a fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles abstract a new fast numerical method for solving the three dimensional stokes equations in the presence of suspended particles is presented the fluid dynamics equations are solved on a lattice a particle is represented by a set of points each of which moves at the local fluid velocity and is not constrained to lie on the lattice these points are coupled by forces which resist deformation of the particle these forces contribute to the force density in the stokes equations as a result a single set of fluid dynamics equations holds at all points of the domain and there are no internal boundaries particle size shape and deformability may be prescribed computational work increases only linearly with the number of particles so large numbers 500 1000 of particles may be studied efficiently the numerical method involves implicit calculation of the particle forces by minimizing an energy function and solution of a finite difference approximation to the stokes equations using the fourier toeplitz method the numerical method has been implemented to run on all cray computers the implementation exploits the cray s vectorized arithmetic and on machines with insufficient central memory it performs efficient disk 1 o while storing most of the data on disk applications of the method to sedimentation of one two and many particle systems are described trajectories and settling speeds for two particle sedimentation and settling speed for multiparticle sedimentation from initial distributions on a cubic lattice or at random give good quantitative agreement with existing theories

a simple direct heating thermal immersed boundary lattice boltzmann method for its application in incompressible flow abstract a simple direct heating thermal immersed boundary lattice boltzmann method for buoyancy driven incompressible flow with complex geometry boundaries is developed to simulate natural convection with curved boundary in the newly developed method both dirichlet and neumann boundary conditions in macroscopic equation are deduced into a novel mesoscopic discrete heat source the mesoscopic discrete heat source consists of simplified explicit discrete heat source scheme which reduces the computational complexities and is introduced into lattice boltzmann equation for temperature field which extends the idea of the previous direct forcing ib lbm both isothermal boundary condition i e dirichlet boundary condition and constant heat flux boundary condition i e neumann boundary condition are considered in our simulations the efficiency and accuracy of the present method are demonstrated by simulating both two dimensional and three dimensional thermal flow with curved boundaries numerical results indicate that the efficiency and accuracy of the present method are well consistent with experimental and the other numerical results the present method has also been successfully applied to three dimensional simulations of natural convection in a thin annulus with adiabatic wall at both vertical sides

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

the immersed boundary lattice boltzmann method for solving fluid particles interaction problems a new computational method the immersed boundary lattice boltzmann method is presented this method is a combination and utilizes the most desirable features of the lattice boltzmann and the immersed boundary methods the method uses a regular eulerian grid for the flow domain and a lagrangian grid to follow particles that are contained in the flow field the rigid body conditions for the fluid and the particles are enforced by a penalty method which assumes that the particle boundary is deformable with a high stiffness constant the velocity field of the fluid and particles is solved by adding a force density term into the lattice boltzmann equation this novel method preserves the advantages of lbm in tracking a group of particles and at the same time provides an alternative and better approach to treating the solid fluid boundary conditions the method also solves the problems of fluctuation of the forces and velocities on the particles when the bounce back boundary conditions are applied this method enables one to simulate problems with particle deformation and fluid structure deformation its results are validated by comparison with results from other methods

comparison of boundary slip for two variants of immersed boundary method in lattice boltzmann framework abstract in this paper the immersed moving boundary lattice boltzmann imb lb method is compared with the single relaxation time and multiple relaxation time versions of the immersed boundary lattice boltzmann ib lb method in terms of the amount of numerical velocity slip produced on solid boundaries the comparisons are performed for both straight and curved boundaries based on the effects of thickness of virtual domain used in the ib method for the first time and relaxation time parameter s of the lb method for the straight boundaries a shear flow problem is studied while for the curved boundaries a falling circular cylinder in an infinite channel is investigated first sensitivities of the ib lb and imb lb methods to the relaxation time parameter s and thickness of virtual domain are presented then the interaction of two solid particles in a shear flow is studied to assess the validity of arguments presented in solving a typical practical problem

a lbm dlm fd method for 3d fluid structure interactions the previously developed lbm dlm fd method derived from the lattice boltzmann method and the distributed lagrange multiplier fictitious domain method is extended to deal with 3d fluid structure interactions in our current algorithm the fluid motion is solved by lbm the deformation of the solid body is solved by the finite element method and the lagrange multiplier is solved on the low order mesh three numerical examples are employed to validate the lbm dlm fd method and reveal the potential of the method to deal with the fluid elastic body interaction problems

application of a ghost fluid approach for a thermal lattice boltzmann method in this paper a ghost fluid gf method is utilized to propose a numerical approach to enhance the capability of thermal lattice boltzmann method tlbm in dealing with complex geometries a ghost fluid approach is imposed on a double population thermal lattice boltzmann method a cartesian grid handles the flow and the boundaries are imposed by a ghost fluid approach the essence of this method is to decompose the unknown distribution functions into equilibrium and non equilibrium parts at each ghost points the major quantities are extrapolated from the image points to the corresponding ghost points to form the equilibrium parts the non equilibrium parts are then determined by using the bounce back scheme the method is relatively easy to apply and second order accurate there is no need to modify the original governing equations and both dirichlet and neumann boundary conditions can be handled the method is applied to couette flow between two concentric circular cylinders natural convection in a square cavity natural convection in an annulus and a forced convection in a lid driven semi circular cavity the results obtained are generally in good agreement with that predicted by other theoretical and numerical efforts

immersed boundary lattice boltzmann model based on multiple relaxation times as an alterative version of the lattice boltzmann models the multiple relaxation time mrt lattice boltzmann model introduces much less numerical boundary slip than the single relaxation time srt lattice boltzmann model if some special relationship between the relaxation time parameters is chosen on the other hand most current versions of the immersed boundary lattice boltzmann method which was first introduced by feng and improved by many other authors suffer from numerical boundary slip as has been investigated by le and zhang to reduce such a numerical boundary slip an immerse boundary lattice boltzmann model based on multiple relaxation times is proposed in this paper a special formula is given between two relaxation time parameters in the model a rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single relaxation time based model

optimum receiver for a realistic transmit receive diversity system in correlated fading a transmit receive diversity system in correlated rayleigh fading in which the receiver estimates the channel through pilot symbols and feeds this information back to the transmitter through a feedback path is considered the imperfect channel state information csi is used by the transmitter to obtain the transmit weight vector for data transmission the optimum receiver in the maximum likelihood ml sense obtained from the conditional distribution of the received signal vector conditioned on the imperfect csi and the transmit weight vector is derived for the system for the case of m ary phase shift keying mpsk an analytical expression for the conditional symbol error probability sep conditioned on the channel estimate and the transmit weight vector is obtained with the transmit weight vector chosen to minimize this conditional sep for the receive only and transmit only correlation scenarios with ill conditioned eigenvalues of the receive and transmit covariance matrices that is some of the eigenvalues are very small we derive expressions for the diversity gain numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading these results show that the optimum receiver typically has about a 0 5 db gain over a conventional receiver when the correlation coefficient exceeds 0 5 and the number of receive antennas is much larger than the number of transmit antennas

an improved momentum exchanged based immersed boundary lattice boltzmann method by using an iterative technique a novel immersed boundary lattice boltzmann method ib lbm is proposed for incompressible viscous flows in complex geometries based on the momentum exchanged based ib lbm an iterative technique is introduced to enforce the non slip boundary condition at the boundary points moreover the proposed ib lbm overcomes the drawback that the numerical results of the previous work wu and shu 2009 which is affected by the distribution of lagrangian points a simple theoretical analysis is developed to obtain the optimal iteration parameters numerical results show that the present scheme has second order accuracy and is not affected by the distribution of lagrangian points it also shows that the non slip boundary condition is satisfied on the boundary this verifies that our ib lbm is capable of simulating flow problems with complex boundaries

navier stokes simulation with constraint forces finite difference method for particle laden flows and complex geometries building on an idea of fogelson and peskin j comput phys 79 50 1988 we describe the implementation and verification of a simulation technique for systems of non brownian particles in fluids at reynolds numbers up to about 20 on the particle scale this direct simulation technique fills a gap between simulations in the viscous regime and high reynolds number modeling it also combines sufficient computational accuracy with numerical efficiency and allows studies of several thousand in principle arbitrarily shaped extended and hydrodynamically interacting particles on regular work stations we verify the algorithm in two and three dimensions for i single falling particles and ii a fluid flowing through a bed of fixed spheres in the context of sedimentation we compute the volume fraction dependence of the mean sedimentation velocity the results are compared with experimental and other numerical results both in the viscous and inertial regime and we find very satisfactory agreement

a non iterative direct forcing immersed boundary method for strongly coupled fluid solid interactions a non iterative direct forcing immersed boundary method is presented for the strongly coupled simulations of fluid solid interactions while it retains many advantages of the immersed boundary framework by yang and stern 2012 30 especially the simplified field extension strategy for moving boundary treatment and the pointwise integration of hydrodynamic force using the momentum forcing term the present approach improves upon the previous method in several aspects including optimized computational cost for a strong coupling scheme reduced algorithm complexity for a straightforward implementation and enhanced numerical stability for low density ratio problems central to these improvements is a simple intermediate step in which the velocity fields around solid bodies are predicted on temporary non inertial reference frames attached to moving solid bodies in a one to one manner this step enables the explicit inverse of the implicit equations for rigid body dynamics thus rendering unnecessary the previous predictor corrector scheme for iteratively adjusting the displacements and velocities of the immersed bodies until reaching a convergence in addition a simple generalized procedure is developed to obtain the interpolation coefficients in a local reconstruction stencil explicitly from the geometric relationship for verification and validation the vortex induced vibration of a circular cylinder and the rotational galloping of a rectangular body are considered first then several particulate flow problems including settling and buoyant particles of low density ratios a settling particle in a small container and the kissing drafting tumbling problem of two settling particles are studied the agreement between the present results and the reference data in the literature is excellent an overall second order accuracy of the algorithm is verified in two systematic grid convergence tests the present idea can be easily applied to similar methods for achieving a strong coupling scheme on top of a weak one with a nominal increase in the computational cost details of the algorithm are provided to facilitate its implementation in other solvers using non boundary conforming grids

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

a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies application to particulate flow abstract in this article we discuss a methodology that allows the direct numerical simulation of incompressible viscous fluid flow past moving rigid bodies the simulation methods rest essentially on the combination of a lagrange multiplier based fictitious domain methods which allow the fluid flow computations to be done in a fixed flow region b finite element approximations of the navier stokes equations occurring in the global model c time discretizations by operator splitting schemes in order to treat optimally the various operators present in the model the above methodology is particularly well suited to the direct numerical simulation of particulate flow such as the flow of mixtures of rigid solid particles and incompressible viscous fluids possibly non newtonian we conclude this article with the presentation of the results of various numerical experiments including the simulation of store separation for rigid airfoils and of sedimentation and fluidization phenomena in two and three dimensions

development of an immersed boundary phase field lattice boltzmann method for neumann boundary condition to study contact line dynamics the implementation of neumann boundary condition in the framework of immersed boundary method ibm is presented in this paper to simulate contact line dynamics using a phase field lattice boltzmann method immersed boundary method 10 is known as an efficient algorithm for modelling fluid solid interaction abundance of prominent works have been devoted to refine ibm 1 11 12 however they are mainly restricted to problems with dirichlet boundary condition research that implements the neumann boundary condition in ibm is very limited to the best of our knowledge this deficiency significantly limits the application of ibm in computational fluid dynamics cfd since physical phenomena associated with neumann boundary conditions are extremely diverse the difficulty is attributed to the fact that implementation of neumann boundary condition is much more complex than that of dirichlet boundary condition in the present work we initiate the first endeavour to implement neumann boundary condition in ibm with assistance of its physical interpretation rather than simple mathematical manipulation concretely speaking rooted from physical conservation law the neumann boundary condition is considered as contribution of flux from the boundary to its relevant physical parameter in a control volume moreover the link between the flux and its corresponding flow field variable is directly manipulated through the immersed boundary concept in this way the neumann boundary conditions can be implemented in ibm the developed method is applied together with phase field lattice boltzmann method to study contact line dynamics the phase field method 27 39 which becomes increasingly popular in multiphase flow simulation can efficiently capture complex interface topology and naturally resolve the contact line singularity meanwhile the lattice boltzmann method is known as an alternative to model fluid dynamics and holds good prospect to simulate multiphase flows with complex geometry 38 in this context the developed immersed boundary phase field lbm is verified in detail for both steady and unsteady contact line problems tests show that the proposed method can correctly reproduce both equilibrium results and dynamic process

analysis of the fully discrete fat boundary method the fat boundary method is a method of the fictitious domain class which was proposed to solve elliptic problems in complex geometries with non conforming meshes it has been designed to recover optimal convergence at any order despite of the non conformity of the mesh and without any change in the discrete laplace operator on the simple shape domain we propose here a detailed proof of this high order convergence and propose some numerical tests to illustrate the actual behaviour of the method

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

a lattice boltzmann front tracking method for interface dynamics with surface tension in two dimensions we propose to combine the lattice boltzmann equation lbe and the front tracking ft method to simulate interfacial dynamics with surface tension in two dimensions 2d in the proposed lbe ft method the flow is modeled by the lbe on a fixed cartesian mesh whereas interfaces are explicitly tracked by a set of markers that are advected by the flow the interface curvature is computed from adjacent markers and is then used to determine surface tension according to laplace s law the local capillary forces evaluated at the markers are distributed to nearby eulerian grid points according to a smearing function to approximate the dirac delta function due to peskin to validate the proposed lbe ft method we simulate 1 a circular bubble in a flow either quiescent or moving with a constant velocity and 2 the decaying capillary waves at the interface of two fluids of equal viscosities and densities for the circular bubble the spurious current measured in the lbe ft is weaker than that observed in the standard volume of fluid method and some existing lbe models for the capillary waves the numerical results of the period t or frequency the attenuation rate the surface tension and the root mean square error of the wave amplitude agree well with the normal mode and prosperetti s solutions the proposed lbe ft method is shown to have a second order rate of convergence we also show that the lbe ft method is superior to the existing lattice bgk diffusive interface method in terms of accuracy of interface representation numerical stability and computational efficiency

a hybrid method to study flow induced deformation of three dimensional capsules a hybrid method is proposed to study the transient deformation of liquid filled capsules with elastic membranes under flow in this method the immersed boundary concept is introduced into the framework of lattice boltzmann method and the multi block strategy is employed to refine the mesh near the capsule to increase the accuracy and efficiency of computation a finite element model is incorporated to obtain the forces acting on the membrane nodes of the three dimensional capsule which is discretized into flat triangular elements the present method was validated by studying the transient deformation of initially spherical and oblate spheroidal capsules with various membrane constitutive laws under shear flow and there were good agreements with previous theory or numerical results the versatility of the present method was demonstrated by studying the effects of inertia on the deformation of capsules in shear flow and the inertia effects were found to be significant the transient deformation of capsules with initially biconcave discoid shape in shear flow was also studied the unsteady tank treading motion was observed in which the capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside to our knowledge this motion of three dimensional biconcave discoid capsules has not been fully recovered by numerical simulation so far

proteus a direct forcing method in the simulations of particulate flows a new and efficient direct numerical method for the simulation of particulate flows is introduced the method combines desired elements of the immersed boundary method the direct forcing method and the lattice boltzmann method adding a forcing term in the momentum equation enforces the no slip condition on the boundary of a moving particle by applying the direct forcing scheme proteus eliminates the need for the determination of free parameters such as the stiffness coefficient in the penalty scheme or the two relaxation parameters in the adaptive forcing scheme the method presents a significant improvement over the previously introduced immersed boundary lattice boltzmann method ib lbm where the forcing term was computed using a penalty method and a user defined parameter the method allows the enforcement of the rigid body motion of a particle in a more efficient way compared to the bounce back scheme used in the conventional lbm the direct forcing method provides a smoother computational boundary for particles and is capable of achieving results at higher reynolds number flows by using a set of lagrangian points to track the boundary of a particle proteus eliminates any need for the determination of the boundary nodes that are prescribed by the bounce back scheme at every time step it also makes computations for particles of irregular shapes simpler and more efficient proteus has been developed in two as well as three dimensions this new method has been validated by comparing its results with those from experimental measurements for a single sphere settling in an enclosure under gravity as a demonstration of the efficiency and capabilities of the present method the settling of a large number 1232 of spherical particles is simulated in a narrow box under two different boundary conditions it is found that when the no slip boundary condition is imposed at the front and rear sides of the box the particles motion is significantly hindered under the periodic boundary conditions the particles move faster the simulations show that the sedimentation characteristics in a box with periodic boundary conditions at the two sides are very close to those found in the sedimentation of two dimensional circular particles

a second order accurate immersed boundary lattice boltzmann method for particle laden flows abstract a new immersed boundary lattice boltzmann method ib lbm is presented for fully resolved simulations of incompressible viscous flows laden with rigid particles the immersed boundary method ibm recently developed by breugem 2012 19 is adopted in the present method development including the retraction technique the multi direct forcing method and the direct account of the inertia of the fluid contained within the particles the present ib lbm is however formulated with further improvement with the implementation of the high order runge kutta schemes in the coupled fluid particle interaction the major challenge to implement high order runge kutta schemes in the lbm is that the flow information such as density and velocity cannot be directly obtained at a fractional time step from the lbm since the lbm only provides the flow information at an integer time step this challenge can be however overcome as given in the present ib lbm by extrapolating the flow field around particles from the known flow field at the previous integer time step the newly calculated fluid particle interactions from the previous fractional time steps of the current integer time step are also accounted for in the extrapolation the ib lbm with high order runge kutta schemes developed in this study is validated by several benchmark applications it is demonstrated for the first time that the ib lbm has the capacity to resolve the translational and rotational motion of particles with the second order accuracy the optimal retraction distances for spheres and tubes that help the method achieve the second order accuracy are found to be around 0 30 and 0 47 times of the lattice spacing respectively simulations of the stokes flow through a simple cubic lattice of rotational spheres indicate that the lift force produced by the magnus effect can be very significant in view of the magnitude of the drag force when the practical rotating speed of the spheres is encountered this finding may lead to more comprehensive studies of the effect of the particle rotation on fluid solid drag laws it is also demonstrated that when the third order or the fourth order runge kutta scheme is used the numerical stability of the present ib lbm is better than that of all methods in the literature including the previous ib lbms and also the methods with the combination of the ibm and the traditional incompressible navier stokes solver

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

immersed boundary method for the simulation of 2d viscous flow based on vorticity velocity formulations a new immersed boundary method based on vorticity velocity formulations for the simulation of 2d incompressible viscous flow is proposed in present paper the velocity and vorticity are respectively divided into two parts one is the velocity and vorticity without the influence of the immersed boundary and the other is the corrected velocity and the corrected vorticity derived from the influence of the immersed boundary the corrected velocity is obtained from the multi direct forcing to ensure the well satisfaction of the no slip boundary condition at the immersed boundary the corrected vorticity is derived from the vorticity transport equation the third order runge kutta for time stepping the fourth order finite difference scheme for spatial derivatives and the fourth order discretized poisson for solving velocity are applied in present flow solver three cases including decaying vortices flow past a stationary circular cylinder and an in line oscillating cylinder in a fluid at rest are conducted to validate the method proposed in this paper and the results of the simulations show good agreements with previous numerical and experimental results this indicates the validity and the accuracy of present immersed boundary method based on vorticity velocity formulations

a second order method for three dimensional particle simulation this paper describes a numerical method for the direct numerical simulation of navier stokes flows with one or more solid spheres the particles may be fixed or mobile and they may have different radii the basic idea of the method stems from the observation that due to the no slip condition in the reference frame of each particle the velocity near the particle boundary is very small so that the stokes equations constitute an excellent approximation to the full navier stokes problem the general analytic solution of the stokes equations can then be used to transfer the no slip condition from the particle surface to the adjacent grid nodes in this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used the method is validated by a detailed comparison with spectral solutions for the flow past a sphere at reynolds numbers of 50 and 100 the existence in these situations of a stokes region near the particle is explicitly demonstrated other numerical experiments to show the performance of the code are also described to illustrate the power and efficiency of the method a simulation of decaying homogeneous turbulence in a cell containing 100 moveable spheres is described as implemented here the method can only be applied to simple body shapes such as spheres and cylinders extensions to more general situations are mentioned in the last section

a pre conditioned implicit direct forcing based immersed boundary method for incompressible viscous flows a novel immersed boundary ib method based on an implicit direct forcing idf scheme is developed for incompressible viscous flows the key idea for the present idf method is to use a block lu decomposition technique in momentum equations with taylor series expansion to construct the implicit ib forcing in a recurrence form which imposes more accurate no slip boundary conditions on the ib surface to accelerate the ib forcing convergence during the iterative procedure a pre conditioner matrix is introduced in the recurrence formulation of the ib forcing a jacobi type parameter is determined in the pre conditioner matrix by minimizing the frobenius norm of the matrix function representing the difference between the ib forcing solution matrix and the pre conditioner matrix in addition the pre conditioning parameter is restricted due to the numerical stability in the recurrence formulation consequently the present pre conditioned idf pidf enables accurate calculation of the ib forcing within a few iterations we perform numerical simulations of two dimensional flows around a circular cylinder and three dimensional flows around a sphere for low and moderate reynolds numbers the result shows that pidf yields a better imposition of no slip boundary conditions on the ib surfaces for low reynolds number with a fairly larger time step than ib methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the ib forcing finally we demonstrate the robustness of the present pidf scheme by numerical simulations of flow around a circular array of cylinders flows around a falling sphere and two sedimenting spheres in gravity

inversion of nonlinear stochastic operators abstract the operator theoretic method adomian and malakian j math anal appl 76 1 1980 183 201 recently extended adomian s solutions of nonlinear stochastic differential equations g adomian stochastic systems analysis in applied stochastic processes nonlinear stochastic differential equations j math anal appl 55 1 1976 441 452 on the modeling and analysis of nonlinear stochastic systems in proceeding international conf on mathematical modeling vol 1 pp 29 40 to provide an efficient computational procedure for differential equations containing polynomial exponential and trigonometric nonlinear terms n y the procedure depends on the calculation of certain quantities an and bn this paper generalizes the calculation of the an and bn to much wider classes of nonlinearities of the form n y y essentially the method provides a systematic computational procedure for differential equations containing any nonlinear terms of physical significance this procedure depends on a recurrence rule from which explicit general formulae are obtained for the quantities an and bn for any order n in a convenient form this paper also demonstrates the significance of the iterative series decomposition proposed by adomian for linear stochastic operators in 1964 and developed since 1976 for nonlinear stochastic operators since both the nonlinear and stochastic behavior is quite general the results are extremely significant for applications processes need not for example be limited to either gaussian processes white noise or small fluctuations

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

a lattice boltzmann based implicit immersed boundary method for fluid structure interaction the immersed boundary method is a practical and effective method for fluid structure interaction problems it has been applied to a variety of problems most of the time stepping schemes used in the method are explicit which suffer a drawback in terms of stability and restriction on the time step we propose a lattice boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step the fully nonlinear algebraic system resulting from discretizations is solved by an inexact newton krylov method in a jacobian free manner the test problem of a flexible filament in a flowing viscous fluid is considered numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost

particulate immersed boundary method for complex fluid particle interaction problems with heat transfer in our recent work zhang et al 2015 a particulate immersed boundary method pibm for simulating fluid particle multiphase flow was proposed and assessed in both two and three dimensional applications in this study the pibm was extended to solve thermal interaction problems between spherical particles and fluid the lattice boltzmann method lbm was adopted to solve the fluid flow and temperature fields the pibm was responsible for the no slip velocity and temperature boundary conditions at the particle surface and the kinematics and trajectory of the solid particles were evaluated by the discrete element method dem four case studies were implemented to demonstrate the capability of the current coupling scheme firstly numerical simulation of natural convection in a two dimensional square cavity with an isothermal concentric annulus was carried out for verification purpose the current results were found to have good agreement with previous references then sedimentation of two and three dimensional isothermal particles in fluid was numerically studied respectively the instantaneous temperature distribution in the cavity was captured the effect of the thermal buoyancy on particle behaviors was discussed finally sedimentation of three dimensional thermosensitive particles in fluid was numerically investigated our results revealed that the lbm pibm dem is a promising scheme for the solution of complex fluid particle interaction problems with heat transfer