a dissipative particle dynamics method for arbitrarily complex geometries dissipative particle dynamics dpd is an effective lagrangian method for modeling complex fluids in the mesoscale regime but so far it has been limited to relatively simple geometries here we formulate a local detection method for dpd involving arbitrarily shaped geometric three dimensional domains by introducing an indicator variable of boundary volume fraction bvf for each fluid particle the boundary of arbitrary shape objects is detected on the fly for the moving fluid particles using only the local particle configuration therefore this approach eliminates the need of an analytical description of the boundary and geometry of objects in dpd simulations and makes it possible to load the geometry of a system directly from experimental images or computer aided designs drawings more specifically the bvf of a fluid particle is defined by the weighted summation over its neighboring particles within a cutoff distance wall penetration is inferred from the value of the bvf and prevented by a predictor corrector algorithm the no slip boundary condition is achieved by employing effective dissipative coefficients for liquid solid interactions quantitative evaluations of the new method are performed for the plane poiseuille flow the plane couette flow and the wannier flow in a cylindrical domain and compared with their corresponding analytical solutions and high order spectral element solution of the navier stokes equations we verify that the proposed method yields correct no slip boundary conditions for velocity and generates negligible fluctuations of density and temperature in the vicinity of the wall surface moreover we construct a very complex 3d geometry the brown pacman microfluidic device to explicitly demonstrate how to construct a dpd system with complex geometry directly from loading a graphical image subsequently we simulate the flow of a surfactant solution through this complex microfluidic device using the new method its effectiveness is demonstrated by examining the rich dynamics of surfactant micelles which are flowing around multiple small cylinders and stenotic regions in the microfluidic device without wall penetration in addition to stationary arbitrary shape objects the new method is particularly useful for problems involving moving and deformable boundaries because it only uses local information of neighboring particles and satisfies the desired boundary conditions on the fly

a theoretically supported scalable tfeti algorithm for the solution of multibody 3d contact problems with friction abstract a total feti tfeti based domain decomposition algorithm with preconditioning by a natural coarse grid defined by the rigid body motions of subdomains is adapted to the solution of multibody contact problems with friction in 3d and proved to be scalable for tresca friction the analysis admits floating bodies the algorithm finds an approximate solution at the cost asymptotically proportional to the number of variables provided the ratio of the decomposition and the discretization parameters is bounded the analysis is based on the classical results by farhat et al on scalability of feti for linear problems and on our development of optimal quadratic programming algorithms the algorithm preserves parallel scalability of the classical feti method both theoretical results and numerical experiments indicate that our algorithm is effective the effectiveness of the method in the inner loop of the fixed point iterations for the solution of the contact problems with coulomb s friction is illustrated on the analysis of a mine support

cylindrical smoothed particle hydrodynamics abstract smoothed particle hydrodynamics sph is formulated in two dimensional axisymmetric coordinates starting with a three dimensional cartesian representation of sph we integrate out the angular component and find a two dimensional cylindrical description a smoothed particle in this formulation becomes a smoothed torus the hoop stress resulting from interactions within the toroidal ring is a natural consequence of the derivation no pathological behavior is observed at the symmetry axis the formulation has been extended to include the entire stress tensor not just the pressure and is therefore applicable to a wide range of materials and flow speeds three calculations are presented and compared to known results

the global cauchy problem for the nls and nlkg with small rough data abstract by using the unit cube decomposition to the frequency spaces we study the cauchy problem for the nonlinear schrodinger equation and the nonlinear klein gordon equation some global well posedness results are obtained for the small cauchy data in some modulation spaces m p 1 s

a primal dual active set algorithm for three dimensional contact problems with coulomb friction in this paper efficient algorithms for contact problems with tresca and coulomb friction in three dimensions are presented and analyzed the numerical approximation is based on mortar methods for nonconforming meshes with dual lagrange multipliers using a nonsmooth complementarity function for the three dimensional friction conditions a primal dual active set algorithm is derived the method determines active contact and friction nodes and at the same time resolves the additional nonlinearity originating from sliding nodes no regularization and no penalization are applied and superlinear convergence can be observed locally in combination with a multigrid method it defines a robust and fast strategy for contact problems with tresca or coulomb friction the efficiency and flexibility of the method is illustrated by several numerical examples

a consistent reflected image particle approach to the treatment of boundary conditions in smoothed particle hydrodynamics the particle deficiency problem in the presence of a rigid wall for smoothed particle hydrodynamics sph is considered the problem arises from insufficient information being available to perform accurate interpolation of data at particles located nearer to the boundary than the support of the interpolation kernel the standard method for overcoming this problem is based on the introduction of image particles to populate the deficient regions and the use of linear extrapolation to determine the velocity of these image particles from that of fluid particles a consistent treatment of boundary conditions utilising the momentum equation to obtain approximations to the velocity of image particles is described the method ensures second order approximation of the boundary conditions it is validated for poiseuille and couette flow for which analytical series solutions exist and shows second order convergence under certain conditions

improved incompressible smoothed particle hydrodynamics method for simulating flow around bluff bodies in this article we present numerical solutions for flow over an airfoil and a square obstacle using incompressible smoothed particle hydrodynamics isph method with an improved solid boundary treatment approach referred to as the multiple boundary tangents mbt method it was shown that the mbt boundary treatment technique is very effective for tackling boundaries of complex shapes also we have proposed the usage of the repulsive component of the lennard jones potential ljp in the advection equation to repair particle fractures occurring in the sph method due to the tendency of sph particles to follow the stream line trajectory this approach is named as the artificial particle displacement method numerical results suggest that the improved isph method which is consisting of the mbt method artificial particle displacement and the corrective sph discretization scheme enables one to obtain very stable and robust sph simulations the square obstacle and naca airfoil geometry with the angle of attacks between 0 and 15 were simulated in a laminar flow field with relatively high reynolds numbers we illustrated that the improved isph method is able to capture the complex physics of bluff body flows naturally such as the flow separation wake formation at the trailing edge and the vortex shedding the sph results are validated with a mesh dependent finite element method fem and excellent agreements among the results were observed

banach spaces related to integrable group representations and their atomic decompositions i abstract we present a general theory of banach spaces which are invariant under the action of an integrable group representation and give their atomic decompositions with respect to coherent states i e the atoms arise from a single element under the group action several well known decomposition theories are contained as special examples and are unified under the aspect of group theory

molecular dynamics smoothed particle applied mechanics and irreversibility abstract we explore the relationship of monaghan s version of smoothed particle hydrodynamics here called smoothed particle applied mechanics to nonequilibrium molecular dynamics we first use smoothed particles to model the simplest possible linear transport problems as well as a liquid drop problem we then consider both gas phase and dense fluid versions of rayleigh benard convection all in two space dimensions we also discuss the possibility of combining the microscopic and macroscopic techniques in a hybrid scheme well suited to the massively parallel modelling of large scale nonequilibrium flows

variational and momentum preservation aspects of smooth particle hydrodynamic formulations this paper presents a new variational framework for various existing smooth particle hydrodynamic sph techniques and presents a new corrected sph formulation the linear and angular momentum preserving properties of sph formulations are also discussed the paper will show that in general in order to preserve angular momentum the sph equations must correctly evaluate the gradient of a linear velocity field a corrected algorithm that combines kernel correction with gradient correction is presented the paper will illustrate the theory presented with several examples relating to simple free surface flows

sph simulations of time dependent poiseuille flow at low reynolds numbers a working smoothed particle hydrodynamics sph formalism for solving the equations of motion of a viscous fluid is presented the method is based on a standard symmetrized sph expression for the viscous forces which involves only first order derivatives of the kernel through a direct evaluation of the viscous stress tensor therefore the interpolation can be performed using low order kernels of compact support without compromising the accuracy and stability of the results in principle the scheme is suitable for treating compressible fluids with arbitrary shear and bulk viscosities here we demonstrate that when it is combined with the pressure gradient correction proposed by morris et al the method is also suitable for solving the navier stokes equations for incompressible flows without any further assumptions simulations using the method show close agreement with the analytic series solutions for plane poiseuille and hagen poiseuille flows at very low reynolds numbers at least for these specific tests the results obtained are essentially independent of employing either a cubic or a quintic spline kernel

frequency uniform decomposition method for the generalized bo kdv and nls equations abstract sufficient and necessary conditions for the embeddings between besov spaces b p q s 1 and modulation spaces m p q s 2 are obtained moreover using the frequency uniform decomposition method we study the cauchy problem for the generalized bo kdv and nls equations for which the global well posedness of solutions with the small rough data in certain modulation spaces m 2 1 s is shown

approximation and numerical realization of 2d contact problems with coulomb friction and a solution dependent coefficient of friction the paper analyzes discrete contact problems with the coulomb law of friction which involves a solution dependent coefficient of friction f solutions to these problems are defined as fixed points of an auxiliary mapping it is shown that there exists at least one solution provided that f is bounded and continuous in r 1 further conditions guaranteeing uniqueness of the solution are studied the paper is completed by numerical results of several model examples

remarks on fourier multipliers and applications to the wave equation exploiting continuity properties of fourier multipliers on modulation spaces and wiener amalgam spaces we study the cauchy problem for the nlw equation local wellposedness for rough data in modulation spaces and wiener amalgam spaces is shown the results formulated in the framework of modulation spaces refine those in a benyi k a okoudjou local well posedness of nonlinear dispersive equations on modulation spaces preprint april 2007 available at arxiv 0704 0833v1 the same arguments may apply to obtain local wellposedness for the nlkg equation

functions operating on modulation spaces and nonlinear dispersive equations abstract the aim of this paper is two fold we show that if a complex function f on c operates in the modulation spaces m p 1 r n by composition then f is real analytic on r 2 c this answers negatively the open question posed in ruzhansky et al 2012 21 regarding the general power type nonlinearity of the form u u we also characterise the functions that operate in the modulation space m 1 1 r n the local well posedness of the nls nlw and nlkg equations for the real entire nonlinearities are also studied in some weighted modulation spaces m s p q r n

modulation spaces wiener amalgam spaces and brownian motions abstract we study the local in time regularity of the brownian motion with respect to localized variants of modulation spaces m s p q and wiener amalgam spaces w s p q we show that the periodic brownian motion belongs locally in time to m s p q t and w s p q t for s 1 q 1 and the condition on the indices is optimal moreover with the wiener measure on t we show that m s p q t and w s p q t form abstract wiener spaces for the same range of indices yielding large deviation estimates we also establish the endpoint regularity of the periodic brownian motion with respect to a besov type space b p s t specifically we prove that the brownian motion belongs to b p s t for s 1 p 1 and it obeys a large deviation estimate finally we revisit the regularity of brownian motion on usual local besov spaces b p q s and indicate the endpoint large deviation estimates

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

a nonsmooth multiscale method for solving frictional two body contact problems in 2d and 3d with multigrid efficiency we present a nonsmooth multiscale method for the numerical solution of frictional contact problems in 2d and 3d the computational effort is comparable to that of solving linear problems our method does not require any regularization neither of the nonpenetration condition nor of the friction law and can be applied to contact problems with tresca friction as well as to contact problems with coulomb friction for the case of tresca friction the global convergence of the method is shown for the more complicated case of coulomb friction we develop a nonsmooth multiscale method which can be directly applied to the corresponding variational quasi inequality no outer iteration is required moreover our multiscale approach is general in the sense that it can be used in the context of geometric as well as algebraic multigrid methods nonconforming domain decomposition techniques or mortar methods are employed in order to enforce the transmission conditions at the interface between different bodies with nonmatching meshes numerical examples illustrate the high robustness and efficiency of our method

nonlinear operations on a class of modulation spaces abstract we discuss when the nonlinear operation f f f maps the modulation space m s p q r n 1 p q to the same space again it is known that m s p q r n is a multiplication algebra when s n n q hence it is true for this space if f is entire we claim that it is still true for non analytic f when q 4 3

hybrid finite element methods for the signorini problem we study three mixed linear finite element methods for the numerical simulation of the two dimensional signorini problem applying falk s lemma and saddle point theory to the resulting discrete mixed variational inequality allows us to state the convergence rate of each of them two of these finite elements provide optimal results under reasonable regularity assumptions on the signorini solution and the numerical investigation shows that the third method also provides optimal accuracy

approximation and numerical realization of 3d contact problems with coulomb friction and a solution dependent coefficient of friction this paper analyzes 3d discrete contact problems with coulomb friction and a coefficient of friction depending on the solution the formulation of this problem is based on a fixed point approach existence of at least one discrete solution is guaranteed for any continuous non negative and bounded function the uniqueness result is established for small enough and lipschitz continuous with a sufficiently small modulus of lipschitz continuity results of several numerical experiments are shown copyright 2009 john wiley sons ltd

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

an incompressible multi phase sph method an incompressible multi phase sph method is proposed in this method a fractional time step method is introduced to enforce both the zero density variation condition and the velocity divergence free condition at each full time step to obtain sharp density and viscosity discontinuities in an incompressible multi phase flow a new multi phase projection formulation in which the discretized gradient and divergence operators do not require a differentiable density or viscosity field is proposed numerical examples for taylor green flow capillary waves drop deformation in shear flows and for rayleigh taylor instability are presented and compared to theoretical solutions or references from literature the results suggest good accuracy and convergence properties of the proposed method

an isph scheme for numerical simulation of multiphase flows with complex interfaces and high density ratios abstract multiphase problems with high density ratios and complex interfaces deal with numerical instabilities and require accurate considerations for capturing the multiphase interfaces an incompressible smoothed particle hydrodynamics isph scheme is presented to simulate such problems in order to keep the present scheme simple and stable well established formulations are used for discretizing the spatial derivatives and a repulsive force is applied at the multiphase interface between particles of different fluids to maintain the interface sharpness special considerations are included to overcome the difficulties to model severe physical discontinuities at the interface and surface tension effects are taken into account different particle shifting schemes are also tested for a range of problems several two phase flows are investigated and the presented scheme is validated against both analytical and numerical solutions a detailed study is also carried out on the influence of the repulsive force in an isph scheme showing that this simple treatment efficiently enhances the interface capturing features the comparisons indicate that the proposed scheme is robust and capable of simulating a wide range of multiphase problems with complex interfaces including low to high ratios for density and viscosity

qualitative analysis of solutions to discrete static contact problems with coulomb friction we analyze properties of solutions to discrete contact problems with coulomb friction which are parametrized by the coeffi cient of frictionf using a generalized variant of the implicit function theo rem we establish conditions under which there exists a local lipschitz continuous branch of solutions around a reference point finally a piecewise smooth continuation algorithm which allows to follow such branches of solutions is proposed y have certain knowledge on the qualitative behavior of their solutions which is not available in the continuous case indeed the discrete model has at least one solution for any friction coeffi cientf and this solution is unique iff is small enough on the other hand the bounds onf guaranteeing uniqueness of the solution are mesh dependent in other words the uniqueness property of the discrete problem depends on the size of the prob lem thus it may happen that a small change off leads to a large change of the solution but this phenomenon appears only when suffi ciently fine discretizations are used this catastrophic behavior can be observed in numerical experiments 8 9 the first step towards better understanding of the discrete model is to estab lish the existence of local lipschitz continuous branches of solutions parametrized byf the present paper ex tends results from 10 where f was assumed to be constant to the case when f depends on the spatial variable such results are important for the development of continuation algorithms which is another goal of this paper

dynamic refinement and boundary contact forces in sph with applications in fluid flow problems this paper presents a general method for dynamic particle refinement in smoothed particle hydrodynamics sph candidate particles are split into several daughter particles according to a given refinement pattern centred about the original particle through the solution of a non linear minimization problem the optimal mass distribution of the daughter particles is obtained so as to reduce the errors introduced to the underlying density field this procedure necessarily conserves the mass of the system conservation of energy and momentum results are also discussed copyright 2007 john wiley sons ltd

extension of the finite volume particle method to viscous flow the finite volume particle method fvpm is a mesh free method for fluid dynamics which allows simple and accurate implementation of boundary conditions and retains the conservation and consistency properties of classical finite volume methods in this article the fvpm is extended to viscous flows using a consistency corrected smoothed particle hydrodynamics sph approximation to evaluate velocity gradients the accuracy of the viscous fvpm is improved by a higher order discretisation of the inviscid flux combined with a second order temporal discretisation the higher order inviscid fvpm is validated for a 1 d shock tube problem in which it demonstrates an enhanced shock capturing ability for two dimensional simulations a small arbitrary lagrange euler correction to fully lagrangian particle motion is beneficial in maintaining a favourable particle distribution over long simulation times the viscous fvpm is validated for two dimensional poiseuille taylor green and lid driven cavity flows and good agreement is achieved with analytic or reference numerical solutions these results establish the viability of fvpm as a tool for mesh free simulation of viscous flows in engineering

continuity properties for modulation spaces with applications to pseudo differential calculus i we discuss continuity for weighted modulation spaces andprove that many such spaces can be obtained in a canonicalway from the corresponding standard modulation spaces we also discussthe trace operator a a 0 acting on modulationspaces the results are used to get inclusions betweenmodulation spaces and besov spaces and proving continuityfor pseudo differential operators and toeplitz operators

qualitative analysis of 3d elastostatic contact problems with orthotropic coulomb friction and solution dependent coefficients of friction this paper analyzes a discrete form of 3d contact problems with local orthotropic coulomb friction and coefficients of friction which may depend on the solution itself the analysis is based on the fixed point reformulation of the original problem conditions guaranteeing the existence and uniqueness of discrete solutions are established finally numerical results of a model example are presented

the dilation property of modulation spaces and their inclusion relation with besov spaces abstract we consider the dilation property of the modulation spaces m p q let d f t f t be the dilation operator and we consider the behavior of the operator norm d m p q m p q with respect to our result determines the best order for it and as an application we establish the optimality of the inclusion relation between the modulation spaces and besov spaces which was proved by toft j toft continuity properties for modulation spaces with applications to pseudo differential calculus i j funct anal 207 2004 399 429

an adaptive sph method for strong shocks we propose an alternative sph scheme to usual sph godunov type methods for simulating supersonic compressible flows with sharp discontinuities the method relies on an adaptive density kernel estimation adke algorithm which allows the width of the kernel interpolant to vary locally in space and time so that the minimum necessary smoothing is applied in regions of low density we have performed a von neumann stability analysis of the sph equations for an ideal gas and derived the corresponding dispersion relation in terms of the local width of the kernel solution of the dispersion relation in the short wavelength limit shows that stability is achieved for a wide range of the adke parameters application of the method to high mach number shocks confirms the predictions of the linear analysis examples of the resolving power of the method are given for a set of difficult problems involving the collision of two strong shocks the strong shock tube test and the interaction of two blast waves

isometric decomposition operators function spaces ep qλ and applications to nonlinear evolution equations abstract by using the isometric decomposition to the frequency spaces we will introduce a new class of function spaces e p q which is a subspace of gevrey 1 class g 1 r n c r n for 0 and we will study the cauchy problem for the nonlinear schrodinger equation the complex ginzburg landau equation and the navier stokes equation some well posed results are obtained for the cauchy data in e 2 1 0 and the regularity behavior in e 2 1 ct g 1 r n for the complex ginzburg landau equation and the navier stokes equation is also obtained as time t 0

sph with the multiple boundary tangent method in this article we present an improved solid boundary treatment formulation for the smoothed particle hydrodynamics sph method benchmark simulations using previously reported boundary treatments can suffer from particle penetration and may produce results that numerically blow up near solid boundaries as well current sph boundary approaches do not properly treat curved boundaries in complicated flow domains these drawbacks have been remedied in a new boundary treatment method presented in this article called the multiple boundary tangent mbt approach in this article we present two important benchmark problems to validate the developed algorithm and show that the multiple boundary tangent treatment produces results that agree with known numerical and experimental solutions the two benchmark problems chosen are the lid driven cavity problem and flow over a cylinder the sph solutions using the mbt approach and the results from literature are in very good agreement these solutions involved solid boundaries but the approach presented herein should be extendable to time evolving free surface boundaries copyright 2008 john wiley sons ltd

unimodular fourier multipliers for modulation spaces abstract we investigate the boundedness of unimodular fourier multipliers on modulation spaces surprisingly the multipliers with general symbol e i where 0 2 are bounded on all modulation spaces but in general fail to be bounded on the usual l p spaces as a consequence the phase space concentration of the solutions to the free schrodinger and wave equations are preserved as a byproduct we also obtain boundedness results on modulation spaces for singular multipliers sin for 0

instability of smoothed particle hydrodynamics applied to poiseuille flows abstract smoothed particle hydrodynamics sph has been widely applied to flows with free surface multi phase flow and systems with complex boundary geometry however it has been shown that sph suffers from transverse instability when applied to simple wall bounded shear flows such as poiseuille and couette flows at moderate and high reynolds number re 1 casting the application of sph to practical situations into doubt where the reynolds number is frequently large here we consider poiseuille flows for a wide range of reynolds number and find that the documented instability of sph can be avoided by using appropriate ratio of smoothing length to particle spacing in combination with a density re initialization technique which has not been systematically investigated in simulations of simple shear flows we also probe the source of the instability and point out the limitations of sph for wall bounded shear flows at high reynolds number

convergence rate of an optimization algorithm for minimizing quadratic functions with separable convex constraints a new active set algorithm for minimizing quadratic functions with separable convex constraints is proposed by combining the conjugate gradient method with the projected gradient it generalizes recently developed algorithms of quadratic programming constrained by simple bounds a linear convergence rate in terms of the hessian spectral condition number is proven numerical experiments including the frictional three dimensional 3d contact problems of linear elasticity illustrate the computational performance

truncation error in mesh free particle methods a truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics sph and related first order consistent methods such as the first order form of the reproducing kernel particle method error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length x h for uniformly spaced particles in one dimension analysis shows that as h is reduced while maintaining constant x h error decays as h2 until a limiting discretization error is reached which is independent of h if x h is reduced while maintaining constant h i e if the number of neighbours per particle is increased error decreases at a rate which depends on the kernel function s smoothness when particles are distributed non uniformly error can grow as h is reduced with constant x h first order consistent methods are shown to remove this divergent behaviour numerical experiments confirm the theoretical analysis for one dimension and indicate that the main results are also true in three dimensions this investigation highlights the complexity of error behaviour in sph and shows that the roles of both h and x h must be considered when choosing particle distributions and smoothing lengths copyright 2005 john wiley sons ltd

α modulation spaces ii derivative nls abstract the current paper is a continuation of our early work 11 we use the techniques and properties of modulation spaces developed in 11 to study the cauchy problem for the derivative nonlinear schrodinger equations by applying some new type of inhomogeneous linear estimate to control the high low frequency interaction appearing from the nonlinearity we obtain the critical regularity index for the global well posedness with small initial data in modulation spaces for one type of derivative nonlinear schrodinger equations we also study the generalized derivative schrodinger equations

a generalized wall boundary condition for smoothed particle hydrodynamics in this paper we present a new formulation of the boundary condition at static and moving solid walls in sph simulations our general approach is both applicable to two and three dimensions and is very simple compared to previous wall boundary formulations based on a local force balance between wall and fluid particles we apply a pressure boundary condition on the solid particles to prevent wall penetration this method can handle sharp corners and complex geometries as is demonstrated with several examples a validation shows that we recover hydrostatic equilibrium conditions in a static tank and a comparison of the classical dam break simulation with state of the art results in literature shows good agreement we simulate various problems such as the flow around a cylinder and the backward facing step at re 100 to demonstrate the general applicability of this new method

a hybridized discontinuous galerkin framework for high order particle mesh operator splitting of the incompressible navier stokes equations abstract a generic particle mesh method using a hybridized discontinuous galerkin hdg framework is presented and validated for the solution of the incompressible navier stokes equations building upon particle in cell concepts the method is formulated in terms of an operator splitting technique in which lagrangian particles are used to discretize an advection operator and an eulerian mesh based hdg method is employed for the constitutive modeling to account for the inter particle interactions key to the method is the variational framework provided by the hdg method this allows to formulate the projections between the lagrangian particle space and the eulerian finite element space in terms of local i e cellwise l 2 projections efficiently furthermore exploiting the hdg framework for solving the constitutive equations results in velocity fields which excellently approach the incompressibility constraint in a local sense by advecting the particles through these velocity fields the particle distribution remains uniform over time obviating the need for additional quality control the presented methodology allows for a straightforward extension to arbitrary order spatial accuracy on general meshes a range of numerical examples shows that optimal convergence rates are obtained in space and given the particular time stepping strategy second order accuracy is obtained in time the model capabilities are further demonstrated by presenting results for the flow over a backward facing step and for the flow around a cylinder

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

an optimal algorithm for minimization of quadratic functions with bounded spectrum subject to separable convex inequality and linear equality constraints an in a sense optimal algorithm for minimization of quadratic functions subject to separable convex inequality and linear equality constraints is presented its unique feature is an error bound in terms of bounds on the spectrum of the hessian of the cost function if applied to a class of problems with the spectrum of the hessians in a given positive interval the algorithm can find approximate solutions in a uniformly bounded number of simple iterations such as matrix vector multiplications moreover if the class of problems admits a sparse representation of the hessian it simply follows that the cost of the solution is proportional to the number of unknowns theoretical results are illustrated by numerical experiments