an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

demiclosedness principle with applications for asymptotically pseudo contractions in hilbert spaces abstract in the present paper we establish a demiclosedness principle for asymptotically pseudo contractions in hilbert spaces as its applications we obtain a new fixed point theorem some weak and strong convergence theorems for asymptotically pseudo contractions the results of this paper are interesting extensions of those known results

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

implicit velocity correction based immersed boundary lattice boltzmann method and its applications a version of immersed boundary lattice boltzmann method ib lbm is proposed in this work it is based on the lattice boltzmann equation with external forcing term proposed by guo et al z guo c zheng b shi discrete lattice effects on the forcing term in the lattice boltzmann method phys rev e 65 2002 046308 which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect in this model the velocity is contributed by two parts one is from the density distribution function and can be termed as intermediate velocity and the other is from the external force and can be considered as velocity correction in the conventional ib lbm the force density external force is explicitly computed in advance as a result we cannot manipulate the velocity correction to enforce the non slip boundary condition at the boundary point in the present work the velocity corrections force density at all boundary points are considered as unknowns which are computed in such a way that the non slip boundary condition at the boundary points is enforced the solution procedure of present ib lbm is exactly the same as the conventional ib lbm except that the non slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results this is not the case for the results obtained by the conventional ib lbm another advantage of the present method is its simple calculation of force on the boundary the force can be directly calculated from the relationship between the velocity correction and the force density

a freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes in this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes the approach consists of three main steps 1 surface partitioning of polygonal meshes into different patches 2 a new freeform perturbation scheme of using the cox de boor basis function over arbitrary polygonal meshes which supports multi resolution shape optimization and does not require cad information 3 freeform shape optimization of arbitrary polygonal or polyhedral meshes numerical experiments indicate the effectiveness of the proposed approach copyright 2004 john wiley sons ltd

how good is recursive bisection the most commonly used p way partitioning method is recursive bisection rb it first divides a graph or a mesh into two equal sized pieces by a good bisection algorithm and then recursively divides the two pieces ideally we would like to use an optimal bisection algorithm because the optimal bisection problem that partitions a graph into two equal sized subgraphs to minimize the number of edges cut is np complete practical rb algorithms use more efficient heuristics in place of an optimal bisection algorithm most such heuristics are designed to find the best possible bisection within allowed time we show that the rb method even when an optimal bisection algorithm is assumed may produce a p way partition that is very far way from the optimal one our negative result is complemented by two positive ones first we show that for some important classes of graphs that occur in practical applications such as well shaped finite element and finite difference meshes rb is within a constant factor of the optimal one almost always second we show that if the balance condition is relaxed so that each block in the p way partition is bounded by 2n p where n is the number of vertices of the graph then a modified rb finds an approximately balanced p way partition whose cost is within an o log p factor of the cost of the optimal p way partition

full scale solutions to particle laden flows multidirect forcing and immersed boundary method towards getting the full scale solutions to particle laden flows a multidirect forcing technique and immersed boundary method are proposed in the present work the immersed solid boundary is represented by lagrangian points and the no slip condition is efficiently satisfied by exerting multidirect forcing the hydrodynamic interactions between the stationary or moving solid boundary and the newtonian fluid are able to be accurately described this method is simple but efficient which is validated by simulating the flows around a stationary circular disc at different reynolds numbers and the free sedimentation of a particle the predicted results agree well with previous experimental and numerical data when applying this method to study particle sedimentation near a vertical wall the rotation shifting phenomenon is observed besides the anomalous rolling and the lateral migration

compactness and the fixed point property in l1 abstract in this paper we prove that compactness can be characterized by means of the existence of a fixed point for some classes of mappings defined on convex closed subsets of the space l 1 nominally our result involves nonexpansive mappings uniformly lipschitzian mappings and cascading nonexpansive mappings we also extend the results to some more general classes of banach spaces

min max boundary domain decomposition domain decomposition is one of the most effective and popular parallel computing techniques for solving large scale numerical systems in the special case when the amount of computation in a subdomain is proportional to the volume of the subdomain domain decomposition amounts to minimizing the surface area of each subdomain while dividing the volume evenly motivated by this fact we study the following min max boundary multi way partitioning problem given a graph g and an integer k 1 we would like to divide g into k subgraphs g1 gk by removing edges such that i gi g k for all i 1 k and ii the maximum boundary size of any subgraph the set of edges connecting it with other subgraphs is minimized we provide an algorithm that given g a well shaped mesh in d dimensions finds a partition of g into k subgraphs g1 gk such that for all i gi has g k vertices and the number of edges connecting gi with the other subgraphs is o g k 1 1 d our algorithm can find such a partition in o g logk time finally we extend our results to vertex weighted and vertex based graph decomposition our results can be used to simultaneously balance the computational and memory loads on a distributed memory parallel computer without incurring large communication overhead

geometric separators for finite element meshes we propose a class of graphs that would occur naturally in finite element and finite difference problems and we prove a bound on separators for this class of graphs graphs in this class are embedded in d dimensional space in a certain manner for d dimensional graphs our separator bound is o n d 1 d which is the best possible bound we also propose a simple randomized algorithm to find this separator in o n time this separator algorithm can be used to partition the mesh among processors of a parallel computer and can also be used for the nested dissection sparse elimination algorithm

geometric mesh partitioning implementation and experiments we investigate a method of dividing an irregular mesh into equal sized pieces with few interconnecting edges the method s novel feature is that it exploits the geometric coordinates of the mesh vertices it is based on theoretical work of miller teng thurston and vavasis who showed that certain classes of well shaped finite element meshes have good separators the geometric method is quite simple to implement we describe a sc matlab code for it in some detail the method is also quite efficient and effective we compare it with some other methods including spectral bisection

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

separators for sphere packings and nearest neighbor graphs a collection of n balls in d dimensions forms a k ply system if no point in the space is covered by more than k balls we show that for every k ply system there is a sphere s that intersects at most o k 1 d n 1 1 d balls of and divides the remainder of into two parts those in the interior and those in the exterior of the sphere s respectively so that the larger part contains at most 1 1 d 2 n balls this bound of o k 1 d n 1 1 d is the best possible in both n and k we also present a simple randomized algorithm to find such a sphere in o n time our result implies that every k nearest neighbor graphs of n points in d dimensions has a separator of size o k 1 d n 1 1 d in conjunction with a result of koebe that every triangulated planar graph is isomorphic to the intersection graph of a disk packing our result not only gives a new geometric proof of the planar separator theorem of lipton and tarjan but also generalizes it to higher dimensions the separator algorithm can be used for point location and geometric divide and conquer in a fixed dimensional space

cut element based immersed boundary method for moving geometries in compressible liquid flows with cavitation the conservative immersed interface method for representing complex immersed solid boundaries or phase interfaces on cartesian grids is improved and extended to allow for the simulation of weakly compressible fluid flows through moving geometries we demonstrate that an approximation of moving interfaces by a level set field results in unphysical oscillations in the vicinity of sharp corners when dealing with weakly compressible fluids such as water by introducing an exact reconstruction of the cut cell properties directly based on a surface triangulation of the immersed boundary we are able to recover the correct flow evolution free of numerical artifacts the new method is based on cut elements it provides sub cell resolution of the geometry and handles flows through narrow closing or opening gaps in a straightforward manner we validate our method with canonical flows around oscillating cylinders we demonstrate that the method allows for an accurate prediction of flows around moving obstacles in weakly compressible liquid flows with cavitation effects in particular we show that the cavitating flow through a closing fuel injector control valve which is an example for a complex application with interaction of stationary and moving parts can be predicted by the method

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

a novel iterative direct forcing immersed boundary method and its finite volume applications we present a novel iterative immersed boundary ib method in which the body force updating is incorporated into the pressure iterations because the body force and pressure are solved simultaneously the boundary condition on the immersed boundary can be fully verified the computational costs of this iterative ib method is comparable to those of conventional ib methods we also introduce an improved body force distribution function which transfers the body force in the discrete volume of ib points to surrounding cartesian grids totally to alleviate the demanding computational requirements of a full resolved direct numerical simulation a wall layer model is presented the accuracy and capability of the present method is verified by a variety of two and three dimensional numerical simulations ranging from laminar flow past a cylinder and a sphere to turbulent flow around a cylinder the improvement of the iterative ib method is fully demonstrated and the influences of different body force distribution strategies is discussed

fixed points of uniformly lipschitzian mappings in spaces with uniformly normal structure dans un espace de banach x on etudie quand reflexivite et structure normale sont suffisantes pour assurer pour de bon 1 la propriete de point fixe pour des auto applications uniformement lipschitziennes

a general reconstruction algorithm for simulating flows with complex 3d immersed boundaries on cartesian grids in the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on cartesian grids is presented in the proposed method an arbitrary three dimensional solid surface immersed in the fluid is discretized using an unstructured triangular mesh and all the cartesian grid nodes near the interface are identified then the solution at these nodes is reconstructed via linear interpolation along the local normal to the body in a way that the desired boundary conditions for both pressure and velocity fields are enforced the overall accuracy of the resulting solver is second order as it is demonstrated in two test cases involving laminar flow past a sphere

implicit heat flux correction based immersed boundary finite volume method for thermal flows with neumann boundary conditions abstract in the frameworks of immersed boundary method ibm and finite volume method fvm an implicit heat flux correction based ib fvm is proposed for thermal flows with neumann boundary conditions with the use of a fractional step technique the preconditioned navier stokes n s equations are solved by the fvm to obtain the intermediate solution in the prediction step and the heat flux is corrected by enforcing the neumann condition in the correction step different from existing ibms the cell face centers are defined as the eulerian points due to the heat flux computation at each face in the fvm the neumann condition is implemented in such a way that the interpolated temperature gradient is equal to the specified boundary value at the same point when the corrected gradient field is interpolated from the face centers to the lagrangian points to achieve an implicit algorithm the temperature derivative corrections at the lagrangian points are set as unknowns and a system of algebraic equations is established by constructing hybrid thin plate splines tps interpolation delta function distribution in the derivative interpolation process the much more accurate tps is introduced because the use of cosine delta function yields a less accurate solution after the distribution process the heat flux correction of a fluid cell is evaluated by using the solved temperature derivative corrections at the face centers but that of a solid cell is calculated by using their additive inverses to supplement the same amount of heat flux into the solid domain as that flowing into the fluid domain across the boundary finally the heat flux of a cell is corrected by adding the correction to the intermediate value and the corrected heat flux is utilized to solve the n s equations in the prediction step as compared with the available implicit ibms for neumann conditions the present method avoids the introduction of auxiliary layers of lagrangian points as well as the approximate conversion from the neumann to dirichlet condition and thus is suitable for an arbitrary geometry the proposed method is verified by simulating several benchmark thermal flows with neumann conditions the natural convection in an annulus and the steady or unsteady forced convection over a stationary or oscillating cylinder all the computed results agree well with the literature data

an iterative method for elliptic problems on regions partitioned into substructures some new preconditioners for discretizations of elliptic boundary problems are studied with these preconditioners the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains analytic estimates are given which guarantee that under appropriate hypotheses the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns numerical examples are presented which illustrate the theoretically predicted iterative convergence rates

provably good partitioning and load balancing algorithms for parallel adaptive n body simulation we present an efficient and provably good partitioning and load balancing algorithm for parallel adaptive n body simulation the main ingredient of our method is a novel geometric characterization of a class of communication graphs that can be used to support hierarchical n body methods such as the fast multipole method fmm and the barnes hut method bh we show that communication graphs of these methods have a good partition that can be found efficiently sequentially and in parallel in particular we show that an n body communication graph either for bh or for fmm can be partitioned into two subgraphs with equal computation load by removing only o sqrt n log n and o n2 3 log n 1 3 number of nodes respectively for two and three dimensions these bounds on node partition imply bounds on edge partition of o sqrt n log n 3 2 and o n2 3 log n 4 3 respectively for two and three dimensions to the best of our knowledge this is the first theoretical result on the quality of partitioning n body communication graphs for nonuniformly distributed particles our results imply that parallel adaptive n body simulation can be made as scalable as computation on regular grids and as efficient as parallel n body simulation on uniformly distributed particles

boundary condition enforced immersed boundary lattice boltzmann flux solver for thermal flows with neumann boundary conditions a boundary condition enforced immersed boundary lattice boltzmann flux solver is proposed in this work for effective simulation of thermal flows with neumann boundary conditions in this method two auxiliary layers of lagrangian points are introduced and respectively placed inside and outside of the solid body on which the temperature corrections related to the heat source are set as unknowns to effectively consider the fluid boundary interaction these unknowns are expressed as algebraic summations of the temperature correction on eulerian points which are in turn obtained from biased distributions of unknown temperature corrections on the immersed boundary by enforcing the temperature gradient at the solid boundary being equal to that approximated by the corrected temperature field a set of algebraic equations are formed and solved to obtain all the unknowns simultaneously they are then distributed biasedly to the inner region of the auxiliary layer so that the diffusion from the smooth delta function can be reduced substantially in addition the solutions of the flow and temperature fields are obtained by the thermal lattice boltzmann flux solver with the second order of accuracy the proposed method is well validated through its applications to simulate several benchmarks of natural forced and mixed convection problems it has been demonstrated that the present solver has about 1 724 order of accuracy and the error between the present result and theoretical value for the temperature gradient on the solid surface is in the order of 10 13 which indicates that the proposed method is able to satisfy the neumann boundary condition accurately

numerical simulation of a cylinder in uniform flow in this study a virtual boundary technique is applied to the numerical simulation of stationary and moving cylinders in uniform flow this approach readily allows the imposition of a no slip boundary within the flow field by a feedback forcing term added to the momentum equations in the present work this technique is used with a high order finite difference method effectively eliminating spurious oscillations caused by the feedback forcing when used with spectrally discretized flow solvers very good agreement is found between the present calculations and previous computational and experimental results for steady and time dependent flow at low reynolds numbers

normal structure coefficients of l p ω let x be a uniformly convex banach space and n x the normal structure coefficient of x in this paper it is proved that n x can be calculated by considering only sets whose points are equidistant from their chebyshev centre this result is applied to prove that n l p min 2 1 1 p 2 1 p being a finite measure space the computation of n l p lets us also calculate some other coefficients related to the normal structure

fixed point theorems for mappings of asymptotically nonexpansive type the purpose of this paper is to provide fixed point theorems for asymptotically nonexpansive type mappings in a banach space with uniform normal structure

an immersed boundary method based on the gas kinetic bgk scheme for incompressible viscous flow in this paper an immersed boundary ib method based on the gas kinetic bhatnagar gross krook bgk scheme is proposed to simulate the incompressible viscous flow around stationary and moving rigid bodies in the presented ib method a set of lagrangian points represent the solid boundary and will exert force on the surrounding eulerian points which are the cell centers within the finite volume framework this force is calculated by a special iterative procedure and has an effect on the flux at the interface of cell which guarantees the fulfillment of the no slip boundary condition and entirely avoids the flow penetration the flow field is obtained from the bgk scheme with local grid refinement without complex mesh generation and transformation the present technique can be conveniently applied to simulations with complex and moving solid boundaries the second order temporal accuracy and better than first order spatial accuracy in l 2 norm are testified by the simulation of stokes first problem other three different test cases including flows around a stationary circular cylinder two circular cylinders in tandem and an oscillating circular cylinder demonstrate the good capability of the present method expanding the immersed boundary ib method to the finite volume gas kinetic bhatnagar gross krook bgk scheme the flux across the cell s interface will be influenced by the immersed boundary force the flow penetration to the immersed boundary is completely eliminated the present method can be conveniently applied to problems with moving objects

numerical navier stokes solutions from gas kinetic theory abstract in order to test the gas kinetic based hydrodynamic scheme given in paper i k h prendergast and k xu j comput phys 109 53 1993 as a navier stokes solver we extend the scheme to two dimensions and exhibit some navier stokes solutions the scheme is a high resolution gas kinetic scheme in both space and time the advective and diffusive fluxes are coupled and solved at the same time by following the time dependent velocity distribution function for particles numerical results for some well defined euler and navier stokes test cases are presented the kolmogorov and the laminar boundary layer problems exhibit the dominance of the real viscosity effects the strong shock interaction test cases show the applicability of the scheme to supersonic gas flow

strong convergence theorems for a family of quasi asymptotic pseudo contractions in hilbert spaces abstract in the present paper we propose two kinds of new algorithms for a family of quasi asymptotic pseudo contractions in real hilbert spaces by using the proposed algorithms we prove several strong convergence theorems for a family of quasi asymptotic pseudo contractions the results of this paper are interesting extensions of those known results

a hierarchical o n force calculation algorithm a novel code for the approximate computation of long range forces between n mutually interacting bodies is presented the code is based on a hierarchical tree of cubic cells and features mutual cell cell interactions which are calculated via a cartesian taylor expansion in a symmetric way such that total momentum is conserved the code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort for n 104 the computational costs are found empirically to rise sublinearly with n for applications in stellar dynamics this is the first competitive code with complexity o n it is faster than the standard tree code by a factor of 10 or more

an lp inequality and its applications to fixed point theory and approximation theory on etablit une inegalite l p pour 1 p 2 et on donne des applications aux points fixes des applications uniformement lipschitziennes et aux meilleures approximations fortement uniques

an improved direct forcing immersed boundary method for finite difference applications a modified immersed boundary method is developed using the direct forcing concept an improved bilinear interpolation extrapolation algorithm is implemented for more accurate boundary forcing expressions and easier implementation detailed discussions of the method are presented on the stability velocity interpolation on the immersed boundary direct forcing extrapolation to the grid points resolution of the immersed boundary points and internal treatment the method can achieve second order accurate solutions the method is then applied to a finite difference scheme to compute flow over a stationary cylinder an oscillating cylinder and a stationary sphere the accuracy of the computational results is verified using numerous computational and experimental results in the literature

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

a new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes in this paper a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes our approach consists of three main steps 1 surface partitioning of polygonal meshes 2 generation of shape design variables on the basis of partitioned surface patches and 3 gradient based shape optimization of the structures by reducing a weighted compliance among all load cases the main contributions of this paper include i that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times compared to the conventional design variable scheme of using each mesh node ii our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch except on its boundary and iii overall our approach can be used to automate time consuming shape optimization of polygonal meshes to a greater extent numerical experiments have been conducted and the results indicate the effectiveness of the approach copyright 2003 john wiley sons ltd

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

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

uniformly normal structure and uniformly lipschitzian semigroups abstract assume that x is a real banach space with uniformly normal structure and c is a nonempty closed convex subset of x we show that a uniformly lipschitzian semigroup of nonlinear self mappings of c admits a common fixed point if the semigroup has a bounded orbit and if is appropriately greater than one this result applies in particular to the framework of uniformly convex banach spaces

a novel immersed boundary velocity correction lattice boltzmann method and its application to simulate flow past a circular cylinder a novel immersed boundary velocity correction lattice boltzmann method is presented and validated in this work by its application to simulate the two dimensional flow over a circular cylinder the present approach is inspired from the conventional immersed boundary method ibm in the conventional ibm the effect of rigid body on the surrounding flow is modeled through a forcing term which is in turn used to correct the surrounding velocity field it was found that this process is actually an iterative procedure trying to satisfy the non slip boundary condition at the solid wall in this work a new concept of immersed boundary velocity correction approach is proposed which directly corrects the velocity to enforce the physical boundary condition the main advantage of the new method is that it is simple in concept and easy for implementation and the convergence of numerical computation is faster and more stable than the conventional ibm one challenging issue of conventional ibm is that some streamlines may pass through the solid body since there is no mechanism to enforce the non slip condition at the boundary as shown in the present numerical results this unphysical phenomenon is avoided in our new method since the non slip condition is enforced the present results for the steady and unsteady flows compare very well with available data in the literature

multiphase lattice boltzmann flux solver for incompressible multiphase flows with large density ratio a multiphase lattice boltzmann flux solver mlbfs is proposed in this paper for incompressible multiphase flows with low and large density ratios in the solver the flow variables at cell centers are given from the solution of macroscopic governing differential equations navier stokes equations recovered by multiphase lattice boltzmann lb model by the finite volume method at each cell interface the viscous and inviscid fluxes are evaluated simultaneously by local reconstruction of solution for the standard lattice boltzmann equation lbe the forcing terms in the governing equations are directly treated by the finite volume discretization the phase interfaces are captured by solving the phase field cahn hilliard equation with a fifth order upwind scheme unlike the conventional multiphase lb models which restrict their applications on uniform grids with fixed time step the mlbfs has the capability and advantage to simulate multiphase flows on non uniform grids the proposed solver is validated by several benchmark problems such as two phase co current flow taylor couette flow in an annulus rayleigh taylor instability and droplet splashing on a thin film at density ratio of 1000 with reynolds numbers ranging from 20 to 1000 numerical results show the reliability of the proposed solver for multiphase flows with high density ratio and high reynolds number

existence and approximation of fixed points of nonlinear mappings in spaces with weak uniform normal structure it is shown that in a banach space x with weak uniform normal structure every demicontinuous asymptotically regular nearly lipschitzian self mapping t with lim sup n h t n

a class of p convex spaces lacking normal structure abstract we prove that for any 1 the space e l 2 where max 2 is p convex it is known that for 2 e lacks normal structure

random fixed points of uniformly lipschitzian mappings abstract let be a measurable space x a banach space c a weakly convex subset of x and t c c a random operator we prove the random version of a deterministic fixed point theorem when t is an asymptotically nonexpansive mapping and the characteristic of convexity e0 x is less than 1 let n x be the normal structure coefficient of x and 0 x its lifschitz constant if t is k uniformly lipschitzian and there exists a constant c such that k c 1 1 4n x 0 x 1 2 we prove that t has a random fixed point

an implicit forcing immersed boundary method for simulating viscous flows in irregular domains abstract we present a method for solving the incompressible navier stokes equations in irregular domains these equations are discretized using finite difference method in a uniform cartesian grid stationary rigid boundaries are embedded in the cartesian grid and singular forces are applied at the rigid boundaries to impose the no slip conditions the singular forces are then distributed to the nearby cartesian grid points using the immersed boundary method in the present work the singular forces are computed implicitly by solving a small system of equations at each time step this system of equations is derived from a second order projection method the main advantage of this method is that it imposes the no slip boundary condition exactly and avoids the need for small time step to maintain stability the ability of the method to simulate viscous flows in irregular domains is demonstrated by applying to 2 dimensional flows past a circular cylinder multiple rigid obstacles and 3 dimensional flow past a sphere

an lp inequality we obtain an inequality for l p spaces 1 p 2 which corrects an inequality claimed by xu and xu 6 and has connections with some quantities of interest in fixed point theory

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory