strongly stable c stationary points for mathematical programs with complementarity constraints in this paper we consider the class of mathematical programs with complementarity constraints mpcc under an appropriate constraint qualification of mangasarian fromovitz type we present a topological and an equivalent algebraic characterization of a strongly stable c stationary point for mpcc strong stability refers to the local uniqueness existence and continuous dependence of a solution for each sufficiently small perturbed problem where perturbations up to second order are allowed this concept of strong stability was originally introduced by kojima for standard nonlinear optimization here its generalization to mpcc demands a sophisticated technique which takes the disjunctive properties of the solution set of mpcc into account

a smoothing method for mathematical programs with equilibrium constraints the mathematical program with equilibrium constraints mpec is an optimization problem with variational inequality constraints mpec problems include bilevel programming problems as a particular case and have a wide range of applications mpec problems with strongly monotone variational inequalities are considered in this paper they are transformed into an equivalent one level nonsmooth optimization problem then a sequence of smooth regular problems that progressively approximate the nonsmooth problem and that can be solved by standard available software for constrained optimization is introduced it is shown that the solutions stationary points of the approximate problems converge to a solution stationary point of the original mpec problem numerical results showing viability of the approach are reported

numerical simulation of creeping fluid flow in reconstruction models of porous media abstract in this paper we examine representative examples of realistic three dimensional models for porous media by comparing their geometry and permeability with those of the original experimental specimen the comparison is based on numerically exact evaluations of permeability porosity specific internal surface mean curvature euler number and local percolation probabilities the experimental specimen is a three dimensional computer tomographic image of fontainebleau sandstone the three models are stochastic reconstructions for which many of the geometrical characteristics coincide with those of the experimental specimen we find that in spite of the similarity in the geometrical properties the permeability and formation factor can differ greatly between models and the experiment

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

a novel mesh regeneration algorithm for 2d fem simulations of flows with moving boundary a novel mesh regeneration algorithm is proposed to maintain the mesh structure during a finite element simulation of flows with moving solid boundary with the current algorithm a new body fitted mesh can be efficiently constructed by solving a set of laplace equations developed to specify the displacements of individual mesh elements these equations are subjected to specific boundary conditions determined by the instantaneous body motion and other flow boundary conditions the proposed mesh regeneration algorithm has been implemented on an arbitrary lagrangian eulerian ale framework that employs an operator splitting technique to solve the navier stokes equations the integrated numerical scheme was validated by the numerical results of four existing problems a flow over a backward facing step a uniform flow over a fixed cylinder the vortex induced vibration of an elastic cylinder in uniformly incident flow and a complementary problem that compares the transient drag coefficient for a cylinder impulsively set into motion to that measured on a fixed cylinder in a starting flow good agreement with the numerical or experimental data in the literature was obtained and new transient flow dynamics was revealed the scheme performance is further examined with respect to the parameter employed in the mesh regeneration algorithm

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

conservative load transfer along curved fluid solid interface with non matching meshes we investigate the effect of curvature on the accuracy of schemes used to transfer loads along the interface in coupled fluid solid simulations involving non matching meshes we analyze two types of load transfer schemes for the coupled system a point to element projection schemes and b common refinement schemes the accuracy of these schemes over the curved interface is assessed with the aid of static and transient problems we show that the point to element projection schemes may yield inaccurate load transfer from the source fluid mesh to the target solid mesh leading to a weak instability in the form of spurious oscillations and overshoots in the interface solution the common refinement scheme resolves this problem by providing an accurate transfer of discrete interface conditions across non matching meshes we show theoretically that the accurate transfer preserves the stability of the coupled system while maintaining the energy conservation over a reference interface finally we introduce simple analytical error functions which correlate well with the numerical errors of the load transfer schemes

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

combined interface boundary condition method for fluid rigid body interaction abstract this research is motivated by the recent work which has presented a new loosely coupled partitioned algorithm for fluid structure interaction fsi r jaiman p geubelle e loth x jiao combined interface boundary condition method for unsteady fluid structure interaction comput methods appl mech engrg 200 2011 27 39 the loosely coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition cibc method in this method correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter that plays an important part in the stability and accuracy of the coupled system the structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem this handling asks for the structural traction before it is corrected by the cibc method in this paper a new formulation for the cibc method is developed to repair the aforementioned inconvenience after simple manipulation the structural traction ratio is removed in constructing the traction correction therefore the structural traction is no more needed in cibc correction terms meantime the ratio t is employed to tune the interfacial corrections instead of the coupling parameter an arbitrary lagrangian eulerian finite element method is used to analyze fsi the characteristic based split cbs scheme is employed to solve incompressible navier stokes equations while the equation for rigid body dynamics is solved by newmark method a numerical technique called moving submesh approach is performed for the mesh deformation for respecting geometric conservation law a mass source term is implanted into the cbs scheme on the moving mesh several numerical examples are tested to validate the proposed methodology for fluid rigid body interaction the obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

application of the lattice bhatnagar gross krook method to the simulation of internal pressure driven flow abstract recent modifications to the two speed two dimensional lattice bhatnagar gross krook method eliminate compressibility errors from the simulation of macroscopic fluids governed by the steady state navier stokes equation we describe the means by which this modified scheme makes it possible to compute both pressure drops and flow fields bringing internal pressure driven isothermal flows within the scope of the method the scheme is applied to the simulation of flow of a viscous incompressible fluid past a sudden expansion in an infinite aspect ratio duct back facing step geometry results are presented and compared with experiment and theory over a range of reynolds number

stabilization of explicit coupling in fluid structure interaction involving fluid incompressibility abstract in this work we propose a stabilized explicit coupling scheme for fluid structure interaction problems involving a viscous incompressible fluid the coupled discrete formulation is based on nitsche s method with a time penalty term giving l 2 control on the fluid pressure variations at the interface for a linear model problem we prove that the scheme is stable in the energy norm irrespectively of the so called added mass effect namely the fluid structure density ratio and the geometry of the domain numerical experiments in the linear and non linear case show that optimal time accuracy can be obtained by performing one defect correction iteration

an efficient lattice boltzmann multiphase model for 3d flows with large density ratios at high reynolds numbers we report on the development implementation and validation of a new lattice boltzmann method lbm for the numerical simulation of three dimensional multiphase flows here with only two components with both high density ratio and high reynolds number this method is based in part on but aims at achieving a higher computational efficiency than inamuro et al s model inamuro et al 2004 here we use a lbm to solve both a pressureless navier stokes equation in which the implementation of viscous terms is improved and a pressure poisson equation using different distribution functions and a d3q19 lattice scheme additionally we propose a new diffusive interface capturing method based on the cahn hilliard equation which is also solved with a lbm to achieve maximum efficiency the entire model is implemented and solved on a heavily parallel gpgpu co processor the proposed algorithm is applied to several test cases such as a splashing droplet a rising bubble and a braking ocean wave in all cases numerical results are found to agree very well with reference data and or to converge with the discretization

applications of statistical physics to the oil industry predicting oil recovery using percolation theory in this paper we apply scaling laws from percolation theory to the problem of estimating the time for a uid injected into an oil eld for the purposes of recovering the oil to breakthrough into a production well the main contribution is to show that percolation theory when applied to a realistic model can be used to obtain the same results as calculated in a more conventional way but signicantly more quickly specically we found that a previously proposed scaling form for the breakthrough time distribution when applied to a real oil eld is in good agreement with more time consuming simulation results consequently these methods can be used in practical engineering circumstances to aid decision making for real eld problems c 1999 elsevier science b v all rights reserved

a stable second order partitioned iterative scheme for freely vibrating low mass bluff bodies in a uniform flow abstract we present a stable partitioned iterative scheme for solving fluid body interaction problems at low structure to fluid mass ratio the scheme relies on the so called nonlinear interface force correction based on aitken s extrapolation process to stabilize the coupled partitioned system employing an arbitrary lagrangian eulerian finite element framework approximate interface force correction is constructed through subiterations to account for the missing effects of off diagonal jacobian terms in the partitioned staggered scheme through the generalized aitken s geometric extrapolation process with a dynamic stabilization parameter the interface corrections allow to satisfy the force equilibrium with arbitrary accuracy while expanding the scope of partitioned iterative schemes for fluid structure interaction with strong added mass effects to assess the proposed iterative scheme against the standard strong coupling effects of mass ratio are investigated for a freely vibrating circular cylinder we show that our second order scheme is stable for low mass density ratio and hence is able to handle strong added mass effects the numerical stability and robustness of the scheme is then demonstrated for a new application of tandem square cylinder undergoing complex wake induced vibration and galloping

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

solving bilevel programs with the kkt approach bilevel programs bl form a special class of optimization problems they appear in many models in economics game theory and mathematical physics bl programs show a more complicated structure than standard finite problems we study the so called kkt approach for solving bilevel problems where the lower level minimality condition is replaced by the kkt or the fj condition this leads to a special structured mathematical program with complementarity constraints we analyze the kkt approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving bl problems numerically

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

shift an implementation for lattice boltzmann simulation in low porosity porous media the lattice boltzmann lb method has proven to be a promising method for simulating fluid dynamics in porous media when fluid flow in pores is the only concern a standard lb implementation which stores one or two sets of particle distribution functions pdfs for both pore and solid cells wastes a large amount of memory especially for low porosity media this paper proposes a lb implementation scheme that stores a single set of pdfs for pore cells only and therefore makes it possible to simulate flow through larger and more realistic porous models a unique feature of this scheme is that it decomposes all pdfs into a set of 1d arrays in such a way that each array corresponds to a set of pore cells that connect one another along a pair of opposite lb velocity directions this allows lb propagation and a standard bounce back rule to be realized together as one or two circular shifting operations on every array for this reason this scheme is called shift although pdfs are not stored in an efficient way for lb collision operation it is shown that the incurred overhead could be reduced by properly arranging pdf arrays according to the pore structures a d3q15 lb implementation of shift using the lattice bhatnagar gross krook model is applied to simulate the stokes flow through models of four natural and synthetic rock samples with porosities ranging from about 10 to 38 results show that shift requires 36 82 less memory than a comparable d3q15 lb does which stores a single set of pdf for both pore and solid cells shift achieves minimum performances of over 11 and 3 8 mega lattice updates per second mlups for the combined propagation and bounce back operation and the collision operation respectively and therefore a minimum of 2 8 mlups in total on a computer with one amd opteron 2218 the performance of the collision operation is significantly improved for all cases when a simple k mean clustering technique is employed to rearrange pdf arrays it is argued and shown that the number of pdf arrays per pore cell and the length frequency of pdf arrays are useful measurements on the geometry and topology of the pore structures and these characteristics are able to explain shift performance variations

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

how stringent is the linear independence assumption for mathematical programs with complementarity constraints the linear independence constraint qualifications licq plays an important role in the analysis of mathematical programs with complementarity constraints mpccs and is a vital ingredient to convergence analyses of sqp type or smoothing methods cf e g fukushima and pang 1999 luo et al 1996 scholtes and sta hr 1999 scholtes 2001 sta hr 2000 we will argue in this paper that licq is not a particularly stringent assumption for mpccs our arguments are based on an extension of jongen s 1977 genericity analysis to mpccs his definitions of nondegenerate critical points and regular programs extend naturally to mpccs and his genericity results generalize straightforwardly to mpccs in standard form an extension is not as straightforward for mpccs with the particular structure induced by lower level stationarity conditions for variational inequalities or optimization problems we show that licq remains a generic property for this class of mpccs

several approaches for the derivation of stationarity conditions for elliptic mpecs with upper level control constraints the derivation of multiplier based optimality conditions for elliptic mathematical programs with equilibrium constraints mpec is essential for the characterization of solutions and development of numerical methods though much can be said for broad classes of elliptic mpecs in both polyhedric and non polyhedric settings the calculation becomes significantly more complicated when additional constraints are imposed on the control in this paper we develop three derivation methods for constrained mpec problems via concepts from variational analysis via penalization of the control constraints and via penalization of the lower level problem with the subsequent regularization of the resulting nonsmoothness the developed methods and obtained results are then compared and contrasted

fluid structure partitioned procedures based on robin transmission conditions in this article we design new partitioned procedures for fluid structure interaction problems based on robin type transmission conditions the choice of the coefficient in the robin conditions is justified via simplified models the strategy is effective whenever an incompressible fluid interacts with a relatively thin membrane as in hemodynamics applications we analyze theoretically the new iterative procedures on a model problem which represents a simplified blood vessel system in particular the robin neumann scheme exhibits enhanced convergence properties with respect to the existing partitioned procedures the theoretical results are checked using numerical experimentation

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 solution adaptive lattice boltzmann method for two dimensional incompressible viscous flows a stencil adaptive lattice boltzmann method lbm is developed in this paper it incorporates the stencil adaptive algorithm developed by ding and shu 26 for the solution of navier stokes n s equations into the lbm calculation based on the uniform mesh the stencil adaptive algorithm refines the mesh by two types of 5 points symmetric stencils which are used in an alternating sequence for increased refinement levels the two types of symmetric stencils can be easily combined to form a 9 points symmetric structure using the one dimensional second order interpolation recently developed by wu and shu 27 along the straight line and the d2q9 model the adaptive lbm calculation can be effectively carried out note that the interpolation coefficients are only related to the lattice velocity and stencil size hence the simplicity of lbm is not broken down and the accuracy is maintained due to the use of adaptive technique much less mesh points are required in the simulation as compared to the standard lbm as a consequence the computational efficiency is greatly enhanced the numerical simulation of two dimensional lid driven cavity flows is carried out accurate results and improved efficiency are reached in addition the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries the obtained results compare well with data in the literature

the c index a new stability concept for quadratic programs with complementarity constraints we introduce nondegeneracy and the c index for c stationary points of a qpcc that is for a mathematical program with a quadratic objective function and linear complementarity constraints the c index characterizes the qualitative local behavior of a qpcc around a nondegenerate c stationary point the article focuses on the structure of the c stationary set of qpccs depending on a real parameter we show that for generic qpcc data the c index changes exactly at turning points of the c stationary set and that it changes by exactly one to illustrate this concept we introduce and analyze two homotopy methods for finding c stationary points numerical results illustrate that for randomly generated test problems the two homotopy methods very often identify b stationary points

domain decomposition method for parallel lattice boltzmann simulation of incompressible flow in porous media the lattice boltzmann method has proven to be a promising method to simulate flow in porous media its practical application often relies on parallel computation because of the demand for a large domain and fine grid resolution to adequately resolve pore heterogeneity the existing domain decomposition methods for parallel computation usually decompose a domain into a number of subdomains first and then recover the interfaces and perform the load balance normally the interface recovery and the load balance have to be performed iteratively until an acceptable load balance is achieved this costs time in this paper we propose a cell based domain decomposition method for parallel lattice boltzmann simulation of flow in porous media unlike the existing methods the cell based method performs the load balance first to divide the total number of fluid cells into a number of groups or subdomains in which the difference of fluid cells in each group is either 0 or 1 depending on if the total number of fluid cells is a multiple of the processor numbers the interfaces between the subdomains are recovered at last the cell based method is to recover the interfaces rather than the load balance it does not need iteration and gives an exact load balance the performance of the proposed method is analyzed and compared using different computer systems the results indicate that it reaches the theoretical parallel efficiency the method is then applied to simulate flow in a three dimensional porous medium obtained with microfocus x ray computed tomography to calculate the permeability and the result shows good agreement with the experimental data

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

characterization of strong stability for c stationary points in mpcc we study mathematical programs with complementarity constraints mpcc special focus will be on c stationary points under the linear independence constraint qualification we characterize strong stability of c stationary points in the sense of kojima by means of first and second order information of the defining functions it turns out that strong stability of c stationary points allows a possible degeneracy of bi active lagrange multipliers some relations to other stationarity concepts such as a m s and b stationarity are shortly discussed

reconstruction of random media using monte carlo methods a simulated annealing algorithm is applied to the reconstruction of two dimensional porous media with prescribed correlation functions the experimental correlation function of an isotropic sample of fontainebleau sandstone and a synthetic correlation function with damped oscillations are used in the reconstructions to reduce the numerical effort we follow a proposal suggesting the evaluation of the correlation functions only along certain directions the results show that this simplification yields significantly different microstructures as compared to a full evaluation of the correlation function in particular we find that the simplified reconstruction method introduces an artificial anisotropy that is originally not present

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

the ortho semi torsional ost spring analogy method for 3d mesh moving boundary problems in this paper a new mesh update technique is presented for the effective treatment of 3d mesh moving boundary problems the proposed mesh update scheme utilizes an ortho semi torsional ost spring analogy concept to construct a fictitious elasticity problem with imposed boundary displacements which is efficiently solved with an algorithm based on the preconditioned conjugate gradient pcg method the pcg based solution algorithm is also applied to three other mesh update techniques available in the literature namely the torsional the semi torsional and the ball vertex spring analogy schemes the four spring analogy methods are comparatively assessed with respect to their robustness and computational efficiency in handling 3d benchmark problems as well as more involved test cases such as the agard wing 445 6 and a 3d three element airfoil it is demonstrated that the ost spring analogy concept combined with a pcg type algorithm for the solution of fictitious elasticity problems provides robustness for substantially distorted meshes and computational efficiency for large scale problems

on boundary conditions of the characteristic based split cbs algorithm for fluid dynamics this paper discusses alternative procedures which can be used in the application of boundary conditions for the cbs algorithm attention is focused on the problem of application of prescribed velocity and traction conditions the paper is illustrated with some incompressible flow problems although previously logical and correct boundary condition specifications were introduced the procedures outlined in this paper simplify calculations and generally make it more accurate copyright 2002 john wiley sons ltd

artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows this note investigates the so called arti cial added mass e ect which is responsible for devastating instabilities within sequentially staggered fluid structure interaction fsi simulations where incompressible fluids are considered a discrete representation of the added mass operatorma is given and instability conditions are evaluated for different temporal discretisation schemes it is proven that for every sequentially staggered scheme and given spatial discretisation of a problem a mass ratio between fluid and structural mass density can be found at which the coupled system becomes unstable the analysis is quite general and does not depend upon the particular spatial discretisation schemes used however here special attention is put on stabilised finite elements employed on the fluid partition numerical investigations further highlight the results

simulation of flows around an impulsively started circular cylinder by taylor series expansion and least squares based lattice boltzmann method the two dimensional incompressible viscous flow past an impulsively started circular cylinder for a wide range of reynolds numbers re 20 9500 is studied computationally by using an explicit taylor series expansion and least squares based lattice boltzmann method the final equation for distribution function in our method is in an explicit form and essentially has no limitation on choice of mesh structure and lattice model it can be easily applied to simulation of flows with curved boundaries such as the problem considered in this work for the flow past an impulsively started circular cylinder numerical results obtained by present method agree very well with experimental data and computational results of navier stokes equations available in the literature

fast dynamic grid deformation based on delaunay graph mapping a simple and efficient dynamic grid deformation technique is proposed for computing unsteady flow problems with geometrical deformation relative body movement or shape changes due to aerodynamic optimisation and fluid structure interaction a delaunay graph of the solution domain is first generated which can be moved easily during the geometric dynamic deformation even for very large distortion a one to one mapping between the delaunay graph and the computational grid is maintained during the movement therefore the new computational grid after the dynamic movement can be generated efficiently through the mapping while maintaining the primary qualities of the grid while most dynamic grid deformation techniques are iterative based on the spring analogy the present method is non iterative and much more efficient on the other hand in comparison with dynamic grid techniques based on transfinite interpolation for structured grids it offers both geometric and cell topology flexibility which is crucial for many unsteady flow problems involving geometric deformation and relative motions the method is demonstrated through some typical unsteady flow test cases including a pitching aerofoil in a fixed domain boundary relative movement between multi element aerofoils due to flap deployment for high lift a deformable sphere in a fixed cube and a three dimensional flexible wing with large deformation

hydraulic permeability of ordered and disordered single layer arrays of cylinders the hydraulic permeability of single layer fibrous media is studied through two dimensional 2d and three dimensional navier stokes based flow simulations as simple representations of such materials one dimensional arrays of parallel cylinders as well as two dimensional arrays of perpendicularly crossing cylinders were used the distance between the cylinders was either constant ordered layers or variable disordered layers for both 1d and 2d ordered layers we propose a geometrical scaling rule for the hydraulic permeability as a function of cylinder radius and solid volume fraction porosity which is a modification of a scaling rule previously reported by clague and co workers the proposed modification is based on theoretical considerations and leads to significantly improved correspondence with simulation results the hydraulic permeability of unstructured layers is found to be higher than that of structured layers of equal porosity for both 1d and 2d arrays we propose a single parameter that can be easily determined experimentally to characterize the degree of disorder as well as a generally valid correction factor in the proposed geometrical scaling rule to account for the influence of disorder on the hydraulic permeability

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

a monolithical fluid structure interaction algorithm applied to the piston problem abstract an investigation of time marching computational fluid structure interaction algorithms is presented the analysis is applied to the piston problem attention is focussed on the time integration properties of the coupling algorithms the staggered scheme is first investigated where fluid and structure are alternately integrated by separate solvers in a predictor corrector fashion this algorithm suffers from a time lag between the integration of the fluid and structure the influence of the time lag is investigated by the comparison of different predictions for the structure a novel monolithical algorithm is then introduced in order to annihilate the time lag this algorithm integrates fluid structure and interaction as a single system by an implicit algorithm linear acoustic as well as nonlinear euler equations for gas dynamics are investigated the numerical results of the staggered scheme reveal a non physical deviation of the mean position of the piston at higher cfl numbers the deviation of the mean position is not present in the calculation with the monolithical scheme stability analysis shows the unconditional stability of the monolithical scheme for the acoustic equations whereas the staggered scheme has a limited domain of stability this domain can be enlarged by an improvement of the structural prediction analysis of the damping shows an energy production in the staggered scheme while the monolithical scheme has no energy production term the analyses lead to the formulation of the interaction consistency law which prescribes the relation for the time discretisation between fluid and structure solvers and their boundary conditions

total enthalpy based lattice boltzmann method with adaptive mesh refinement for solid liquid phase change a total enthalpy based lattice boltzmann lb method with adaptive mesh refinement amr is developed in this paper to efficiently simulate solid liquid phase change problem where variables vary significantly near the phase interface and thus finer grid is required for the total enthalpy based lb method the velocity field is solved by an incompressible lb model with multiple relaxation time mrt collision scheme and the temperature field is solved by a total enthalpy based mrt lb model with the phase interface effects considered and the deviation term eliminated with a kinetic assumption that the density distribution function for solid phase is at equilibrium state a volumetric lb scheme is proposed to accurately realize the nonslip velocity condition on the diffusive phase interface and in the solid phase as compared with the previous schemes this scheme can avoid nonphysical flow in the solid phase as for the amr approach it is developed based on multiblock grids an indicator function is introduced to control the adaptive generation of multiblock grids which can guarantee the existence of overlap area between adjacent blocks for information exchange since mrt collision schemes are used the information exchange is directly carried out in the moment space numerical tests are firstly performed to validate the strict satisfaction of the nonslip velocity condition and then melting problems in a square cavity with different prandtl numbers and rayleigh numbers are simulated which demonstrate that the present method can handle solid liquid phase change problem with high efficiency and accuracy

lifting mathematical programs with complementarity constraints we present a new smoothing approach for mathematical programs with complementarity constraints based on the orthogonal projection of a smooth manifold we study regularity of the lifted feasible set and since the corresponding optimality conditions are inherently degenerate introduce a regularization approach involving a novel concept of tilting stability a correspondence between the c index in the original problem and the quadratic index in the lifted problem is shown in particular a local minimizer of the mathematical program with complementarity constraints may numerically be found by minimization of the lifted smooth problem we report preliminary computational experience with the lifting approach

lattice boltzmann and finite difference simulations for the permeability for three dimensional porous media numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7 5 microm one of the samples is a microtomographic image of fontainebleau sandstone two of the samples are stochastic reconstructions with the same porosity specific surface area and two point correlation function as the fontainebleau sample the fourth sample is a physical model that mimics the processes of sedimentation compaction and diagenesis of fontainebleau sandstone the permeabilities of these samples are determined by numerically solving at low reynolds numbers the appropriate stokes equations in the pore spaces of the samples the physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude this finding confirms earlier qualitative predictions based on local porosity theory two numerical algorithms were used in these simulations one is based on the lattice boltzmann method and the other on conventional finite difference techniques the accuracy of these two methods is discussed and compared also with experiment

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

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

reconstructing random media we formulate a procedure to reconstruct the structure of general random heterogeneous media from limited morphological information by extending the methodology of rintoul and torquato j colloid interface sci bold 186 467 1997 developed for dispersions the procedure has the advantages that it is simple to implement and generally applicable to multidimensional multiphase and anisotropic structures furthermore an extremely useful feature is that it can incorporate any type and number of correlation functions in order to provide as much morphological information as is necessary for accurate reconstruction we consider a variety of one and two dimensional reconstructions including periodic and random arrays of rods various distribution of disks debye random media and a fontainebleau sandstone sample we also use our algorithm to construct heterogeneous media from specified hypothetical correlation functions including an exponentially damped oscillating function as well as physically unrealizable ones copyright ital 1998 ital the american physical society

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

parallel domain decomposition method with non blocking communication for flow through porous media this paper introduces a domain decomposition method for numerically solving the stokes equation for very large complex geometries examples arise from realistic porous media the computational method is based on the simple semi implicit method for pressure linked equations algorithm which uses a finite differences approach for discretizing the underlying equations it achieves comparable speed and efficiency as lattice boltzmann methods the domain decomposition method splits a large three dimensional region into slices that can be processed in parallel on multi processor computation environments with only minimal communication between the computation nodes with this method the flow through a porous medium with grid sizes up to 20483 voxel has been calculated

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

mpcc critical point theory we study mathematical programs with complementarity constraints mpcc from a topological point of view special focus will be on c stationary points under the linear independence constraint qualification licq we derive an equivariant morse lemma at nondegenerate c stationary points then two basic theorems from morse theory deformation theorem and cell attachment theorem are proved outside the c stationary point set continuous deformation of lower level sets can be performed as a consequence the topological data such as the number of connected components then remain invariant however when passing a c stationary level the topology of the lower level set changes via the attachment of a q dimensional cell the dimension q equals the stationary c index of the nondegenerate c stationary point the stationary c index depends on both the restricted hessian of the lagrangian and the lagrange multipliers related to biactive complementarity constraints finally some relations with other stationarity concepts such as w a m s and b stationarity are discussed