on minima of a functional of the gradient necessary conditions in this paper we propose a new method for texture segmentation based on the use of texture feature detectors derived from a decorrelation procedure of a modified version of a pseudo wigner distribution pwd the decorrelation procedure is accomplished by a cascade recursive least squared crls principal component pc neural network the goal is to obtain a more eacient analysis of images by combining the advantages of using a high resolution joint representation given by the pwd with an eaective adaptive principal component analysis pca through the use of feedforward neural networks 1999 elsevier science b v all rights reserved

a solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion in this paper a stochastic model is presented to simulate the flow of gases which are not in thermodynamic equilibrium like in rarefied or micro situations for the interaction of a particle with others statistical moments of the local ensemble have to be evaluated but unlike in molecular dynamics simulations or dsmc no collisions between computational particles are considered in addition a novel integration technique allows for time steps independent of the stochastic time scale the stochastic model represents a fokker planck equation in the kinetic description which can be viewed as an approximation to the boltzmann equation this allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations the fluid dynamic equations of navier stokes and fourier are fully recovered for small relaxation times while for larger values the new model extents into the kinetic regime numerical studies demonstrate that the stochastic model is consistent with navier stokes in that limit but also that the results become significantly different if the conditions for equilibrium are invalid the application to the knudsen paradox demonstrates the correctness and relevance of this development and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages moreover results of a test case with geometrically complex boundaries are presented

enhanced closure scheme for lattice boltzmann equation hydrodynamics a simple and adaptable closure algorithm for the edge nodes of a lattice boltzmann fluid simulation space is presented its rules are designed to be correct at every instant to maintain local mass and to produce a specified fluid velocity and crucially the correct strain rate tensor at the resulting fluid boundary further our algorithm models the fluid on boundary nodes to the same accuracy as on the bulk nodes and in a demonstrably equivalent manner requiring only a specified boundary velocity the fluid boundary pressure emerging illustrative results for steady and time dependent flows together with outline generalizations are presented

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

a tour of the theory of absolutely minimizing functions a detailed analysis of the class of absolutely minimizing functions in euclidean spaces and the relationship to the infinity laplace equation

lattice boltzmann schemes for the nonlinear schrodinger equation the lattice boltzmann lb method is applied to solve the time dependent nonlinear schr odinger nls equation through approximating the reaction term at different orders of accuracy three diffusion reaction lb schemes are constructed for the cubic nls equation a lb initial condition is proposed to include the first order nonequilibrium distribution function these lb schemes are used to solve the one soliton propagation and the homoclinic orbit problems detailed simulation results confirm that the high order reaction term and the lb initial condition are effective in reducing the truncation errors compared with the crank nicolson finite difference scheme the lb scheme is found to give at least comparable and generally more accurate approximation for the cubic nls equation

three dimensional unsaturated flow modeling using cellular automata 1 the parabolic partial differential equation describing fluid flow in partially saturated porous media richards equation is highly nonlinear due to pressure head dependencies in the specific soil moisture capacity and relative hydraulic conductivity terms in order to solve richards equation several numerical techniques have been developed which starting from the discretization of the partial differential equation produced even more accurate models leading to complex and computationally expensive simulations for large scale systems a three dimensional unsaturated flow modeling developed through a simulation environment based on cellular automata ca is described in this paper the proposed model represents an extension of the original computational paradigm of cellular automata because it uses a macroscopic ca approach where local laws with a clear physical meaning govern interactions among automata this ca structure aimed at simulating a large scale system is based on functionalities capable of increasing its computational capacity both in terms of working environment and in terms of the optimal number of processors available for parallel computing the model has been validated with reference multidimensional solutions taken from benchmarks in literature showing a good agreement even in the cases where nonlinearity is very marked furthermore some analyses have been carried out considering quantization techniques aimed at transforming the ca model into an asynchronous structure the use of these techniques in a three dimensional benchmark allowed a considerable reduction in the number of local interactions among adjacent automata without changing the efficiency of the model especially when simulations are characterized by scarce mass exchanges finally from a computational point of view the higher efficiency values were achieved running the model on a parallel architecture obtaining a high speedup very close to the optimal with the maximum number of processors available

application of the lattice bhatnagar gross krook method to the simulation of internal pressure driven flow abstract recent modifications to the two speed two dimensional lattice bhatnagar gross krook method eliminate compressibility errors from the simulation of macroscopic fluids governed by the steady state navier stokes equation we describe the means by which this modified scheme makes it possible to compute both pressure drops and flow fields bringing internal pressure driven isothermal flows within the scope of the method the scheme is applied to the simulation of flow of a viscous incompressible fluid past a sudden expansion in an infinite aspect ratio duct back facing step geometry results are presented and compared with experiment and theory over a range of reynolds number

lattice boltzmann equation hydrodynamics by inserting position and time dependent source or forcing terms into the microscopic evolution equation of a lattice boltzmann fluid and treating the generalized scheme within the usual chapman enskog methodology we show that the emergent dynamics of the lattice fluid may be usefully transformed our method of adjustment is demonstrated by implementing the cylindrical polar coordinate form of the continuity and momentum equations on a rectangular lattice and generating results for pipe flow with straightforward systematic adjustment of the simulation our approach produces results in excellent agreement with theory

on lower subdifferentiable functions this paper studies the notion of lower subdifferentiability from the view point of generalized conjugation by this method the main properties of lower sub differentiable functions are analysed a related conjugation theory for holder and lipschitz functions is developed which is used to characterize those functions which can be expressed as a supremum of holder functions some applications to quasiconvex optimization and optimal control theory are examined

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

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

an improved lattice boltzmann method for simulating advective diffusive processes in fluids abstract lattice boltzmann methods are widely used to simulate advective diffusive processes in fluids lattice bhatnagar gross krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations we present and demonstrate here a formulation that produces no such second order errors this formulation suggests that a subtle but important adjustment is all it takes to improve the accuracy of the method the key to the improved accuracy of this new model is the non standard definition of the concentration that relates to the distribution function describing the advection diffusion in lattice boltzmann the main advantage of the algorithm comes to view when simulating situations where fluid density variations appear the present formulation of the advection diffusion algorithm will by taking into account these fluid density variations drastically reduce the errors produced compared to the standard formulations we also show how a source term is included in this new formulation without it losing its second order spatial accuracy

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

striated populations in disordered environments with advection abstract growth in static and controlled environments such as a petri dish can be used to study the spatial population dynamics of microorganisms however natural populations such as marine microbes experience fluid advection and often grow up in heterogeneous environments we investigate a generalized fisher kolmogorov petrovsky piscounov fkpp equation describing single species population subject to a constant flow field and quenched random spatially inhomogeneous growth rates with a fertile overall growth condition we analytically and numerically demonstrate that the non equilibrium steady state population density develops a flow driven striation pattern the striations are highly asymmetric with a longitudinal correlation length that diverges linearly with the flow speed and a transverse correlation length that approaches a finite velocity independent value linear response theory is developed to study the statistics of the steady states theoretical predictions show excellent agreement with the numerical steady states of the generalized fkpp equation obtained from lattice boltzmann simulations these findings suggest that although the growth disorder can be spatially uncorrelated correlated population structures with striations emerge naturally at sufficiently strong advection

existence of minimizers for non quasiconvex integrals keywords quasiconvexity existence of minimizers reference caa article 1995 002doi 10 1007 bf00380915 record created on 2008 11 25 modified on 2017 05 12

convexity criteria and uniqueness of absolutely minimizing functions we show that an absolutely minimizing function with respect to a convex hamiltonian h mathbb r n rightarrow mathbb r is uniquely determined by its boundary values under minimal assumptions on h along the way we extend the known equivalences between comparison with cones convexity criteria and absolutely minimizing properties to this generality these results perfect a long development in the uniqueness existence theory of the archetypal problem of the calculus of variations in l

a two dimensional lattice boltzmann model for uniform channel flows in this paper a novel two dimensional lattice boltzmann model lbm is developed for uniform channel flows the axial velocity is solved from a momentum diffusion equation over the cross sectional plane an extrapolation boundary condition is also introduced to enhance the no slip boundary in the momentum equation this boundary treatment can also be applied to lbm simulations of other diffusion processes the algorithm and boundary treatment are validated by simulations of steady poiseuille and pulsatile womersley flows in circular pipes the numerical convergence and accuracy are comparable to those of existing models moreover comparison with general three dimensional lattice boltzmann simulations demonstrates the advantages of our two dimensional model including lower computational resource requirements memory and time easier boundary treatment for arbitrary cross sectional shapes and no velocity constraint these features are attractive for practical applications with uniform channel flows

the euler equation and absolute minimizers of l functionals the aronsson euler equation for the functional on w g 1 m i e w 1 with boundary data g is this equation has been derived for smooth absolute minimizers i e a function which minimizes f on every subdomain we prove in this paper that for m 1 n 1 or n 1 m 1 an absolute minimizer of f exists in w g 1 m and for m 1 n 1 any absolute minimizer of f must be a viscosity solution of the aronsson euler equation

heat transfer in lattice bgk modeled fluid the thermal lattice bgk model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics the quality of the lattice bgk simulation is checked in this paper by calculating temperature profiles in the couette flow under different eckert and mach numbers a revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect especially in the flow regime with a higher mach number

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

boltzmann cellular automata studies of the spinodal decomposition abstract a nonlinear galilean invariant 2 color boltzmann cellular automaton is used to study spinodal decomposition in 2 dimensional systems the initial conditions for the process correspond to a well mixed state of two fluids present in equal proportions we specify two types of such initial conditions corresponding to a correlated quench and to a deep quench in the former case a specific color is assigned randomly to each site in the latter individual states on each site are populated by the two colors about evenly with small fluctuations in the correlated quench situation the domain growth exponent is initially equal to 0 33 0 06 and for the late time stage it is equal to 0 66 0 06 in the deep quench situation on the other hand the effective exponent from initial value of 0 33 takes on the value of 0 82 0 05 for intermediate time scales and only at later times it crosses over to the exponent corresponding to the correlated quench spinodal decomposition taking place in a porous medium is slower and the effective exponents are nonuniversal inadequacies in the existing models of the surface tension in cellular automata are pointed out

an immersed boundary lattice boltzmann method for the simulation of the flow past an impulsively started cylinder we present a lattice boltzmann method coupled with an immersed boundary technique for the simulation of bluff body flows the lattice boltzmann method for the modeling of the navier stokes equations is enhanced by a forcing term to account for the no slip boundary condition on a non grid conforming boundary we investigate two alternatives of coupling the boundary forcing term with the grid nodes namely the direct and the interpolated forcing techniques the present lb ib methods are validated in simulations of the incompressible flow past an impulsively started cylinder at low and moderate reynolds numbers we present diagnostics such as the near wall vorticity field and the drag coefficient and comparisons with previous computational and experimental works and assess the advantages and drawbacks of the two techniques

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

generalized lattice boltzmann method with multirange pseudopotential the physical behavior of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces in particular an extended pseudopotential method is developed which permits to tune the equation of state and surface tension independently of each other the spurious velocity contributions of this extended model are shown to vanish in the limit of high grid refinement and or high order isotropy higher order schemes to implement self consistent forcings are rigorously computed for 2d and 3d models the extended scenario developed in this work clarifies the theoretical foundations of the shan chen methodology for the lattice boltzmann method and enhances its applicability and flexibility to the simulation of multiphase flows to density ratios up to o 100

lattice boltzmann equation calculation of internal pressure driven turbulent flow we describe a mixing length extension of the lattice boltzmann approach to the simulation of an incompressible liquid in turbulent flow the method uses a simple adaptable closure algorithm to bound the lattice boltzmann fluid incorporating a law of the wall the test application of an internal pressure driven and smooth duct flow recovers correct velocity profiles for reynolds number to 1 25 105 in addition the reynolds number dependence of the friction factor in the smooth wall branch of the moody chart is correctly recovered the method promises a straightforward extension to other curves of the moody chart and to cylindrical pipe flow

a method for near equilibrium discrete velocity gas flows we present a simulation scheme for discrete velocity gases based on local thermodynamic equilibrium exploting the kinetic nature of discrete velocity gases in that context results in a natural splitting of fluxes and the resultant scheme strongly resembles the original process the kinetic nature of the scheme and the modeling of the infinite collision rate limit result in a small value of the coefficient of numerical viscosity the behavior of which is remarkably physical a first order method and two second order methods using the total variation diminishing principle are developed and an example application is presented given the same computer resources it is expected that with this approach a much higher reynold s number will be achievable than presently possible with either lattice gas automata or lattice boltzmann approaches the ideas being general the scheme is applicable to any discrete velocity model and to lattice gases as well

simulations of complex fluids by mixed lattice boltzmann finite difference methods abstract we present the numerical results of simulations of complex fluids under shear flow we employ a mixed approach which combines the lattice boltzmann method for solving the navier stokes equation and a finite difference scheme for the convection diffusion equation the evolution in time of shear banding phenomenon is studied this is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow

existence of minimizers for nonlevel convex supremal functionals the paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem inf mathop rm ess sup x in omega f nabla u x u in u 0 w 1 infty 0 omega when the supremand f is not necessarily level convex these conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum several conditions of convexity for the supremand f are also investigated

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

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

study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network the d1q3 lattice boltzmann lb shallow water equation is analyzed in detail and compared with other numerical schemes analytical results are derived and used to discuss the accuracy and stability of the model we show how such d1q3 lb models for canal reaches may be easily coupled with various hydraulic interconnection structures to build models of complex irrigation networks

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

method and apparatus for fundamental frequency extraction or detection in speech an object is to provide a method of extracting sound source information which method enables the characteristics of fixed points of mapping from filter center frequency to output instantaneous frequency to be detected from instantaneous data as a value which can be interpreted quantitatively in a method of extracting sound source information by use of fixed points of mapping from frequency to instantaneous frequency instantaneous frequency of each filter 2 9 is partial differentiated with respect to frequency by an instantaneous frequency frequency differentiation circuit 3 10 to thereby obtain a first value output of each filter is partial differentiated with respect to frequency and then with respect to time by an instantaneous frequency time frequency differentiation circuit 4 11 to thereby obtain a second value and proper weights are imparted to the first and second values and short time weighted integration with respect to time is performed by a carrier to noise ratio calculation circuit 5 12 to estimate a carrier to noise ratio of each filter thus a carrier to noise ratio is obtained and an estimated value of evaluation value is obtained

nonlinear stability of compressible thermal lattice bgk models the nonlinear stability of thermal lattice bgk models is examined by means of computer simulation for the case of one and two dimensional compressible flows it is shown that in one dimension 1d the method is stable on a sizeable range of flow speeds and temperatures in two dimensions 2d the method is stable even in the presence of negative distribution functions but on a smaller stability domain the computational efficiency of the method compares favorably with classical algorithms for compressible flows such as the lambda scheme and the lax wendroff scheme

efficient fft based upscaling of the permeability of porous media discretized on uniform grids with estimation of rve size abstract an efficient numerical scheme at the crossroad of fourier based methods and boundary element methods is derived to upscale the permeability of porous media from stokes flow within the pore space the method relies on a variational framework which involves trial force fields and the green function the discretization of the trial force fields is carried out on a uniform grid which allows for the use of fast fourier transforms to evaluate the convolution product arising from the green function a discretization of the green function consistent with the variational framework is introduced to ensure the upper bound status of the homogenized permeability the energy consistent discretization is compared to six alternative discretizations arising from truncation of fourier series or from various finite difference schemes in terms of accuracy of the homogenized permeability and of the local velocity fields as well as on the number of iterations required for convergence of the iterative solver the method is combined to a strategy to estimate the representative volume element rve size at a target accuracy level from a single simulation on a large sample to study the permeability and associated rve size for the voronoi cell model over the whole range of porosity

the lattice boltzmann equation a new tool for computational fluid dynamics abstract we present a series of applications which demonstrate that the lattice boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes ranging from laminar to fully turbulent flows in two and three dimensions

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

interpolation methods and the accuracy of lattice boltzmann mesh refinement a lattice boltzmann model to solve the equivalent of the navier stokes equations on adaptively refined grids is presented a method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite volume representations this new approach relies on a space time interpolation and solving constrained least squares problems to ensure conservation the effectiveness of this method at maintaining the second order accuracy of lattice boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies these results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation examples highlighting the mesh adaptivity of this method are also provided

uniqueness of lipschitz extensions minimizing the sup norm of the gradient in this paper we examine the problem of minimizing the sup norm of the gradient of a function with prescribed boundary values geometrically this can be interpreted as finding a minimal lipschitz extension due to the weak convexity of the functional associated to this problem solutions are generally nonunique by adopting g aronsson s notion of absolutely minimizing we are able to prove uniqueness by characterizing minimizers as the unique solutions of an associated partial differential equation in fact we actually prove a weak maximum principle for this partial differential equation which in some sense is the euler equation for the minimization problem this is significantly difficult because the partial differential equation is both fully nonlinear and has very degenerate ellipticity to overcome this difficulty we use the weak solutions of m g crandall and p l lions also known as viscosity solutions in conjunction with some arguments using integration by parts

phase separation of incompressible binary fluids with lattice boltzmann methods we introduce new versions of lattice boltzmann methods lbm for incompressible binary mixtures where fluctuations of total density are inhibited as a test for the improved algorithms we consider the problem of phase separation of two dimensional binary mixtures quenched from a disordered state into the coexistence region we find that the stability properties of lbm are greatly improved the control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent

numerical study of the ordering properties of lamellar phase the quench of a binary mixture into a stable lamellar phase is numerically investigated we present a novel approach to study the phenomenological equations governing the system dynamics basedon the combination of lattice boltzmann and1nite d equations we can access large systems on time scales long enough to 1nd evidence of dynamical scaling regime in the ordering process when hydrodynamics is operating c

an improved immersed boundary lattice boltzmann method for simulating three dimensional incompressible flows the recently proposed boundary condition enforced immersed boundary lattice boltzmann method ib lbm 14 is improved in this work to simulate three dimensional incompressible viscous flows in the conventional ib lbm the restoring force is pre calculated and the non slip boundary condition is not enforced as compared to body fitted solvers as a result there is a flow penetration to the solid boundary this drawback was removed by the new version of ib lbm 14 in which the restoring force is considered as unknown and is determined in such a way that the non slip boundary condition is enforced since eulerian points are also defined inside the solid boundary the computational domain is usually regular and the cartesian mesh is used on the other hand to well capture the boundary layer and in the meantime to save the computational effort we often use non uniform mesh in ib lbm applications in our previous two dimensional simulations 14 the taylor series expansion and least squares based lattice boltzmann method tllbm was used on the non uniform cartesian mesh to get the flow field the final expression of tllbm is an algebraic formulation with some weighting coefficients these coefficients could be computed in advance and stored for the following computations however this way may become impractical for 3d cases as the memory requirement often exceeds the machine capacity the other way is to calculate the coefficients at every time step as a result extra time is consumed significantly to overcome this drawback in this study we propose a more efficient approach to solve lattice boltzmann equation on the non uniform cartesian mesh as compared to tllbm the proposed approach needs much less computational time and virtual storage its good accuracy and efficiency are well demonstrated by its application to simulate the 3d lid driven cubic cavity flow to valid the combination of proposed approach with the new version of ibm 14 for 3d flows with curved boundaries the flows over a sphere and torus are simulated the obtained numerical results compare very well with available data in the literature

hopf lax type formula forut h u du 0 abstract an explicit formula is derived for the hamilton jacobi equation u t h u du 0 on 0 r n with u 0 x g x the hamiltonian h p is assumed to be nondecreasing in r 1 and convex and positively homogeneous of degree 1 in p r n the unique solution is given by formula where h is a quasiconvex function given as the quasiconvex dual of h that is h q inf r 1 h p p q p

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

short time fourier transform using a bank of low pass filters the purpose of this paper is to present some experimental results estimating instantaneous frequencies of fm frequency modulation signals using the short time fourier transform stft method the relevant stft coefficients were computed using a bank of simple one pole low pass filters which estimates the cross correlation of a given signal and complex sinusoids also it is shown that computing the stft coefficients is equivalent to finding the least square solution which best approximates the given signal as a weighted sum of complex sinusoids

local second order boundary methods for lattice boltzmann models a new way to implement solid obstacles in lattice boltzmann models is presented the unknown populations at the boundary nodes are derived from the locally known populations with the help of a second order chapman enskog expansion and dirichlet boundary conditions with a given momentum steady flows near a flat wall arbitrarily inclined with respect to the lattice links are then obtained with a third order error in particular couette and poiseuille flows are exactly recovered without the knudsen layers produced for inclined walls by the bounce back condition

lattice boltzmann simulations of blood flow non newtonian rheology and clotting processes the numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent in this paper we consider a lattice boltzmann lb approach to bloodflow modeling and we implement a non newtonian correction in order to reproduce more realistic flow profiles we obtain a good agreement between simulations and casson s model of blood rheology in a simple geometry finally we discuss how by using a passive scalar suspension model with aggregation on top of the lb dynamics we can describe the clotting processes in the aneurysm

time frequency analysis of seismic data using local attributes time frequency analysis is an important technology in seismic data processing and interpretation to localize frequency content in time we have developed a novel method for computing a time frequency map for nonstationary signals using an iterative inversion framework we calculated time varying fourier coefficients by solving a least squares problem that uses regularized nonstationary regression we defined the time frequency map as the norm of time varying coefficients time varying average frequency of the seismic data can also be estimated from the time frequency map calculated by our method we tested the method on benchmark synthetic signals and compared it with the well known s transform two field data examples showed applications of the proposed method for delineation of sand channels and for detection of low frequency anomalies

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

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

relaxed minimax control the relaxation of the optimal control problem with cost functional which is the supremum in time of some function h t x z is determined the trajectory is convexified in the usual way but the cost functional is convexified in a nonobvious manner thus if the original value function is v t x inf zeta in z left h s xi s zeta s right l infty t t cr then the relaxed value function is hat v t x mathop inf limits mu in hat z left t t right left left h s hat xi s z right l infty rm z mu s right l infty left t t right cr where the inner norm is the essential sup of h over z in rm z cr with respect to the measure mu s cr we prove that v and hat v coincide

an immersed boundary method based on the lattice boltzmann approach in three dimensions with application the immersed boundary ib method originated by peskin has been popular in modeling and simulating problems involving the interaction of a flexible structure and a viscous incompressible fluid the navier stokes n s equations in the ib method are usually solved using numerical methods such as fft and projection methods here in our work the n s equations are solved by an alternative approach the lattice boltzmann method lbm compared to many conventional n s solvers the lbm can be easier to implement and more convenient for modeling additional physics in a problem this alternative approach adds extra versatility to the immersed boundary method in this paper we discuss the use of a 3d lattice boltzmann model d3q19 within the ib method we use this hybrid approach to simulate a viscous flow past a flexible sheet tethered at its middle line in a 3d channel and determine a drag scaling law for the sheet our main conclusions are 1 the hybrid method is convergent with first order accuracy which is consistent with the immersed boundary method in general 2 the drag of the flexible sheet appears to scale with the inflow speed which is in sharp contrast with the square law for a rigid body in a viscous flow

computational time and domain size analysis of porous media flows using the lattice boltzmann method the purpose of this study is to investigate the computational time required to describe the fluid flow behavior through a porous medium and its relation to the corresponding domain size the fluid flow behavior is recovered using the lattice boltzmann method lbm the selected methodology has been applied because of its feasibility for mimicking the fluid flow behavior in complex geometries and moving boundaries in this study three different porosities are selected to calculate for several sizes domain the required computational time to reach the steady state two different cases are implemented 1 increasing the transversal area but keeping the layer thickness as a constant and 2 increasing the total volume of the pore domain by increasing all the dimensions of the volume equally the porous media are digitally generated by placing the solid obstacles randomly but uniformly distributed in the whole domain several relationships relating the computational time domain size and porosity are proposed additionally an expression that relates the hydraulic tortuosity to the porosity is proposed

boundary induced nonlinearities at small reynolds numbers we investigate the importance of boundary slip at finite reynolds numbers for mixed boundary conditions nonlinear effects are induced by the non homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction to explain the observed drag modification exact reciprocal relations in the presence of heterogeneous boundary conditions are derived the small reynolds number limit predicts a reduction of the mean flow rate from the creeping flow to be proportional to the second power of the reynolds number to further support our theoretical analysis numerical simulations with the lattice boltzmann method lbm and finite difference method fdm are performed and reveal a pronounced numerical efficiency of lbm with respect to fdm

two dimensional turbulence with the lattice boltzmann equation the authors investigate the ability of the lattice boltzmann equation to reproduce the basic physics of fully turbulent two dimensional flows and present a qualitative estimate of its computational efficiency with respect to other conventional techniques