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

acceleration of steady state lattice boltzmann simulations for exterior flows the simulation of a stationary fluid flow past an obstacle by the lattice boltzmann method lbm in two dimensions is discussed the combination of second order expressions for far field boundary conditions and a suitable treatment of the no slip boundary condition at the obstacle surface with the nested grid refinement technique can be applied to the lbm resulting in a highly efficient method for the treatment of exterior flows furthermore via replacing the nested time stepping by local time stepping the resolution process can be substantially accelerated a highly accurate drag coefficient was used to make an error assessment for various no slip boundary conditions imposed on the obstacle surface the analysis showed that the equilibrium method for treating the no slip conditions is superior to halfway bounce back and full way bounce back no slip conditions when the relaxation time ensuremath tau 1 also a ensuremath tau dependence test was made to evaluate the performance of different methods in the treatment of the no slip boundary conditions

on constraints in pole assignment by static feedback abstract a design method based on pole assignment considerations for an nth order linear time invariant single input p output system by means of static constant gain feedback is presented for the case in which the rank p of an output matrix c is less than the number of system states n the constraints in pole assignment are described in the form of linear relationships between the coefficients of the closed loop characteristic polynomial and some open loop system parameters it has been shown that the problem of pole assignment is equivalent to the problem of solving a set of n linear equations with p unknowns in such a way that n p equations are made linearly dependent by proper choice of coefficients of the closed loop characteristic polynomial as a result all n system poles can be shifted to selected locations which satisfy the constraints of particular interest are the design methods for the cases when the number of arbitrarily assigned poles are equal to p and p i

massively parallel algorithms for the lattice boltzmann method on nonuniform grids the lattice boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large scale nonstationary flow simulations reaching up to a trillion 10 12 grid nodes additionally grid refinement can lead to substantial savings in memory and compute time these savings however come at the cost of much more complex data structures and algorithms in particular the interface between subdomains with different grid sizes must receive special treatment in this article we present parallel algorithms distributed data structures and communication routines that are implemented in the software framework walberla in order to support large scale massively parallel lattice boltzmann based simulations on nonuniform grids additionally we evaluate the performance of our approach on two current petascale supercomputers on an ibm blue gene q system the largest weak scaling benchmarks with refined grids are executed with almost 2 mi

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

a simplified finite volume lattice boltzmann method for simulations of fluid flows from laminar to turbulent regime part i numerical framework and its application to laminar flow simulation abstract in this paper an unstructured grid based finite volume lattice boltzmann method fvlbm that can be used for the simulation of incompressible laminar flows is presented and studied in detail this method is derived from a simple modification of the cell vertex unstructured grid based fvlbm proposed by stiebler et al 2006 compared with other complex flux reconstruction methods the present scheme has a low computational cost and can also achieve second order spatial accuracy furthermore depending on the use of the different temporal discretization schemes the temporal accuracy can be adjusted for both steady and unsteady flows besides some comparisons of the computational cost and accuracy with another fvlbm scheme are also presented meanwhile different boundary conditions are illustrated that are easy to implement on complex geometries to validate the present method four cases are carried out including a couette flow driven by one plate for an accuracy test flow in a square cavity flow around a single circular cylinder and a more complex flow around double circular cylinders numerical experiments show that the present scheme can simulate steady and unsteady flows at relatively high reynolds number with relatively few grid cells thus demonstrating the good capability of the present method

inhomogeneous dirichlet boundary value problem for one dimensional nonlinear schrodinger equations via factorization techniques abstract we consider the inhomogeneous dirichlet boundary value problem for the cubic nonlinear schrodinger equations on the half line we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to equations by using the classical energy method and factorization techniques

acceleration of lattice bgk schemes with grid refinement abstract the lbgk method with local grid refinement has been shown to be an efficient and accurate tool for the simulation of incompressible viscous flows over complex geometries in the present study further improvement of this concept is proposed enabling the use of smaller amount of time steps on refined grids without impairing the spatial or temporal accuracy this extension of the lbgk method has been proved by analytical and numerical investigations the gain in computational time was found to be significant

asymptotic analysis of lattice boltzmann boundary conditions in this article we use a general method for the analysis of finite difference schemes to investigate lattice boltzmann algorithms for navier stokes problems with dirichlet boundary conditions several link based boundary conditions for commonly used lattice boltzmann bgk models are considered with our method the accuracy of the algorithms can be exactly predicted moreover the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity the analysis is applicable to general geometries and instationary flows

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

an improved bounce back scheme for complex boundary conditions in lattice boltzmann method in recent years the lattice boltzmann method lbm has been widely adopted to simulate various fluid systems and the boundary treatment has been an active topic during the lbm development in this paper we present a novel approach to improve the bounce back boundary treatment for moving surfaces with arbitrary configurations we follow the framework originally proposed by ladd a j c ladd numerical simulations of particulate suspensions via a discretized boltzman equation part 1 theoretical foundation journal of fluid mechanics 271 1994 285 309 however the adjustment in the density distribution during the bouncing back process at the boundary is calculated using the midpoint velocity inter extrapolated from the boundary and fluid velocities instead of the real boundary velocity in the ladd method this modification ensures that the bouncing back process and the density distribution adjustment both take place at a same location the midpoint of a boundary lattice link and thus removes the discrepancy of bouncing back at the midpoint but density distribution adjustment at the boundary point in the original ladd method when compared with other existing boundary models this method involves a simpler algorithm and exhibits a comparable or even better accuracy in describing flow field and flow structure interaction as demonstrated by several test simulations therefore this boundary method could be considered as a competitive alternative for boundary treatment in lbm simulations especially for particulate and porous flows with large fluid solid interfacial areas

a mass conserving boundary condition for the lattice boltzmann equation method in lattice boltzmann lb simulations the widely used wall boundary conditions bcs proposed by filipova and hanel fh and mei luo and shyy mls result in constant mass leakage in certain circumstances in this paper we have analyzed the source of the leakage based on this analysis we propose a second order accurate mass conserving wall bc in our bc the distribution function at a wall node is decomposed into its equilibrium and non equilibrium parts the mass conservation is guaranteed by enforcing a mass conserving rule in the construction of the fictitious equilibrium distribution part we have shown through several benchmark test problems involving steady and unsteady flows that our new bc not only eliminates the constant mass leakage but also has many other advantages over the fh and mls bcs

inhomogeneous neumann boundary value problem for one dimensional nonlinear schrodinger equations via factorization techniques we consider the inhomogeneous neumann boundary value problem for the nonlinear schrodinger equations on the half line we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques we consider the inhomogeneous neumann boundary value problem for the nonlinear schrodinger equations on the half line we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques

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

hybrid simulation combining two space time discretization of the discrete velocity boltzmann equation abstract despite the efficiency and low dissipation of the stream collide scheme of the discrete velocity boltzmann equation which is nowadays implemented in many lattice boltzmann solvers a major drawback exists over alternative discretization schemes i e finite volume or finite difference that is the limitation to cartesian uniform grids in this paper an algorithm is presented that combines the positive features of each scheme in a hybrid lattice boltzmann method in particular the node based streaming of the distribution functions is coupled with a second order finite volume discretization of the advection term of the boltzmann equation under the bhatnagar gross krook approximation the algorithm is established on a multi domain configuration with the individual schemes being solved on separate sub domains and connected by an overlapping interface of at least 2 grid cells a critical parameter in the coupling is the cfl number equal to unity which is imposed by the stream collide algorithm nevertheless a semi implicit treatment of the collision term in the finite volume formulation allows us to obtain a stable solution for this condition the algorithm is validated in the scope of three different test cases on a 2d periodic mesh it is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved the overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms finally we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the fv domain

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

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

a new sufficient condition for generic pole assignment by output feedback we show that for strictly proper systems with m outputs l inputs m geq l mcmillan degree n and controllability indexes lambda 1 geq lambda 2 geq geq lambda 1 0 one can in the generic case arbitrarily assign min q 1 m q b l 1 n q closed loop poles with a proper order q compensator this represents an improvement over results reported earlier in the literature

galilean invariance study on different lattice boltzmann fluid solid interface approaches for vortex induced vibrations abstract the present work compares fluid solid interface approaches for the lattice boltzmann method lbm to study vortex induced vibrations viv two classes of fluid solid interface approaches namely the partially saturated methods psm noble and torczynski 1998 holdych 2003 krause et al 2017 trunk et al 2018 and moving boundary methods mbm bouzidi et al 2001 lallemand and luo 2003 yu et al 2003 ginzburg et al 2008 and filippova and hanel 1998 mei et al 1999 2000 are investigated first the galilean invariance of aerodynamic coefficients obtained by each scheme is examined the bhatnagar gross krook bgk lbm is utilized to simulate an eccentrically positioned cylinder in a transient couette flow in addition various refill methods for mbm and volume approximation techniques for psm are tested besides different error norms and a grid independence study of each method the galilean invariance violating frequencies are studied as well these error calculations are used to choose a representative for each class to simulate vortex shedding the viv test case describes a transverse oscillation of a cylinder in a freestream at a reynolds number of 100 both free and forced cylinder oscillations are examined to study known phenomena as lock in and lock out zones the results of mbm and psm are in good agreement to literature values and prove the suitability for viv simulations

grid refinement in lattice boltzmann methods based on volumetric formulation abstract we describe a general algorithmic concept for grid refinement in the lattice boltzmann method unlike most of the previously known approaches the present one is based on volumetric formulation so that conservation laws are exactly guaranteed

a new differential lattice boltzmann equation and its application to simulate incompressible flows on non uniform grids a new differential lattice boltzmann equation lbe is presented in this work which is derived from the standard lbe by using taylor series expansion only in spatial direction with truncation to the second order derivatives the obtained differential equation is not a wave like equation when a uniform grid is used the new differential lbe can be exactly reduced to the standard lbe the new differential lbe can be applied to solve irregular problems with the help of coordinate transformation the present scheme inherits the merits of the standard lbe the 2 d driven cavity flow is chosen as a test case to validate the present method favorable results are obtained and indicate that the present scheme has good prospects in practical applications

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

phase field lattice kinetic scheme for the numerical simulation of dendritic growth a phase field lattice kinetic model is presented for the numerical simulation of the dendritic growth of a pure crystal in the presence of thermal transport a finite difference scheme for the phase field is combined with an explicit lattice kinetic scheme for the temperature field the resulting scheme is advanced in time with an adaptive time marching procedure which permits us to achieve long simulation times with larger time steps than explicit finite difference and previous kinetic methods the method is demonstrated for the case of dendritic growth of a single crystal over a wide range of stefan and capillarity numbers

on the application of the lattice boltzmann method to the investigation of glottal flow the production of voice is directly related to the vibration of the vocal folds which is generated by the interaction between the glottal flow and the tissue of the vocal folds in the current study the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations the numerical investigation is based on the lattice boltzmann method lbm which is an alternative approach within computational fluid dynamics compared to the traditional navier stokes computational fluid dynamics methods the lbm is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator the multiple relaxation time model was used to improve the numerical stability the results obtained with lbm were compared to the results provided by a traditional navier stokes solver and experimental data it was shown that lbm results are satisfactory for all the investigated cases

lattice boltzmann model for exterior flows with an annealing preconditioning method in this paper we propose a highly efficient and stable lattice boltzmann method for solving low reynolds number exterior flows using a preconditioning technique the present method is based on replacing the constant preconditioning parameter gamma within uniform grids guo phys rev e 70 066706 2004 by a space and time dependent one in a nested mesh refined domain to do this for the transition from a fine to the neighboring coarser grid gamma has been divided by a factor k which is large initially and anneals stepwise to a small value after some iterations with this technique more than one order of magnitude larger convergence rate can be achieved and several orders of magnitude larger system size can be treated

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

a remark on the blowing up of solutions to the cauchy problem for nonlinear schrodinger equations on considere des solutions de iu t u u p 1 u u o u 0 ou x appartient a un domaine lisse cr n et on demontre que sous de bonnes conditions sur p n et u 0 h 2 h 0 1 u t l 2 eclate en un temps fini

discrete unified gas kinetic scheme for all knudsen number flows ii thermal compressible case this paper is a continuation of our work on the development of multiscale numerical scheme from low speed isothermal flow to compressible flows at high mach numbers in our earlier work z l guo et al phys rev e 88 033305 2013 a discrete unified gas kinetic scheme dugks was developed for low speed flows in which the mach number is small so that the flow is nearly incompressible in the current work we extend the scheme to compressible flows with the inclusion of thermal effect and shock discontinuity based on the gas kinetic shakhov model this method is an explicit finite volume scheme with the coupling of particle transport and collision in the flux evaluation at a cell interface as a result the time step of the method is not limited by the particle collision time with the variation of the ratio between the time step and particle collision time the scheme is an asymptotic preserving ap method where both the chapman enskog expansion for the navier stokes solution in the continuum regime and the free transport mechanism in the rarefied limit can be precisely recovered with a second order accuracy in both space and time the dugks is an idealized multiscale method for all knudsen number flow simulations a number of numerical tests including the shock structure problem the sod tube problem in a whole range of degree of rarefaction and the two dimensional riemann problem in both continuum and rarefied regimes are performed to validate the scheme comparisons with the results of direct simulation monte carlo dsmc and other benchmark data demonstrate that the dugks is a reliable and efficient method for multiscale flow problems

achieving robust stability by sensing additional system outputs in this note we investigate the problem of robust stability in the context of linear time invariant multivariable systems which are affected by structured parametric type uncertainty we demonstrate that by generating additional outputs which are then made available for feedback and thus using sensors for more measurements robust closed loop system stability can be achieved we state and prove results that suggest when this is possible and show how it can be done

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

an interpretation and derivation of the lattice boltzmann method using strang splitting the lattice boltzmann space time discretisation as usually derived from integration along characteristics is shown to correspond to a strang splitting between decoupled streaming and collision steps strang splitting offers a second order accurate approximation to evolution under the combination of two non commuting operators here identified with the streaming and collision terms in the discrete boltzmann partial differential equation strang splitting achieves second order accuracy through a symmetric decomposition in which one operator is applied twice for half timesteps and the other operator is applied once for a full timestep we show that a natural definition of a half timestep of collisions leads to the same change of variables that was previously introduced using different reasoning to obtain a second order accurate and explicit scheme from an integration of the discrete boltzmann equation along characteristics this approach extends easily to include general matrix collision operators and also body forces finally we show that the validity of the lattice boltzmann discretisation for grid scale reynolds numbers larger than unity depends crucially on the use of a crank nicolson approximation to discretise the collision operator replacing this approximation with the readily available exact solution for collisions uncoupled from streaming leads to a scheme that becomes much too diffusive due to the splitting error unless the grid scale reynolds number remains well below unity

comparative study of the lattice boltzmann models for allen cahn and cahn hilliard equations in this paper a comparative study of the lattice boltzmann lb models for the allen cahn a c and cahn hilliard c h equations is conducted to this end a new lb model for the a c equation is first proposed where the equilibrium distribution function and the source term distribution function are delicately designed to recover the a c equation correctly the gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the a c equation and the recently developed lb model h liang et al phys rev e 89 053320 2014 for the c h equation in terms of tracking the interface of two phase flow the results show that the present lb model for the a c equation is more accurate and more stable and also has a second order convergence rate in space while the convergence rate of the previous lb model for the c h equation is only about 1 5

boundary conditions for lattice boltzmann simulations with complex geometry flows boundary conditions of lattice boltzmann method to simulate flows embedded with a solid object is proposed the closest nodes adjacent to the boundary in the fluid domain are used as boundary nodes of the flow domain the fluid velocity of the boundary node is obtained by linear interpolation between the velocities of the solid object and the second fluid node further away then distribution functions originating from the solid domain at the boundary nodes are modified using known distribution functions and correctors to satisfy the momentum this boundary condition is an extended form of a method proposed by hou et al c f hou c chang c a lin consistent boundary conditions for 2d and 3d lattice boltzmann simulations submitted for publication for plane wall and regular geometry the technique is examined by simulating decaying vortex transient flow induced by an abruptly rotating ring and flow over an asymmetrically placed cylinder numerical simulations indicate that this method is second order accurate and all the numerical results are compatible with the benchmark solutions

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

proteus a coupled iterative force correction immersed boundary multi domain cascaded lattice boltzmann solver abstract most realistic fluid flow problems are characterized by high reynolds numbers and complex boundaries over the last ten years immersed boundary methods that are able to cope with realistic geometries have been applied to lattice boltzmann lb methods these methods however have normally been applied to low reynolds number problems here we present a novel coupling between an iterative force correction immersed boundary zhang et al 2016 and a multi domain cascaded lb method the iterative force correction immersed boundary method has been selected due to the improved accuracy of the computation while the cascaded lb formulation is used due to its superior stability at high reynolds numbers the coupling is shown to improve both the stability and numerical accuracy of the solution the resulting solver has been applied to viscous flow up to a reynolds number of 100000 passed a naca 0012 airfoil at a 10 degree angle of attack good agreement with results obtained using a body fitted navier stokes solver has been obtained the formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries

on solutions of the initial value problem for the nonlinear schrodinger equations in one space dimension t 0 xe has a regularizing property that the solutions become smooth instantly for t 0 even if their initial data are not smooth for example in l n our aim of this paper is to show that the nls equation 1 1 1 2 has a similar regularizing effect more precisely all solutions of finite energy to 1 1 1 2 are smooth for tq 0 provided the initial functions in hi n or in

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

smoothing effect for nonlinear schrodinger equations in exterior domains abstract we consider the following nonlinear schrodinger equations in exterior domains i t u 1 2 u u 2 u t x r x d u 0 x x x d u t x 0 or u t6v 0 t x r x d where d x rn x r d r 0 and v denotes the outward normal unit vector at x d in this paper we prove the radially symmetric solutions of have a smoothing property

finite volume scheme for the lattice boltzmann method on unstructured meshes department of mathematics and statistics bowling green state university bowling green ohio 43403 received 9 september 1998 a nite volume scheme for the lattice boltzmann method is developed for unstructured triangular meshes intwo dimensions the accuracy of this new scheme is demonstrated by comparing the numerical results with theexact solutions to the navier stokes equations for taylor vortex ow shear ow between two parallel plates shear ow between two rotating cylinders and poiseuille ow the agreement between the numerical andanalytical results is very good for each of these tests s1063 651x 99 07804 6 pacs number s 47 10 1g 47 11 1j 05 20 ddi introduction

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

on solutions of the initial value problem for the nonlinear schrodinger equations on considere le probleme aux valeurs initiales pour l equation de schrodinger non lineaire de la forme iu t u f u 2 u t x r r n u 0 x x x r n on etudie la regularite des solutions quand les fonctions initiales ne sont pas regulieres

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

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

generic pole assignment using dynamic output feedback a method is presented for assigning min n q q 1 m q closed loop poles of an nth order linear time invariant system m outputs l inputs m l using a linear time invariant proper output feedback compensator of order q it is also shown how the locations of remaining unassigned poles could be controlled the compensator parameters are obtained by solving a linear matrix equation this research has been supported by nsf under grant ecs 8006896 and partially supported by afosr under grant afosr 80 0155

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

discrete unified gas kinetic scheme for all knudsen number flows low speed isothermal case based on the boltzmann bgk bhatnagar gross krook equation in this paper a discrete unified gas kinetic scheme dugks is developed for low speed isothermal flows the dugks is a finite volume scheme with the discretization of particle velocity space after the introduction of two auxiliary distribution functions with the inclusion of collision effect the dugks becomes a fully explicit scheme for the update of distribution function furthermore the scheme is an asymptotic preserving method where the time step is only determined by the courant friedricks lewy condition in the continuum limit numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current dugks the comparison between the dugks and the well defined lattice boltzmann equation method d2q9 is presented as well

lattice boltzmann model for dense suspended particles based on improved bounce back method abstract we develop an efficient and accurate lattice boltzmann model for dense suspended particles based on improved bounce back it is difficult to model flow with dense suspended particles because there are not enough fluid nodes surrounding each particle to apply many existing algorithms and mass leakage due to interpolated bounce back is more significant when dealing with many particles we propose a new curved boundary treatment and fresh node initialization scheme both of which are still effective when two particles get close to contact we further propose a method to calculate the hydrodynamic interaction accurately when two solid particles get very close to each other without leaving any fluid node between their surfaces an easy redistributing method is developed to fix mass leakage resulting from curved boundaries to make the algorithm more stable we combine implicit particle velocity updating and galilean invariant momentum exchange we validate the second order accuracy of this curved boundary method by channel flow and other simulations are carried out to show that this model is more accurate and stable in dealing with particle particle interaction finally simulations of magnetic particle flows are conducted to show that this model is suitable for dense suspended particles

multidimensional inhomogeneous mixed initial boundary value problem for the nonlinear schrodinger equation abstract we consider the inhomogeneous mixed initial boundary value problem for the nonlinear multidimensional schrodinger equation formulated on upper right quarter plane we study traditionally important problems of the theory of nonlinear partial differential equations such as global in time existence of solutions to the initial boundary value problem and the asymptotic behavior of solutions for large time also we are interested in the study of the influence of the mixta boundary data on the asymptotic behavior of solutions our approach to get well posedness of nonlinear problems is based on the studying a linear theory and then using the fixed point argument to get a linear theory for the multidimensional model we propose general method based on laplace approach and theory cauchy type integral equations to get smooth solutions in l we modify a method based on the factorization for the free schrodinger evolution group the advantage of our approach is that it can also be applied to non integrable equations and arbitrary boundary conditions this approach is new and it is not standard we believe that the results of this paper could be applicable to study a wide class of dissipative multidimensional nonlinear equations by the use of techniques of nonlinear analysis

the lattice boltzmann equation on irregular lattices a general framework to extend the lattice boltzmann equation to arbitrary lattice geometries is presented and numerically demonstrated for the case of a two dimensional poiseuille flow the new scheme considerably extends the range of applicability of the boltzmann method to problems requiring the use of nonuniform grids

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

one point boundary condition for the lattice boltzmann method we propose a correction to the bounce back boundary condition for lattice boltzmann algorithms which improves the accuracy of pressure from zero to first order and the accuracy of velocity from first to second order compared to interpolation based corrections our method has the advantage of being completely local in fact methods using interpolation face difficulties at boundary points where not enough neighboring nodes are available we show that a combination with our method offers a natural solution to this problem

inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity on the upper half plane abstract we consider the inhomogeneous dirichlet boundary value problem for nonlinear schrodinger equations with a power nonlinearity in the upper half plane we present sufficient conditions of initial and boundary data which ensure asymptotic behavior of small solutions to the problem by using the classical energy method and factorization techniques

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

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

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

boundary conditions for thermal lattice boltzmann equation method we propose a thermal boundary condition treatment based on the bounce back idea and interpolation of the distribution functions for both the dirichlet and neumann normal derivative conditions in the thermal lattice boltzmann equation tlbe method the coefficients for the distribution functions involved are determined to satisfy the dirichlet or neumann condition with second order accuracy for the dirichlet condition there is an adjustable parameter in the treatment and three particular schemes are selected for demonstration while for the neumann condition the second order accurate scheme is unique when applied to inclined or curved boundaries the dirichlet condition treatment can be directly used while the neumann condition given in the normal direction of the boundary should be converted into derivative conditions in the discrete velocity directions of the tlbe model a spatially coupled formula relating the boundary temperature boundary normal heat flux and the distribution functions near the boundary is thus derived for the neumann problems on curved boundaries the applicability and accuracy of the present boundary treatments are examined with several numerical tests for which analytical solutions are available including the 2 dimensional 2 d steady state channel flow the 1 d transient heat conduction in an inclined semi infinite solid the 2 d steady state and transient heat conduction inside a circle and the 3 d steady state circular pipe flow while the dirichlet condition treatment leads to second order accuracy for the temperature field it only gives a first order accurate boundary heat flux because of the irregularity of the cuts by the curved boundary with the lattices with the neumann condition on the curved boundary the accuracy for the temperature field obtained is first order when the tangential temperature gradient on the boundary is decoupled second order convergence of the temperature field can be obtained with neumann conditions

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

a note on robust stabilization for systems with parameters we consider the problem of stabilizing a linear time invariant multivariable system whose transfer function admits a factorization which contains parametric type uncertainties the parameters are known to take values in some region a we first give a sufficient condition for robust stability when a proper feedback compensator is used here it is important to note that no assumption is made about the number of unstable plant poles following this we focus attention on how to compute an appropriate robustly stabilizing compensator this is done in a two step procedure initially the solutions of a diophantine equation generate a class of proper compensators each of which stabilizes the nominal closed loop system this is followed by a nyquist theorem inspired minimization which yields the final choice an illustrative physical example is given the compensator thus constructed guarantees stability over u a discussion about how to compute the size of the attainable robust stability region u is also included

algebraic theory for robust stability of interconnected systems necessary and sufficient conditions we consider an interconnected system s o made of linear mulrivariable subsystems which are specified by matrix fractions with elements in a ring of stable scalar transfer functions h given that the k th subsystem is perturbed from g k n rk d k 1 to tilde g k n rk delta n rk d k delta d k 1 and that the system s o is h stable we derive a computationally efficient necessary and sufficient condition for the h stability of the perturbed system these fractional perturbations are more general than the conventional additive and multiplicative perturbations the result is generalized to handle simultaneous perturbations of two or more subsystems

arbitrary adaptive pole placement for linear multivariable systems this paper presents a methodology for adaptively assigning the closed loop poles of either continuous or discrete time linear mnltivariable systems the scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified rather the control parameters and an equivalent plant parameterization are simultaneously estimated from input output data using linear parameter estimation procedures implementation of the scheme requires only knowledge of the system controllability indexes and an upper bound on the observabilily index

some generic invariant factor assignment results using dynamic output feedback abstract working with input output transfer functions in the frequency domain and exploiting a formulation involving generalized sylvester resultants we are able to derive necessary and sufficient conditions for generic invariant factor assignment in several cases using proper dynamic output feedback compensators

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

volumetric formulation of the lattice boltzmann method for fluid dynamics basic concept a lattice boltzmann algorithm based on a volumetric representation is formulated for achieving properties consistent with the standard form at finer resolution in contrast to pointwise interpolation schemes this approach can be applied to arbitrary meshes without compromising exact conservation or equilibrium properties

flow simulation around cambered airfoil by using conformal mapping and intermediate domain in lattice boltzmann method in this paper the developed interpolation lattice boltzmann method is used for simulation of unsteady fluid flow it combines the desirable features of the lattice boltzmann and the joukowski transformation methods this approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system simulation of unsteady flow around a cambered airfoil in a non uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long term periodic flow phenomena the developed solver is also coupled with a fast adaptive grid generator in addition the new approach retains all the advantages of the standard lattice boltzmann method the strouhal number the pressure the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations numerical studies for various test cases illustrate the strength of this new approach

a multivariable self tuning controller based on pole placement design abstract the design problem of controller for discrete time linear multi input output systems is discussed the basic idea is to use pole placement approach a new pole placement tracking problem formulation and its solution is given the design of controller requires no a priori information either about stability or minimum phase of controlled plants the designed controller consists of a feedback part a feedforward part and a new precompensator and is suitable for self tuning control of continuous systems with differing and unknown dead times in each path the controller can have integral action the number of outputs can be different from the number of inputs of the controlled system a reference vector sequence and an effect of the initial state on the system output are given as a left matrix fraction the self tuning algorithm is based on identification of explicit plant model the self tuning algorithm is illustrated by examples

theory and applications of an alternative lattice boltzmann grid refinement algorithm this contribution proposes an alternative lattice boltzmann grid refinement algorithm that overcomes the drawbacks that plague existing approaches we demonstrate that this algorithm is accurate and applicable for all values of the relaxation time we also show that this algorithm can significantly speed up the flow settlement process by using a hierarchy of grid levels the stationary regime can be approached up to a thousand times faster than with a single grid resolution

lattice boltzmann method on unstructured grids further developments we discuss further developments of the finite volume lattice boltzmann formulation on unstructured grids it is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size a theoretical argument of plausibility for such a property is presented in addition a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows

lattice boltzmann method on curvilinear coordinates system using an interpolation based strategy the lattice boltzmann method is extended to apply to general curvilinear coordinate systems as an example a cylindrical coordinate system is used to simulate two dimensional flow around a circular cylinder numerical simulations are carried out for impulsive initial conditions with reynolds numbers up to 104 the agreement of our results with previous computational and experimental results is satisfactory compared with previous lattice boltzmann simulations of the same problem our new approach greatly enhances the computational efficiency

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

a consistent grid coupling method for lattice boltzmann schemes a method of coupling grids of different mesh size is developed for classical lattice boltzmann lb algorithms on uniform grids the approach is based on an asymptotic analysis revealing suitable quantities equalized along the grid interfaces for exchanging information between the subgrids in contrast to other couplings the method works without overlap zones moreover the grid velocity mach number is not kept constant as the time step depends not linearly but quadratically on the grid spacing to illustrate the basic idea we use a simple lb algorithm solving the advection diffusion equation the proposed grid coupling is validated by numerical convergence studies indicating that the coupling does not affect the second order convergence behavior of the lb algorithm which is observed on uniform grids in order to demonstrate its principal applicability to other lb models the coupling is generalized to the standard d2p9 model for navier stokes flow and tested numerically as we use analytic tools different from the chapman enskog expansion the theoretical background material is given in two appendices in particular the results of numerical experiments are confirmed with a consistency analysis

numerical simulation of viscous flow over non smooth surfaces the incompressible viscous flow over several non smooth surfaces is simulated numerically by using the lattice boltzmann method a numerical strategy for dealing with a curved boundary with second order accuracy for velocity field is presented the drag evaluation is performed by the momentum exchange method the streamline contours are obtained over surfaces with different shapes including circular concave circular convex triangular concave triangular convex regular sinusoidal wavy and irregular sinusoidal wavy are obtained the flow patterns are discussed in detail the velocity profiles over different kinds of non smooth surfaces are investigated the numerical results show that the lattice boltzmann method is reliable accurate easy to implement and can provide valuable help for some engineering practices

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

an investigation into curved and moving boundary treatments in the lattice boltzmann method curved boundary treatments provide a means of improving the computational accuracy of the conventional stair shaped approximation used in lattice boltzmann lb simulations furthermore curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions at the solid surface this study commences by investigating three conventional interpolating treatments for curved boundaries in lb problems namely the filippova and hanel fh model o filippova d hanel grid refinement for lattice bgk models j comput phys 147 1998 219 228 bouzidi s model m bouzidi m firdaouss p lallemand momentum transfer of a boltzmann lattice fluid with boundaries phys fluids 13 11 2001 3452 3459 and yu s model d yu r mei w shyy a unified boundary treatment in lattice boltzmann method aiaa 2003 0953 new york 2003 previous investigations have indicated that the interpolations would break the mass conservation at the boundaries since the inaccuracy in evaluation of the momentum transfer at boundary leads to a net mass flux based on this reason a concept of the interpolation free treatment for modeling the curved and moving boundary conditions is proposed to overcome the drawback of these interpolation based curved boundary treatments in present study two interpolation free models are then proposed namely on site interpolation free osif and composite interpolation free cpif models these proposed models are initially applied to simulate the flow in the channels containing a stationary square block positioned at various locations along the longitudinal axis the simulations results are then compared with those obtained using the three conventional interpolating treatments the interpolation free models are then applied to the case of moving boundary problems in which a square block and a cylindrical block respectively move with a constant speed along a channel containing stationary flows to test the galilean effect of the proposed cpif model a couette flow past the stationary square cylinder block with the moving top bottom walls is simulated overall the numerical results show that the proposed interpolation free curved treatment models significantly improve the accuracy of the mass flux computation near the solid surface and thus enhance the accuracy of the momentum interaction at the moving boundaries

pole assignment using dynamic output feedback compensators abstract the design of dynamic output feedback compensators for the pole assignment of linear time invariant multivariable systems is considered a systematic procedure is developed for the synthesis of the transfer function matrix of the compensator a certain number of poles can be arbitrarily assigned by the proposed compensator moreover in order to assign more poles using a compensator of the same order as before a new approximate assignment approach based on the least square error algorithm is proposed a numerical example is given to demonstrate the effectiveness of the proposed approaches

dynamically adaptive lattice boltzmann simulation of shallow water flows with the peano framework we present a dynamically adaptive lattice boltzmann lb implementation for solving the shallow water equations swes our implementation extends an existing lb component of the peano framework we revise the modular design with respect to the incorporation of new simulation aspects and lb models the basic swe lb implementation is validated in different breaking dam scenarios we further provide a numerical study on stability of the mrt collision operator used in our simulations

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

diffuse interface modeling of three phase contact line dynamics on curved boundaries we introduce a simple and efficient lattice boltzmann method for immiscible multiphase flows capable of handling large density and viscosity contrasts the model is based on a diffuse interface phase field approach within this context we propose a new algorithm for specifying the three phase contact angle on curved boundaries within the framework of structured cartesian grids the proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases we test the model by applying it to four benchmark problems i wetting and dewetting of a droplet on a flat surface and ii on a cylindrical surface iii multiphase flow past a circular cylinder at an intermediate reynolds number and iv a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions where available our results show good agreement with analytical solutions and or existing experimental data highlighting strengths of this new approach

reduced order adaptive pole placement for multivariable systems a method is suggested for adaptively assigning the closed loop poles of a continuous time linear multivariable system the resulting design significantly reduces the complexity in comparison to any other known multivariable scheme for implementation one needs to know the order of the system and an upper bound on the observability index