h c1 maps and elliptic spdes with polynomial and exponential perturbations of nelson s euclidean free field abstract elliptic stochastic partial differential equations spde with polynomial and exponential perturbation terms defined in terms of nelson s euclidean free field on rd are studied using results by s kusuoka and a s ustunel and m zakai concerning transformation of measures on abstract wiener space spdes of this type arise in particular in euclidean quantum field theory with interactions of the polynomial or exponential type the probability laws of the solutions of such spdes are given by girsanov probability measures that are non linearly transformed measures of the probability law of nelson s free field defined on subspaces of schwartz space of tempered distributions

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

least squares based lattice boltzmann method a meshless approach for simulation of flows with complex geometry a version of lattice boltzmann method lbm is presented in this work which is derived from the standard lbm by using taylor series expansion and optimized by the least squares method the method is basically meshless and can be applied to any complex geometry and nonuniform grids it can also be applied to different lattice models the proposed method explicitly updates the distribution functions at mesh points by an algebraic formulation in which the relevant coefficients are precomputed from the coordinates of mesh points we have successfully applied this method to simulate many two dimensional incompressible viscous flows the numerical results are very accurate and the computational time needed is much less as compared with other existing methods in this paper we mainly show the method

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

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

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

stochastic boundary value problems a white noise functional approach we give a program for solving stochastic boundary value problems involving functionals of multiparameter white noise as an example we solve the stochastic schrodinger equation ie391 1 wherev is a positive noisy potential we represent the potentialv by a white noise functional and interpret the product of the two distribution valued processesv andu as a wick productv u such an interpretation is in accordance with the usual interpretation of a white noise product in ordinary stochastic differential equations the solutionu will not be a generalized white noise functional but can be represented as anl 1 functional process

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

global flows with invariant gibbs measures for euler and navier stokes two dimensional fluids we construct a family of probability spaces p 0 associated with the euler equation for a two dimensional inviscid incompressible fluid which carries a pointwise flow t time evolution leavingp globally invariant t is obtained as the limit of galerkin approximations associated with euler equations p is also in invariant measure for a stochastic process associated with a navier stokes equation with viscosity stochastically perturbed by a white noise force

generalized stochastic processes in algebras of generalized functions stochastic processes with paths in a generalized function algebra are defined and it is shown that there exists an embedding of generalized functional stochastic processes into such ones gaussian stochastic processes with paths in an algebra of generalized functions are characterized by their first and second moments and an application to stochastic differential equations is given

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

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

traveling wave oscillatory patterns in a signed kuramoto sivashinsky equation with absorption abstract in this paper a proof of a part of a conjecture raised in galaktionov and svirshchevskii 2007 concerning existence and global uniqueness of an asymptotically stable periodic orbit in a fourth order piecewise linear ordinary differential equation is presented the fourth order equation comes from the study of traveling wave patterns in a signed kuramoto sivashinsky equation with absorption the proof is twofold first the problem of solving for the periodic orbit is transformed into a zero finding problem on r 4 which is solved with a computer assisted proof based on newton s method and the contraction mapping theorem second the rigorous bounds about the periodic orbit in phase space are combined with the theory of discontinuous dynamical systems to prove that the orbit is asymptotically stable

stationary solutions of stochastic parabolic and hyperbolic sine gordon equations the authors consider the damped sine gordon equation perturbed by thermal space time noise in the form it arises in the theory of the josephson junction and charge density waves they announce a rigorous proof that the coupling constant expansion of the solution of the initial value problem converges for small coupling taking the limit of the initial time t0 to infinity they obtain a stationary solution it is shown that the stationary solution is localized both in time and space even if the solution at finite time is not

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 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

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

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

back in the saddle again a computer assisted study of the kuramoto sivashinsky equation a numerical and analytical study of the kuramoto sivashinsky partial differential equation pde in one spatial dimension with periodic boundary conditions is presented the structure stability and bifurcation characteristics of steady state and time dependent solutions of the pde for values of the parameter alpha less than 40 are examined the numerically observed primary and secondary bifurcations of steady states as well as bifurcations to constant speed traveling waves limit cycles are analytically verified persistent homoclinic and heteroclinic saddle connections are observed and explained via the system symmetries and fixed point subspaces of appropriate isotropy subgroups of o 2 their effect on the system dynamics is discussed and several tertiary bifurcations observed numerically are presented

taylor series expansion and least squares based lattice boltzmann method two dimensional formulation and its applications an explicit lattice boltzmann method lbm is developed in this paper to simulate flows in an arbitrary geometry the method is based on the standard lbm taylor series expansion and the least squares approach the final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model theoretical analysis for the one dimensional 1d case showed that the version of the lbm could recover the navier stokes equations with second order accuracy a generalized hydrodynamic analysis is conducted to study the wave number dependence of shear viscosity for the method numerical simulations of the 2d lid driven flow in a square cavity and a polar cavity flow as well as the no flow simulation in a square cavity have been carried out favorable results were obtained and compared well with available data in the literature indicating that the present method has good prospects in practical applications

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

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

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

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

blow up profile for solutions of a fourth order nonlinear equation abstract it is well known that the nontrivial solutions of the equation u r u r f u r 0 blow up in finite time under suitable hypotheses on the initial data and f these solutions blow up with large oscillations knowledge of the blow up profile of these solutions is of great importance for instance in studying the dynamics of suspension bridges the equation is also commonly referred to as extended fisher kolmogorov equation or swift hohenberg equation in this paper we provide details of the blow up profile the key idea is to relate this blow up profile to the existence of periodic solutions for an auxiliary equation

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

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

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

nonlinear parabolic stochastic differential equations with additive colored noise on bf r d times bf r _ a regulated stochastic quantization we prove the existence of solutions to the nonlinear parabolic stochastic differential equation partial mathord left vphantom partial partial t right kern nulldelimiterspace partial t delta varphi v varphi eta c for polynomialsv of even degree with positive leading coefficient and c a gaussian colored noise process onr d r when c is colored enough that the gaussian solution to the linear problem has holder continuous covariance the nongaussian processes are almost surely realized by continuous functions uniqueness regularity properties asymptotic perturbation expansions and nonperturbative fluctuation bounds are obtained for the infinite volume processes these equations are a cutoff version of the parisi wu stochastic quantization procedure forp d models and the results of this paper rigorously establish the nonperturbative nature of regularization via modification of the noise process in the limit c gaussian white noise we find that the asymptotic expansion and the rigorous bounds agree for processes corresponding to the regulated stochastic quantization of super renormalizable and small coupling strictly renormalizable scalar field theories and disagree for nonrenormalizable models

lattice boltzmann method for conjugate natural convection with heat generation on non uniform meshes abstract in this paper the taylor series expansion and least square based lattice boltzmann method tllbm is combined with a local lattice boltzmann lb conjugate heat transfer scheme to simulate different conjugate natural convection problems in a differentially heated enclosure on non uniform meshes four case studies are designed not only to verify the developed basic tllbm fortran code but also to validate the results of the tllbm for different conjugate natural convection problems the convergence study of the presented tllbm is also carried out and the order of accuracy of the method is reported in different mesh regions it is concluded that the results of streamlines isotherms temperature distributions along a test line and average nusselt numbers calculated on the cold and hot walls of the enclosure are compared well with those available in the literature from conventional numerical methods as well as the standard lbm the computational efficiency of the tllbm is also examined through comparing the results of simulations on uniform standard lbm and non uniform tllbm meshes in terms of the accuracy and cpu time needed for solutions to converge it is shown that the tllbm is able to give accurate results with lower cpu time and mesh sizes than the standard lbm

tempered generalized functions and hermite expansions in this work we introduce an algebra of tempered generalized functions the tempered distributions are embedded in this algebra via their hermite expansions the fourier transform is naturally extended to this algebra in such a way that the usual relations involving multiplication convolution and differentiation are valid furthermore we give a generalized ito formula in this context and some applications to stochastic analysis

strong solutions to the stochastic quantization equations we prove the existence and uniqueness of a strong solution of the stochastic quantization equation in dimension 2 for almost all initial data with respect to the invariant measure the method is based on a fixed point result in suitable besov spaces

stochastic quantization of field theory in finite and infinite volume abstract using the theory of dirichlet forms a distribution valued symmetric markov process is constructed so that it has the 4 2 measure as its invariant probability measure several properties of this process are proved and a finite to infinite volume limit theorem is established

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

sliding motion in filippov differential systems theoretical results and a computational approach in this work we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right hand sides of filippov type in particular i we propose second order corrections to the theory of filippov ii we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity and iii we propose and implement a numerical method to approximate a trajectory of systems with discontinuous right hand sides and illustrate its performance on a few examples

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

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

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

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

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

generalized stochastic processes in algebras of generalized functions independence stationarity and spdes abstract stochastic processes are regarded in the framework of colombeau type algebras of generalized functions colombeau stochastic processes with independent values and stationary colombeau stochastic processes are studied with special attention paid to the property of translational invariance of generalized functions processes with stationary increments are characterized via stationarity of their gradient gaussian stationary solutions are analyzed for linear stochastic partial differential equations with generalized constant coefficients in the framework of colombeau stochastic processes

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

validated continuation for equilibria of pdes one of the most efficient methods for determining the equilibria of a continuous parameterized family of differential equations is to use predictor corrector continuation techniques in the case of partial differential equations this procedure must be applied to some finite dimensional approximation which of course raises the question of the validity of the output we introduce a new technique that combines the information obtained from the predictor corrector steps with ideas from rigorous computations and verifies that the numerically produced equilibrium for the finite dimensional system can be used to explicitly define a set which contains a unique equilibrium for the infinite dimensional partial differential equation using the cahn hilliard and swift hohenberg equations as models we demonstrate that the cost of this new validated continuation is less than twice the cost of the standard continuation method alone

strong uniqueness for both dirichlet operators and stochastic dynamics to gibbs measures on a path space with exponential interactions abstract we prove l p uniqueness of dirichlet operators for gibbs measures on the path space c r r d associated with exponential type interactions in infinite volume by extending an spde approach presented in previous work by the last two named authors we also give an spde characterization of the corresponding dynamics in particular for the first time we prove existence and uniqueness of a strong solution for the spde though the self interaction potential is not assumed to be differentiable hence the drift is possibly discontinuous as examples to which our results apply we mention the stochastic quantization of p 1 exp 1 and trigonometric quantum fields in infinite volume in particular our results imply essential self adjointness of the generator of the stochastic dynamics for these models finally as an application of the strong uniqueness result for the spde we prove some functional inequalities for diffusion semigroups generated by the above dirichlet operators

a white noise approach to a class of non linear stochastic heat equations abstract cauchy problems for a class of non linear stochastic evolution equations are studied they are formulated as integral equations for generalized random fields by methods of white noise analysis s transformation characterization theorem etc these problems are reduced to fixed point problems in appropriatly constructed banach spaces this technique provides a systematic treatment of existence and uniqueness questions for a variety of equations the method is applied to non linear heat equations non linear volterra equations and non linear ordinary differential equations which may all be anticipating for each case examples are given such as the stochastic burgers equation and stochastic reaction diffusion equations

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

generalized solutions of the multidimensional stochastic burgers equation abstract we introduce a new concept of weak solution for the conservative stochastic burgers equation in any dimension the definition is based on weak solution concepts introduced by various authors in order to make sense of equations which do not have solutions in the sense of distributions in one dimension the solution reduces to the classical distributional solution of the 1 d stochastic burgers equation

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

order and complexity in the kuramoto sivashinsky model of weakly turbulent interfaces abstract we present a large number of new geometric ergodic and statistical properties of the kuramoto sivashinsky equation modeling interfacial turbulence in various physical contexts in addition this equation has the remarkable property of inertial manifolds where some finite dimensional dynamical system is rigorously equivalent to this infinite dimensional partial differential equation in moderate size domains up to ten periods in length a low dimensional vector field skeleton underpins even strongly chaotic regimes and controls the bifurcations of the inertial manifold the extreme numerical sensitivity of chaos in this dissipative pde requires very high precision methods despite the geometrical complexities of the bifurcation structure some statistical properties remain remarkably simple there is overwhelming evidence that for some parameter values a permanent unsteady state exists an unexpectedly simple diffusive relaxation of the large scale fluctuations is extracted from extensive numerical simulations in these calculations we observe long time tails for the correlation functions of relevant quantities we propose an explanation in terms of an effective viscosity and compare the transport in the weakly turbulent interface with related theories for random interfaces and developed turbulence

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

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

a two space dimensional semilinear heat equation perturbed by gaussian white noise a two space dimensional heat equation perturbed by a white noise in a bounded volume is considered the equation is perturbed by a non linearity of the type f au where means wick re ordering with respect to the free solution a are small parameters u denotes a solution f is the fourier transform of a complex measure with compact support

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

numerical simulation of natural convection in a concentric annulus between a square outer cylinder and a circular inner cylinder using the taylor series expansion and least squares based lattice boltzmann method in this paper natural convective heat transfer in a horizontal concentric annulus between a square outer cylinder and a heated circular inner cylinder is numerically studied using the taylor series expansion and least squares based lattice boltzmann method tllbm the tllbm is used to extend the current thermal model to more practical applications since the tllbm is basically a meshless approach and can be applied to any complex geometry we can easily use it to solve the complex thermal problem accurately and effectively the present method is validated by comparing its numerical results with available data in the literature and very good agreement has been achieved

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

unstable recurrent patterns in kuramoto sivashinsky dynamics we undertake an exploration of recurrent patterns in the antisymmetric subspace of the one dimensional kuramoto sivashinsky system for a small but already rather turbulent system the long time dynamics takes place on a low dimensional invariant manifold a set of equilibria offers a coarse geometrical partition of this manifold the newton descent method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions the attracting set appears surprisingly thin its backbone consists of several smale horseshoe repellers well approximated by intrinsic local one dimensional return maps each with an approximate symbolic dynamics the dynamics appears decomposable into chaotic dynamics within such local repellers interspersed by rapid jumps between them

positivity and positive definiteness in generalized function algebras the definitions of positivity and positive definiteness are extended to generalized function algebras in coherence with the corresponding notions for distributions versions of bochner s theorem for a positive definite colombeau generalized function are given