system is called convergent if all its solutions converge to some bounded globally asymptotically stable steady state solution the notions of exponential uniform and quadratic convergence are introduced and studied it is shown that for non linear systems with discontinuous right hand sides quadratic convergence i e convergence with a quadratic lyapunov function implies exponential convergence for pwa systems with continuous right hand sides it is shown that quadratic convergence is equivalent to the existence of a common quadratic lyapunov function for the linear parts of the system dynamics in every mode for discontinuous bimodal pwa systems it is proved that quadratic convergence is equivalent to the requirements that the system has some special structure and that certain passivity like condition is satisfied for a general multimodal pwa system these conditions become sufficient for quadratic convergence an example illustrating the application of the obtained results to a mechanical system with a one sided restoring characteristic which is equivalent to an electric circuit with a switching capacitor is provided the obtained results facilitate bifurcation analysis of pwa systems excited by periodic inputs substantiate numerical methods for computing the corresponding periodic responses and help in controller design for pwa systems

stability and stabilization of the lattice boltzmann method we revisit the classical stability versus accuracy dilemma for the lattice boltzmann methods lbm our goal is a stable method of second order accuracy for fluid dynamics based on the lattice bhatnager gross krook method lbgk the lbgk scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution in this framework the stability and accuracy analysis are more natural we find the necessary and sufficient conditions for second order accurate fluid dynamics modeling in particular it is proven that in order to guarantee second order accuracy the distribution should belong to a distinguished surface the invariant film up to second order in the time step this surface is the trajectory of the quasi equilibrium distribution surface under free flight the main instability mechanisms are identified the simplest recipes for stabilization add no artificial dissipation up to second order and provide second order accuracy of the method two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup demonstration of the proposed stable lbgk schemes are provided by the numerical simulation of a one dimensional 1d shock tube and the unsteady 2d flow around a square cylinder up to reynolds number mathrm re ensuremath sim 20 phantom rule 0 2em 0ex 000

direct and large eddy simulation of turbulent flows on composite multi resolution grids by the lattice boltzmann method in order to properly address the simulation of complex weakly compressible turbulent flows the lattice boltzmann method originally designed for uniform structured grids needs to be extended to composite multi domain grids displaying various levels of spatial resolution therefore physical conditions must be specified to determine the mapping of statistical information about the populations of moving particles at the interface between two domains of different resolutions quite simply in terms of the probability distributions of the underlying discrete velocity boltzmann equation namely the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions whereas the discontinuity of the rate of strain tensor is ensured by applying a spatial transformation to the collision term of the discrete velocity boltzmann equation the latter condition allows us to explicitly account for the subgrid scale modeling in the treatment of resolution changes test computations of a turbulent plane channel flow have been carried out the lattice boltzmann scheme relies on the standard d3q19 lattice in a cell vertex representation and uses the bgk approximation for the collision term a shear improved variant of the smagorinsky viscosity is used to account for possible subgrid scale dynamics in a quasi direct numerical simulation at re t 180 with two levels of grid resolution the results are found in excellent agreement with reference data obtained by a high resolution pseudo spectral simulation in a large eddy simulation les at re t 395 with three levels of grid resolution the results compare reasonably well with high resolution reference data the accuracy is improved in comparison with a standard finite volume les performed with the same subgrid scale viscosity and comparable grid resolution by combining the simplicity and physical relevance of the shear improved smagorinsky model and the computational efficiency of the lattice boltzmann scheme here extended to composite multi resolution grids we believe that our proposal offers a high potential for the simulation of complex turbulent flows

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

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

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

an arbitrary lagrangian eulerian approach for the simulation of immersed moving solids with lattice boltzmann method the flow structure interactions streaming from the motion of an immersed solid body are investigated through an arbitrary lagrangian eulerian ale approach applied to the lattice boltzmann method lbm the method is based on the use of a moving grid to describe the flow around the solid body while the physical domain is resolved by the use of an eulerian frame fixed grid the moving grid displacements follows the same moving law of the body and its shape does not change during the simulation the communication between the moving grid and the fixed grid is performed at the beginning of each time step through interpolation the ale lbm approach has been derived from the discretized boltzmann equation by a chapman enskog expansion procedure the equivalence of the proposed method with the navier stokes equations for a weakly compressible athermal flow being recovered numerical simulations of academical test cases have been performed in order to assess the method and to investigate the sensitivity of the error to the simulation parameters three different test cases have been considered in order to perform a robust assessment of the ale lbm approach more specifically the uniform flow the poiseuille flow and the plane wave test cases have been studied and the limits of application of the approach have been defined and discussed finally the case of a rotating two dimensional square cylinder immersed in a poiseuille flow re 80 has been numerically investigated the results confirm that the ale lbm approach is able to correctly represent the physical flow features and in particular the transition zone between the two grids used is smooth and continuous a sign that the error due to the interpolation process is bounded and does not diverge in time

a family of low dispersive and low dissipative explicit schemes for flow and noise computations explicit numerical methods for spatial derivation filtering and time integration are proposed they are developed with the aim of computing flow and noise with high accuracy and fidelity all the methods are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to k x 2 corresponding to four points per wavelength they are shown to be more accurate and also more efficient numerically than most of the standard explicit high order methods for uniform and slowly non uniform grids two problems involving long range sound propagation are resolved to illustrate their respective precisions remarks about their practical applications are then made especially about the connection with the boundary conditions finally their relevance for the simulation of turbulent flows is emphasized

adaptive filtering for the lattice boltzmann method in this study a new selective filtering technique is proposed for the lattice boltzmann method this technique is based on an adaptive implementation of the selective filter coefficient the proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur different parameters are tested on 2d test cases sensitive to numerical stability and on a 3d decaying taylorgreen vortex the results are compared to the classical static filtering technique and to the use of a standard subgrid scale model and give significant improvements in particular for low order filter consistent with the lbm stencil

design of stabilizing switching laws for mixed switched affine systems this technical note presents stability analysis and stabilization for a general class of switched systems characterized by nonlinear functions the proposed approach is composed of approximating the switched nonlinear system with a switched affine system that has a mixture of controlled and autonomous switching behavior utilizing a joint polyhedral partitioning approach a stabilizing switching law based on quadratic lyapunov functions and with considering the autonomous switching between polyhedral regions is proposed to ensure the decrease of the overall lyapunov function two approaches are proposed 1 guarantee continuity of the lyapunov function over boundaries of polyhedral regions and 2 relax the continuity requirement by using additional matrix inequalities the second approach is less conservative but with more variables and matrix inequalities than in the first method with fixing one scalar variable the stabilization conditions will have the form of linear matrix inequalities lmis further the sufficient conditions for stabilizing the original switched nonlinear system using the proposed switching schemes are presented finally through two examples the performance of the proposed stabilization methods is demonstrated

lyapunov stability for piecewise affine systems via cone copositivity cone copositive piecewise quadratic lyapunov functions pwq lfs for the stability analysis of continuous time piecewise affine pwa systems are proposed the state space is assumed to be partitioned into a finite number of convex possibly unbounded polyhedra preliminary conditions on pwq functions for their sign in the polyhedra and continuity over the common boundaries are provided the sign of each quadratic function is studied by means of cone constrained matrix inequalities which are translated into linear matrix inequalities lmis via cone copositivity the continuity is guaranteed by adding equality constraints over the polyhedra intersections an asymptotic stability result for pwa systems is then obtained by finding a continuous pwq lf through the solution of a set of constrained lmis the effectiveness of the proposed approach is shown by analyzing an opinion dynamics model and two saturating control systems