lattice boltzmann simulations of a time dependent natural convection problem a two dimensional double multiple relaxation time thermal lattice boltzmann method is used to simulate natural convection flows in differentially heated cavities the buoyancy effects are considered under the boussinesq assumption flow and temperature fields are respectively solved with nine and five discrete velocities models boundary conditions are implemented with the classical bounce back or an on node approach the latter uses the popular zou and he and counter slip formulations this paper evaluates the differences between the two implementations for steady and time dependent flows as well as the space and time convergence orders

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

lateral migration and nonuniform rotation of suspended ellipse in poiseuille flow abstract suspensions of an elliptical particle in poiseuille flow are investigated by using the multiple relaxation time lattice boltzmann method coupled with the galilean invariant momentum exchange method the elliptical particle shows lateral migration and final equilibrium which are similar to the classical segre silberberg effect because the elliptical shape interacts with the parabolic velocity distribution of the poiseuille flow the particulate behaviors remarkably contain regular wave accompanied by nonuniform rotation when the blockage ratio grows up the equilibrium position of the particle moves towards the channel centerline and the rotation period becomes long with the increase of the aspect ratio the rotation period becomes short the equilibrium position shows a shape of saddle and reaches its bottom at nearby aspect ratio 0 5 surprisingly the numerical results show that the equilibrium position is insensitive to reynolds number re of poiseuille flows in the range 3 r e 300 this work can make active promotions to the researches of blood circulation of birds whose red blood cell is oval or elliptical in shape

effect of the forcing term in the multiple relaxation time lattice boltzmann equation on the shear stress or the strain rate tensor in this work the effect of the forcing term or external force in the multiple relaxation time lattice boltzmann equation mrtlbe on the shear stress or the strain rate tensor is studied theoretically and numerically through a chapman enskog analysis and numerical simulations we show that the shear stress or the strain rate tensor derived from the mrtlbe is second order accurate in space we then examine the influence of the forcing term on the shear stress or the strain rate tensor and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function

discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method abstract a discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice boltzmann method lbm with multiple relaxation times mrt is developed the lattice boltzmann fluid solver is supplemented by a porosity model using a darcy force the continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels the adjoint lbm equation which is used to compute the gradient of the optimization objective with respect to the design variables is derived in moment space and found to be as simple as the original lbm the moment based spatial momentum derivatives used to express the discrete objective functional cost function have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field this is particularly useful if dissipation is a design criterion as demonstrated in this paper the method is validated by a detailed comparison with results obtained by borrvall et al for stokes flow while their approach is only valid for stokes flow i e very low reynolds numbers our approach in its present form can in principle be applied for flows of different reynolds numbers just like the navier stokes equation based approaches this point is demonstrated with a bending pipe example for various reynolds numbers

central moment lattice boltzmann schemes with fixed and moving immersed boundaries lattice boltzmann lb schemes based on the relaxation of central moments have recently proved valuable in simulating flows with an improved stability with respect to the original single relaxation time bgk formulation while preserving the accuracy of the latter this has been assessed mainly for flows in simple geometries e g in periodic domains or with fixed rigid straight boundaries in the present study the properties of central moment lb schemes have been investigated against flow configurations involving arbitrarily shaped possibly moving boundaries within the framework of the so called immersed boundary ib method namely the presence of boundaries is accounted by an external force acting on the fluid that is encompassed in the central moment lb algorithm accuracy and stability issues are examined in comparison with existing results from the literature and lb simulations based on the original bgk scheme our results show that central moment lb schemes accompanied by the ib method provide an efficient tool for fluid structure interaction simulations

half canonical series on algebraic curves preprint enviat per a la seva publicacio en una revista cientifica transactions of the american mathematical society vol 302 no 1 1987 pp 99 115 https www jstor org stable 2000899

uniruledness of strata of holomorphic differentials in small genus abstract we address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials we show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on k3 and del pezzo surfaces respectively restricting to genus 3 g 6 we construct projective bundles over a rational varieties that dominate the holomorphic strata with length at most g 1 hence showing in addition that these strata are unirational

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

a hydrodynamically consistent mrt lattice boltzmann model on a 2d rectangular grid a multiple relaxation time mrt lattice boltzmann lb model on a d2q9 rectangular grid is designed theoretically and validated numerically in the present work by introducing stress components into the equilibrium moments this mrt lb model restores the isotropy of diffusive momentum transport at the macroscopic level or in the continuum limit leading to moment equations that are fully consistent with the navierstokes equations the model is derived by an inverse design process which is described in detail except one moment associated with the energy square all other eight equilibrium moments can be theoretically and uniquely determined the model is then carefully validated using both the two dimensional decaying taylorgreen vortex flow and lid driven cavity flow with different grid aspect ratios the corresponding results from an earlier model bouzidi et al 2001 28 are also presented for comparison the results of bouzidi et al s model show problems associated with anisotropy of viscosity coefficients while the present model exhibits full isotropy and is accurate and stable

numerics of the lattice boltzmann method effects of collision models on the lattice boltzmann simulations we conduct a comparative study to evaluate several lattice boltzmann lb models for solving the near incompressible navier stokes equations including the lattice boltzmann equation with the multiple relaxation time mrt the two relaxation time trt the single relaxation time srt collision models and the entropic lattice boltzmann equation elbe the lid driven square cavity flow in two dimensions is used as a benchmark test our results demonstrate that the elbe does not improve the numerical stability of the srt or the lattice bhatnagar gross krook lbgk model our results also show that the mrt and trt lb models are superior to the elbe and lbgk models in terms of accuracy stability and computational efficiency and that the elbe scheme is the most inferior among the lb models tested in this study thus is unfit for carrying out numerical simulations in practice our study suggests that to optimize the accuracy stability and efficiency in the mrt model it requires at least three independently adjustable relaxation rates one for the shear viscosity ensuremath nu or the reynolds number text re one for the bulk viscosity ensuremath zeta and one to satisfy the criterion imposed by the dirichlet boundary conditions which are realized by the bounce back type boundary conditions

link wise artificial compressibility method the artificial compressibility method acm for the incompressible navier stokes equations is link wise reformulated referred to as lw acm by a finite set of discrete directions links on a regular cartesian mesh in analogy with the lattice boltzmann method lbm the main advantage is the possibility of exploiting well established technologies originally developed for lbm and classical computational fluid dynamics with special emphasis on finite differences at least in the present paper at the cost of minor changes for instance wall boundaries not aligned with the background cartesian mesh can be taken into account by tracing the intersections of each link with the wall analogously to lbm technology lw acm requires no high order moments beyond hydrodynamics often referred to as ghost moments and no kinetic expansion like finite difference schemes only standard taylor expansion is needed for analyzing consistency preliminary efforts towards optimal implementations have shown that lw acm is capable of similar computational speed as optimized bgk lbm in addition the memory demand is significantly smaller than bgk lbm importantly with an efficient implementation this algorithm may be among the few which are compute bound and not memory bound two and three dimensional benchmarks are investigated and an extensive comparative study between the present approach and state of the art methods from the literature is carried out numerical evidences suggest that lw acm represents an excellent alternative in terms of simplicity stability and accuracy

entropic lattice boltzmann method for turbulent flow simulations boundary conditions abstract we introduce a new concept of boundary conditions for realization of the lattice boltzmann simulations of turbulent flows the key innovation is the use of a universal distribution function for particles analogous to the tamm mott smith solution for the shock wave in the classical boltzmann kinetic equation turbulent channel flow simulations demonstrate that the new boundary enables accurate results even with severely under resolved grids generalization to complex boundary is illustrated with an example of turbulent flow past a circular cylinder

lattice boltzmann model for the axisymmetric electro thermo convection abstract a lattice boltzmann model for the axisymmetric electro thermo convection is proposed in this paper the axisymmetric governing equations in the cylindrical coordinate system including the navier stokes equations the energy equation the conservation equation of charge density and the poisson s equation for electric potential are solved by the lattice boltzmann method in the cartesian coordinate system all additional source terms can be calculated locally the present model is validated by three simple numerical examples the electro thermo convection in an annulus between two coaxial vertical cylinders is also investigated by the present model the effect of the electric rayleigh number on heat transfer enhancement is discussed

lattice boltzmann method based on dual mrt model for three dimensional natural convection and entropy generation in cuo water nanofluid filled cuboid enclosure included with discrete active walls abstract in the present study the three dimensional natural convection and entropy generation in a cuboid enclosure included with various discrete active walls is analyzed using lattice boltzmann method the enclosure is filled with cuo water nanofluid to predict thermo physical properties dynamic viscosity and thermal conductivity of cuo water nanofluid the kkl model is applied to consider the effect of brownian motion on nanofluid properties in lattice boltzmann simulation two different mrt models are used to solve the problem the d3q7 mrt model is used to solve the temperature filed and the d3q19 is employed to solve the fluid flow of natural convection within the enclosure the influences of different rayleigh numbers 1 0 3 r a 1 0 6 and solid volume fractions 0 0 04 and four different arrangements of discrete active walls on the fluid flow heat transfer total entropy generation local heat transfer irreversibility and local fluid friction irreversibility are presented comprehensively

an alternative lattice boltzmann model for three dimensional incompressible flow abstract in this work an alternative lattice boltzmann lb model for three dimensional 3d incompressible flow is proposed the equilibrium distribution function edf of the present model is directly derived in accordance with the incompressibility conditions by applying the hermite expansion moreover an alternative formula for pressure computation is designed from the second order moment of the distribution function the present 3d lb model inherits the advantageous features of guo s lb model the density is a constant the fluid pressure is independent of density and the navier stokes n s equations for incompressible flow can be derived two benchmark tests flow over a backward facing step and the lid driven cavity flow are applied to validate the present model accurate results for these tests are obtained with the present model and further comparisons with the previous lb models the standard lb model the he luo model and guo s lb model demonstrate that the present model provides better accuracy in the region of high deviatoric stress and such advantage is further enhanced by using the d3q27 lattice

conditioned limit theorems for products of random matrices consider the product g n g n dots g 1 of the random matrices g 1 dots g n in gl left d mathbb r right and the random process g n v g n dots g 1 v in mathbb r d starting at point v in mathbb r d smallsetminus left 0 right it is well known that under appropriate assumptions the sequence left log left vert g n v right vert right n geq 1 behaves like a sum of i i d r v s and satisfies standard classical properties such as the law of large numbers law of iterated logarithm and the central limit theorem denote by mathbb b the closed unit ball in mathbb r d and by mathbb b c its complement for any v in mathbb b c define the exit time of the random process g n v from mathbb b c by tau v min left n geq 1 g n v in mathbb b right we establish the asymptotic as n rightarrow infty of the probability of the event left tau v n right and find the limit law for the quantity frac 1 sqrt n log left vert g n v right vert conditioned that tau v n

derivatives of wronskians with applications to families of special weierstrass points let 7r 3s be a flat proper family of smooth co nnected projective curves parametrized by some smooth scheme of finite type over c on every such a family suitable derivatives along the fibers in the sense of lax of the relative wronskian as defined by laksov and thorup are constructed they are sections of suitable jets extensions of the g g 1 2 th tensor power of the relative canonical bundle of the family itself the geometrical meaning of such sections is discussed the zero schemes of the k 1 th derivative k 1 of a relative wronskian correspond to families of weierstrass points wp s having weight at least k the locus in mg the coarse moduli space of smooth projective curves of genus g of curves possessing a wp of weight at least k is denoted by wt k the fact that wt 2 has the expected dimension for all g 2 was implicitly known in the literature the main result of this paper hence consists in showing that wt 3 has the expected dimension for all g 4 as an application we compute the codimension 2 chow q class of wt 3 for all g 4 the main ingredient being the definition of the k th derivative of a relative wronskian which is the crucial tool which the paper is built on in the concluding remarks we show how this result may be used to get relations among some codimension 2 chow q classes in m4 g 4 corresponding to varieties of curves having a point p with a suitable prescribed weierstrass gap sequence relating to previous work of lax