regular multivariate sampling and approximation in lp shift invariant spaces abstract in this paper some results about regular multivariate generalized sampling in the l p setting 1 p are proven thus stable multivariate regular sampling formulas are derived for l p shift invariant spaces v p i e the l p closure of the linear span of the shifts of a finite set of generators these sampling formulas include regular samples of the function its derivatives and or some filtered versions of the function itself taken at a lattice of r d approximation schemes using these generalized sampling formulas are also included

multiphase cascaded lattice boltzmann method to improve the stability of the lattice boltzmann method lbm at high reynolds number the cascaded lbm has recently been introduced as in the multiple relaxation time mrt method the cascaded lbm introduces additional relaxation times into the collision operator but does so in a co moving reference frame this has been shown to significantly increase stability at low viscosity in the single phase case here the cascaded lbm is further developed to include multiphase flow for this the force term is calculated by the interaction potential method and introduced into the collision operator via the exact difference method edm comparisons are made with the lattice bhatnagar gross krook lbgk method and an mrt implementation both the cascaded and mrt methods are shown to significantly reduce spurious velocities over the lbgk method for the particular case of the shan chen interparticle force term calculation with the edm the cascaded lbm is successfully combined with a multiphase method and shown to perform as well as the more established mrt method the cascaded lbm is found to be a considerably improved approach to the simulation of multiphase flow over the lbgk significantly increasing the stability range of both density ratio and reynolds number additionally the importance of including third order velocity terms in the equilibria of both the cascaded and mrt methods is discussed

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

nonorthogonal central moments based lattice boltzmann scheme in three dimensions we present an alternative three dimensional lattice boltzmann collision operator consisting of a nonorthogonal basis of central moments our formulation is characterized by an intelligible derivation with a relatively simple and quite general implementation it is successfully validated against several established well consolidated well defined benchmark problems showing excellent properties in terms of accuracy and convergence if compared to the adoption of the classical bhatnagar gross krook operator our model possesses superior stability

adjoint lattice boltzmann for topology optimization on multi gpu architecture in this paper we present a topology optimization technique applicable to a broad range of flow design problems we propose also a discrete adjoint formulation effective for a wide class of lattice boltzmann methods lbm this adjoint formulation is used to calculate sensitivity of the lbm solution to several type of parameters both global and local the numerical scheme for solving the adjoint problem has many properties of the original system including locality and explicit time stepping thus it is possible to integrate it with the standard lbm solver allowing for straightforward and efficient parallelization overcoming limitations typical for the discrete adjoint solvers this approach is successfully used for the channel flow to design a free topology mixer and a heat exchanger both resulting geometries being very complex maximize their objective functions while keeping viscous losses at acceptable level

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

multiple relaxation time lattice boltzmann method for immiscible fluids at high reynolds numbers the lattice boltzmann method for immiscible multiphase flows with large density ratio is extended to high reynolds number flows using a multiple relaxation time mrt collision operator and its stability and accuracy are assessed by simulating the kelvin helmholtz instability the mrt model is successful at damping high frequency oscillations in the kinetic energy emerging from traveling waves generated by the inclusion of curvature numerical results are shown to be in good agreement with prior studies using adaptive mesh refinement techniques applied to the navier stokes equations effects of viscosity and surface tension as well as density ratio are investigated in terms of the reynolds and weber numbers it is shown that increasing the reynolds number results in a more chaotic interface evolution and eventually shattering of the interface while surface tension is shown to have a stabilizing effect

generalized local equilibrium in the cascaded lattice boltzmann method by realizing the insufficient degree of galilean invariance of the traditional multiple relaxation time collision operators geier et al phys rev e 73 066705 2006 proposed to relax differently the moments shifted by the macroscopic velocity leading to the so called cascaded lattice boltzmann method lbm this paper points out that a the cascaded lbm essentially consists in adopting a generalized local equilibrium in the frame at rest b this new equilibrium does not affect the consistency of lbm and finally c if the raw moments are relaxed in the frame at rest as usual and the number of relaxation frequencies is reduced the proposed derivation leads to the two relaxation time collisional operator with proper polynomial equilibrium

a conservative phase field method for solving incompressible two phase flows in this paper a conservative phase field method based on the work of sun and beckermann y sun c beckermann sharp interface tracking using the phase field equation j comput phys 220 2007 626 653 for solving the two and three dimensional two phase incompressible navier stokes equations is proposed the present method can preserve the total mass as the cahn hilliard equation but the calculation and implementation are much simpler than that the dispersion relation preserving schemes are utilized for the advection terms while the helmholtz smoother is applied to compute the surface tension force term to verify the proposed method several benchmarks are examined and shown to have good agreements with previous results it also shows that the satisfactions of mass conservations are guaranteed

cascaded lattice boltzmann method with improved forcing scheme for large density ratio multiphase flow at high reynolds and weber numbers a recently developed forcing scheme has allowed the pseudopotential multiphase lattice boltzmann method to correctly reproduce coexistence curves while expanding its range to lower surface tensions and arbitrarily high density ratios lycett brown and luo phys rev e 91 023305 2015 pleee81539 375510 1103 physreve 91 023305 here a third order chapman enskog analysis is used to extend this result from the single relaxation time collision operator to a multiple relaxation time cascaded collision operator whose additional relaxation rates allow a significant increase in stability numerical results confirm that the proposed scheme enables almost independent control of density ratio surface tension interface width viscosity and the additional relaxation rates of the cascaded collision operator this allows simulation of large density ratio flows at simultaneously high reynolds and weber numbers which is demonstrated through binary collisions of water droplets in air with density ratio up to 1000 reynolds number 6200 and weber number 440 this model represents a significant improvement in multiphase flow simulation by the pseudopotential lattice boltzmann method in which real world parameters are finally achievable

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

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

a cascaded phase field lattice boltzmann model for the simulation of incompressible immiscible fluids with high density contrast abstract in this work a conservative phase field model for the simulation of immiscible multiphase flows is developed using an incompressible velocity based cascaded lattice boltzmann method clbm extensions are made to the lattice boltzmann lb equations for interface tracking and incompressible hydrodynamics proposed by fakhari et al 1 by performing relaxation operations in central moment space this was motivated by the work of fei et al 2 3 where promising results from such a transformation were observed the relaxation of central moments is defined in a reference frame moving with the fluid while the existing multiple relaxation time 4 5 scheme performs collision in a fixed frame of reference moreover the derivations make use of continuous maxwellian distribution functions as a result the clbm enhances the galilean invariance and stability of the method when high lattice mach numbers are evident the cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo potential model where it allowed for high density and viscosity contrasts to be captured 6 7 here the clbm is implemented within the phase field framework and is verified through the analysis of a layered poiseuille flow the performance of the clbm is then investigated in terms of spurious currents galilean invariance and computational efficiency finally the work of fakhari et al 1 is extended by validating the model s ability to capture the relation between surface tension and the rise velocity of a planar taylor bubble in both stagnant and flowing fluids new counter current results indicate that the rise velocity model of ha ngoc and fabre 8 also applies in this regime

the bispectral property of a q deformation of the schur polynomials and the q kdv hierarchy we show that appropriate q analogues of the schur polynomials provide rational solutions of a q deformation of the nth kdv hierarchy this allows us to construct explicit examples of bispectral commutative rings of q difference operators

cascaded digital lattice boltzmann automata for high reynolds number flow lattice boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit we observe that this is caused by an insufficient degree of galilean invariance of the relaxation type lattice boltzmann collision operator the cascaded digital lattice boltzmann automata described here provides a method with which to achieve stable collision operators down to the limit of zero viscosity

a three dimensional lattice model for thermal compressible flow on standard lattices a three dimensional double distribution function thermal lattice boltzmann model has been developed for simulation of thermal compressible flows in the low mach number limit both the flow field and energy conservation equation are solved by lb approach a higher order density distribution function on standard lattices is used to solve the flow field while an energy distribution function is employed to compute the temperature field the equation of state of thermal perfect gas is recovered by higher order hermite polynomial expansions in navier stokes fourier equations the equilibrium distribution functions of d3q15 d3q19 and d3q27 lattices are obtained from the hermite expansion they exhibit slight differences originating in differences in the discrete lattice symmetries the correction terms in lb models for third order derivation are added using an external force in orthogonal polynomials form present models are successfully assessed considering several test cases namely the thermal couette flow rayleigh benard convection natural convection in square cavity and a spherical explosion in a 3d enclosed box the numerical results are in good agreement with both analytical solution and results given by previous authors

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

nonhydrodynamic modes and a priori construction of shallow water lattice boltzmann equations lattice boltzmann equations for the isothermal navier stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory applied to the shallow water equations with its different equation of state the same approach yields discrete equilibria that are subject to a grid scale computational instability different and stable equilibria were previously constructed by salmon j marine res 57 503 1999 the two sets of equilibria differ through a nonhydrodynamic or ghost mode that has no direct effect on the hydrodynamic behavior derived in the slowly varying limit however salmon s equilibria eliminate a coupling between hydrodynamic and ghost modes one that leads to instability with a growth rate increasing with wave number previous work has usually assumed that truncated moment expansions lead to stable schemes such instabilities have implications for lattice boltzmann equations that simulate other nonideal equations of state or that simulate fully compressible nonisothermal fluids using additional particles

a consistent solution of the re initialization equation in the conservative level set method in this paper a new re initialization method for the conservative level set function is put forward first it has been shown that the re initialization and advection equations of the conservative level set function are mathematically equivalent to the re initialization and advection equations of the localized signed distance function next a new discretization for the spatial derivatives of the conservative level set function has been proposed this new discretization is consistent with the re initialization procedure and it guarantees a second order convergence rate of the interface curvature on gradually refined grids the new re initialization method does not introduce artificial deformations to stationary and non stationary interfaces even when the number of re initialization steps is large we derive the re initialization equation of the localized signed distance function we show the analytical relation between the vof and ls methods we introduce the consistent method for computation of the interface curvature the new re initialization method does not deform interfaces and conserves mass second order convergence of curvature is achieved with second order accurate method

isotropic finite differences new finite differences called isotropic finite differences where the lowest order error terms are without any directional bias are proposed an accurate simulation of 6 fold symmetric dendritic solidification is presented using a numerical scheme based on these finite differences