numerical simulation of unsteady viscous free surface flow abstract a finite element method is presented for the numerical simulation of time dependent incompressible viscous free surface flows the time dependent primitive equations are solved sequentially using explicit time marching procedure the method is based on a velocity correction approach to the time integration of the navier stokes equations in which only the incompressibility condition is treated implicitly a special arbitrary mixed lagrangian eulerian description has been used to avoid the typical problems encountered in a purely lagrangian description the method appears applicable for small computers problems requiring several thousand nodes can be solved on personal computers numerical experiments have been performed that show that this approach is reasonably efficient and robust for a range of complicated highly nonlinear problems

interpolation operators in orlicz sobolev spaces we study classical interpolation operators for finite elements like the scott zhang operator in the context of orlicz sobolev spaces furthermore we show estimates for these operators with respect to quasi norms which appear in the study of systems of p laplace type

on the finite element approximation of p stokes systems in this paper we study the finite element approximation of systems of p stokes type for p in 1 infty we derive in some cases optimal error estimates for finite element approximation of the velocity and for the pressure in a suitable functional setting the results are supported by numerical experiments

simulation of wave structure interaction by hybrid cartesian immersed boundary and arbitrary lagrangian eulerian finite element method this article aims to develop a cartesian grid based numerical model to study the interaction between free surface flow and stationary or oscillating immersed obstacle in a viscous fluid to incorporate the effect of the free surface motion an arbitrary lagrangian eulerian ale scheme is employed to accurately capture the configuration of free surface to deal with the complex submerged obstacle in the fluid a hybrid cartesian immersed boundary hcib method is adopted which allows easy implementation of the solid boundary conditions for a fixed structured grid the two numerical techniques are combined to study the wave structure interaction problems the major merit of the proposed model is that the fluid grid is fixed throughout the computations during the transients while the immersed body can move arbitrarily through the cartesian grid the meshes deform smoothly over the solid and free surface boundaries especially for representing sharp interface there is no re meshing process needed since this scheme only depends on the simple mesh generation to promote the efficiency of calculation some numerical examples are displayed respectively to validate the robustness and accuracy of the hcib method the ale based finite element scheme and their combinations in addition the other two numerical applications are carried out to simulate the wave structure interaction with stationary and moving immersed body in case studies some physical characteristics are also discussed for a range of amplitude of free surface wave reynolds numbers and the proximity of structure under the liquid surface the feasibility of the developed novel numerical model is shown through five numerical experiments

a front remeshing technique for a lagrangian description of moving interfaces in two fluid flows the numerical analysis of two fluid flows involves the treatment of a discontinuity that appears at the separating interface classical lagrangian schemes applied to update the front position between two immiscible incompressible fluids have been long recognized to provide a sharp representation of the interface however the main drawback of these approaches is the progressive distortion in the distribution of the markers used to identify the material front to avoid this problem an interface remeshing algorithm based on the diffuse approximation of the interface curvature is proposed in this work in addition the remeshed front is enforced to preserve the global volume these new aspects are incorporated in an existing fluid dynamics formulation for the analysis of two fluid flows problems the resulting formulation is called in this work as the moving lagrangian interface remeshing technique mlirt copyright 2005 john wiley sons ltd

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

quasi newton minimization for the p x laplacian problem we propose a quasi newton minimization approach for the solution of the p x laplacian elliptic problem x r m this method outperforms those existing for the p x variable case which are based on general purpose minimizers such as bfgs moreover when compared to ad hoc techniques available in literature for the p constant case and usually referred to as mesh independent the present method turns out to be generally superior thanks to better descent directions given by the quadratic model

fluid structure interaction for non conforming interfaces based on a dual mortar formulation abstract in the present work the problem of fluid structure interaction fsi with independently space discretized fluid and structure fields is addressed in the context of finite elements to be able to deal with non conforming meshes at the fluid structure interface we propose the integration of a dual mortar method into the general fsi framework this method has lately been used successfully to impose interface constraints in other contexts such as finite deformation contact the main focus is set on monolithic coupling algorithms for fsi here in these cases the dual mortar approach allows for the elimination of the additional lagrange multiplier degrees of freedom from the global system by condensation the resulting system matrices have the same block structure as their counterparts for the conforming case and permit the same numerical treatment partitioned dirichlet neumann coupling is also considered briefly and it is shown that the dual mortar approach permits a numerically efficient mapping between fluid and structure quantities at the interface numerical examples demonstrate the efficiency and robustness of the proposed method we present results for a variety of different element formulations for the fluid and the structure field indicating that the proposed method is not limited to any specific formulation furthermore the applicability of state of the art iterative solvers is considered and the convergence behavior is shown to be comparable to standard simulations with conforming discretizations at the interface

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

convergence analysis for a finite element approximation of a steady model for electrorheological fluids in this paper we study the finite element approximation of systems of p cdot p stokes type where p cdot p is a non constant given function of the space variables we derive in some cases optimal error estimates for finite element approximation of the velocity and of the pressure in a suitable functional setting

a comparison of polynomial time completeness notions ladner lynch and selman 1975 showed the differences among the power of several types of polynomial time reductions for dext c 0dtime 2cn but questions concerning complete degrees w r t these reductions have remained open here we show in dext almost all the possible differences between the completeness notions w r t any pair of the following reductions pt ptt pp n tt pc pd pbtt pk tt pm differences between several types of truth table completenesses we introduce the notion f easy subset for each pr reduction we first prove the property that all pr complete sets for dext have f easy subsets where the class f depends on each reduction type r then the construction of a ps complete set which is not pr complete becomes a simple diagonalization argument these constructions also work for all deterministic superpolynomial complexity classes which have a pm complete set in order to construct a set which is pt complete for dext but not ptt complete for dext we use strings which are not polynomially producible from small sized inputs these strings are said to have large generalized kolmogorov complexity cf hartmanis 1983

eulerian lagrangian treatment of nondilute two phase gels we develop a three dimensional eulerian lagrangian two phase mixture model for a gel in which fluid is represented in eulerian coordinates and network in lagrangian coordinates the equations of motion and boundary conditions in their respective frames are derived using a principle of virtual power the volume fractions of each material at each point of eulerian space are calculated using the position and volume density of network particles network and fluid have separate velocity fields and the model includes viscous elastic and applied forces as well as those due to chemical potentials pressure and intermaterial drag we also develop a second order accurate numerical method for solving the model equations in one dimension illustrations of model behavior under a variety of conditions are shown

separation of np completeness notions we use hypotheses of structural complexity theory to separate various np completeness notions in particular we introduce an hypothesis from which we describe a set in np that is mbox leq rm p rm t complete but not mbox leq rm p tt complete we provide fairly thorough analyses of the hypotheses that we introduce

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

on the c1 γ ω w2 2 ω regularity for a class of electro rheological fluids abstract we are concerned with a system of nonlinear partial differential equations with p x structure 1 p p x p 0 and no slip boundary conditions we prove the existence and uniqueness of a c 1 w 2 2 solution corresponding to small data without further restrictions on the bounds p p 0 in particular this result is applicable to the steady motion of shear dependent electro rheological fluids

quasi ale finite element method for nonlinear water waves this paper presents a newly developed quasi arbitrary lagrangian eulerian finite element method qale fem for simulating water waves based on fully nonlinear potential theory the main difference of this method from the conventional finite element method developed by one of authors of this paper and others see e g q w ma g x wu r eatock taylor finite element simulation of fully non linear interaction between vertical cylinders and steep waves part 1 methodology and numerical procedure and part 2 numerical results and validation int j numer methods fluids 36 2001 265 308 and g x wu z z hu simulation of nonlinear interactions between waves and floating bodies through a finite element based numerical tank proc r soc a 460 2004 2050 3037 3058 is that the complex mesh is generated only once at the beginning and is moved at all other time steps in order to conform to the motion of the free surface and structures this feature allows one to use an unstructured mesh with any degree of complexity without the need of regenerating it every time step which is generally inevitable and very costly due to this feature the qale fem has high potential in enhancing computational efficiency when applied to problems associated with the complex interaction between large steep waves and structures since the use of an unstructured mesh in such a case is likely to be necessary to achieve overall high efficiency the numerical techniques involved in the qale fem are developed including the method to move interior nodes technique to re distribute the nodes on the free surface scheme to calculate velocities and so on the model is validated by water waves generated by a wavemaker in a tank and the interaction between water waves and periodic bars on the bed of tank satisfactory agreement is achieved with analytical solutions experimental data and numerical results from other methods

arbitrary lagrangian eulerian finite element analysis of free surface flow an arbitrary lagrangian eulerian ale description of newtonian fluid flow is presented it allows the simulation of free surfaces with the finite element method fem we develop a robust node repositioning algorithm which consists of two parts an energy minimization principle controls the positions of the internal nodes a good approximation of the boundaries is ensured by explicitly enforcing the free surface conditions numerical examples are done employing the mini element

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

regularity results for stationary electro rheological fluids we prove regularity results for weak solutions to systems modelling electro rheological fluids in the stationary case as proposed in 27 31 a particular case of the system we consider is

arbitrary lagrangian eulerian finite element method for computation of two phase flows with soluble surfactants a finite element scheme based on a coupled arbitrary lagrangian eulerian and lagrangian approach is developed for the computation of interface flows with soluble surfactants the numerical scheme is designed to solve the time dependent navier stokes equations and an evolution equation for the surfactant concentration in the bulk phase and simultaneously an evolution equation for the surfactant concentration on the interface second order isoparametric finite elements on moving meshes and second order isoparametric surface finite elements are used to solve these equations the interface resolved moving meshes allow the accurate incorporation of surface forces marangoni forces and jumps in the material parameters the lower dimensional finite element meshes for solving the surface evolution equation are part of the interface resolved moving meshes the numerical scheme is validated for problems with known analytical solutions a number of computations to study the influence of the surfactants in 3d axisymmetric rising bubbles have been performed the proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant

lagrangian finite element analysis of newtonian fluid flows a fully lagrangian nite element method for the analysis of newtonian ows is developed the approach furnishes in eect a lagrangian implementation of the compressible navier stokes equations as the ow proceeds the mesh is maintained undistorted through continuous and adaptive remeshing of the uid mass the principal advantage of the present approach lies in the treatment of boundary conditions at material surfaces such as free boundaries uid uid or uid solid interfaces in contrast to eulerian approaches boundary conditions are enforced at material surfaces ab initio and therefore require no special attention consistent tangents are obtained for lagrangian implicit analysis of a newtonian uid ow which may exhibit compressibility eects the accuracy of the approach is assessed by comparison of the solution for a sloshing problem with existing numerical results and its versatility demonstrated through a simulation of wave breaking the nite element mesh is maintained undistorted throughout the computation by recourse to frequent and adaptive remeshing 1998 john wiley sons ltd

front tracking with moving least squares surfaces the representation of interfaces by means of the algebraic moving least squares amls technique is addressed this technique in which the interface is represented by an unconnected set of points is interesting for evolving fluid interfaces since there is no surface connectivity the position of the surface points can thus be updated without concerns about the quality of any surface triangulation we introduce a novel amls technique especially designed for evolving interfaces applications that we denote ramls for robust amls the main advantages with respect to previous amls techniques are increased robustness computational efficiency and being free of user tuned parameters further we propose a new front tracking method based on the lagrangian advection of the unconnected point set that defines the ramls surface we assume that a background eulerian grid is defined with some grid spacing h the advection of the point set makes the surface evolve in time the point cloud can be regenerated at any time in particular we regenerate it each time step by intersecting the gridlines with the evolved surface which guarantees that the density of points on the surface is always well balanced the intersection algorithm is essentially a ray tracing algorithm well studied in computer graphics in which a line ray is traced so as to detect all intersections with a surface also the tracing of each gridline is independent and can thus be performed in parallel several tests are reported assessing first the accuracy of the proposed ramls technique and then of the front tracking method based on it comparison with previous eulerian lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications

adaptive tetrahedral mesh generation by constrained delaunay refinement this paper presents a tetrahedral mesh generation method for numerically solving partial differential equations using finite element or finite volume methods in three dimensional space the main issues are the mesh quality and mesh size which directly affect the accuracy of the numerical solution and the computational cost two basic problems need to be resolved namely boundary conformity and field points distribution the proposed method utilizes a special three dimensional triangulation so called constrained delaunay tetrahedraliwtion to conform the domain boundary and create field points simultaneously good quality tetrahedra and graded mesh size can be theoretically guaranteed for a large class of mesh domains in addition an isotropic size field associated with the numerical solution can be supplied the field points will then be distributed according to it good mesh size conformity can be achieved for smooth sizing informations the proposed method has been implemented various examples are provided to illustrate its theoretical aspects as well as practical performance

transfinite mappings and their application to grid generation the two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain mesh generators or grid generators are preprocessors whicd decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils a number of such techiques have been developed over the past decade to alleviate the frustation and reduce the time involved in the tedious manual subdividing of a complex shaped region or 3 d structure into finite elements our purpose here is to describe how the techniques of bivariate and trivariate blending function interpolation which were originally developed for and applied to geometric problems of computer aided design of sculptured surface and 3 d solids can be adapted and applied to the geometric problems of grid generation in contrast to other techniques which require the numerical solution of complex partial differential equations and hence a great deal of computing the transfinite methods proposed herein are computationally inexpensive

adaptive coupled arbitrary lagrangian eulerian finite element and meshfree method for injection molding process this paper presents an adaptive method that couples the finite element fe method and the meshfree mf method in the arbitrary lagrangian eulerian ale description for numerical simulation of injection molding processes the ale feature is used to accurately capture moving free surfaces of flow problems and meanwhile to alleviate mesh distortion and its influence on the accuracy and robustness of numerical solutions based on the continuous blending method originally presented for properly imposing the essential boundary conditions in mf methods the coupled ale fe and mf method is developed to exploit the respective advantages of both fe and mf methods but to avoid their respective weak points the method features self adaptivity in view of the fact that moving free surfaces in an injection molding process are continuously advanced the pressure stabilized fractional step algorithm in which the modified version of the finite increment calculus process is extended to the coupled ale fe and mf method is used to solve incompressible navier stokes equations governing the injected polymer flow so that equal low order u p interpolations that violate the lbb condition can be effectively used numerical experiments demonstrate the significance and ability of the proposed method for numerical simulation of injection molding processes copyright 2007 john wiley sons ltd

numerical simulation of high schmidt number flow over a droplet by using moving unstructured mesh a direct numerical simulation code for flow over a droplet which rises freely deforms in shape and dissolves into a continuous phase was developed a two phase flow field was discretised by a cell centred arbitrary lagrangian eulerian finite volume formulation by using three dimensional hybrid unstructured meshes which consist of triangular prisms near interface for the resolution of viscous boundary layer and tetrahedrons in the other part since mass boundary layer is much thinner than that of momentum for high schmidt number problems very thin layer cells are generated within one layer of the prisms attached to the interface only for solving mass transfer this can be claimed as a novelty of the present simulation method from the simulation results the mechanisms of shape deformation and or oscillation trajectory morphology and vortex shedding are elucidated and correlated to mass transfer at moderately high reynolds number

finite element approximation of the p laplacian in this paper we consider the continuous piecewise linear finite el ement approximation of the following problem given p 1 oo and g find u such that v vu 2vu f iniicr2 u g on a the finite element approximation is defined over i2 a union of regular tri angles yielding a polygonal approximation to q for sufficiently regular so lutions u achievable for a subclass of data g and i2 we prove optimal error bounds for this approximation in the norm wlq q 1 q p for p 2 under the additional assumption that qh c 2 numerical results demonstrating these bounds are also presented

an ale formulation based on spatial and material settings of continuum mechanics part 1 generic hyperelastic formulation abstract the present contribution deals with the derivation of a generic hyperelastic arbitrary lagrangian eulerian formulation on the basis of a consistent variational framework the governing equations follow straightforwardly from the dirichlet principle for conservative mechanical systems thereby the key idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed material and at fixed spatial coordinates the corresponding euler lagrange equations define the spatial and the material motion version of the balance of linear momentum i e the balance of spatial and material forces in a consistent dual format in the discretised setting the governing equations are solved simultaneously rendering the spatial and the material configuration which minimise the overall potential energy of the system the remeshing strategy of the ale formulation is thus no longer user defined but objective in the sense of energy minimisation if the governing equations are derived from a potential i e either from an incremental potential or from a total potential as in the present case they are inherently symmetric both in the continuous case and in the discrete case this symmetry property is particularly appealing since it ensures symmetric system matrices upon discretisation

a 3d moving mesh finite element method for two phase flows a 3d ale finite element method is developed to study two phase flow phenomena using a new discretization method to compute the surface tension forces the computational method is based on the arbitrary lagrangian eulerian formulation ale and the finite element method fem creating a two phase method with an improved model for the liquid gas interface an adaptive mesh update procedure is also proposed for effective management of the mesh to remove add and repair elements since the computational mesh nodes move according to the flow the ale description explicitly defines the two phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary including the role of the surface tension the proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics this paper focuses on the description of the proposed methodology with particular emphasis on the discretization of the surface tension force the new remeshing technique and the validation results additionally a microchannel simulation in complex geometry is presented for two elongated bubbles c 2014 elsevier inc all rights reserved

p selectivity intersections and indices the p selective sets selman 1979 are those sets for which there is a polynomial time algorithm that given any two strings determines which is more likely to belong to the set if either of the strings is in the set the algorithm chooses one that is in the set we prove that for each k the k ary boolean connectives under which the p selective sets are closed are exactly those that are either completely degenerate or almost completely degenerate we determine the complexity of the index set of the r e p selective sets 30 complete

an adaptive remeshing strategy for flows with moving boundaries and fluid structure interaction the primary objective of this work is to extend the capability of the arbitrary lagrangian eulerian ale based strategy for solving fluid structure interaction problems this is driven by the fact that the ale mesh movement techniques will not be able to treat problems in which fluid structure interface experiences large motion in addition for certain problems the need arises to capture accurately flow features such as a region with high gradients of the solution variables this can be achieved by incorporating an adaptive remeshing procedure into the solution strategy as in our previous works comput methods appl mech eng 2006 195 1633 1666 comput methods appl mech eng 2006 195 5754 5779 here the fluid flow is governed by the incompressible navier stokes equations and modelled by using stabilized low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the flexible structure is represented by means of appropriate standard finite element formulations while the motion of the rigid body is described by rigid body dynamics for temporal discretization of both fluid and solid bodies the discrete implicit generalized method is employed the resulting strongly coupled set of non linear equations is then solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearization of the overall incremental problem within the adaptive solution strategy the quality of fluid mesh and the solution quality indicator are evaluated regularly and compared against the appropriate remeshing criteria to decide whether a remeshing step is required the adaptive remeshing procedure follows closely the standard computational procedure in which the adaptive remeshing process produces a mesh that can capture salient features of the flow field for the problems under consideration in this work the motion of the fluid boundary very often results in boundaries with very high curvatures and a fluid domain that contain areas with small cross sections to be able to generate meshes that give result with acceptable accuracy these local geometrical features need to be included in determining the element density distribution the numerical examples demonstrate the robustness and efficiency of the methodology copyright 2007 john wiley sons ltd

a natural element updated lagrangian strategy for free surface fluid dynamics we present a novel algorithm to simulate free surface fluid dynamics phenomena at low reynolds numbers in an updated lagrangian framework it is based on the use of one of the most recent meshless methods the so called natural element method free surface tracking is performed by employing a particular instance of shape constructors called a shapes this means that at each time step the geometry of the domain is extracted by employing a particular member of the finite set of shapes described by the nodal cloud the lagrangian framework allows us to integrate the inertial terms of the navier stokes equations by employing the method of characteristics which are precisely the nodal pathlines a theoretical description of the method is included together with some examples showing its performance

on helping by robust oracle machines abstract the concept of helping by robust oracle turing machines introduced recently by schoning is extended to the notion of one sided helping and its relations to the structural properties of np sets are investigated various results on who can help whom have been obtained on sets in bpp in r in up and sparse sets sets which do not help any set are studied and two types of sets defined by structural properties are demonstrated to help no sets except those in p sest which help themselves are also studied and are shown to be related to self reducible sets several previously known structural results on np sets are reproved from the point of view of helping

query monotonic turing reductions we study reductions that limit the extreme adaptivity of turing reductions in particular we study reductions that make a rapid structured progression through the set to which they are reducing each query is strictly longer shorter than the previous one we call these reductions query increasing query decreasing turing reductions we also study query nonincreasing query nondecreasing turing reductions these are turing reductions in which the sequence of query lengths is nonincreasing nondecreasing we ask whether these restrictions in fact limit the power of reductions we prove that query increasing and query decreasing turing reductions are incomparable with that is are neither strictly stronger than nor strictly weaker than truth table reductions and are strictly weaker than turing reductions in addition we prove that query nonincreasing and query nondecreasing turing reductions are strictly stronger than truth table reductions and strictly weaker than turing reductions despite the fact that we prove query increasing and query decreasing turing reductions to in the general case be strictly weaker than turing reductions we identify a broad class of sets a for which any set that turing reduces to a will also reduce to a via both query increasing and query decreasing turing reductions in particular this holds for all tight paddable sets where a set is said to be tight paddable exactly if it is paddable via a function whose output length is bounded tightly both from above and from below in the length of the input we prove that many natural np complete problems such as satisfiability clique and vertex cover are tight paddable

immunity relativizations and nondeterminism it is known 8 13 that there is a recursive set a such that text np a contains a set that is text p a immune that is there is an infinite set l in text np a such that no infinite subset of l is in text p a the first result generalizes this fact to situations where the running times of the machines specifying the larger class bound the size of the sets of strings queried in the computation trees of the machines specifying the smaller class the second result is of a different type for relativized complexity classes specified by bounds on the number of oracle queries and the number of nondeterministic steps allowed in computations it is known 14 that one can describe a set a such that there is an infinite hierarchy of classes relative to a where each new class in the hierarchy is obtained by increasing the amount of nondeterminism here it is shown that the conditions allowing infinite hierarchies to exist also allow for each i geqq 0 the existence of a set

space time discontinuous galerkin method for nonlinear water waves a space time discontinuous galerkin dg finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented the space time dg method results in a conservative numerical discretization on time dependent deforming meshes which follow the free surface evolution the algorithm is higher order accurate both in space and time and closely related to an arbitrary lagrangian eulerian ale approach a detailed derivation of the numerical algorithm is given including an efficient procedure to solve the nonlinear algebraic equations resulting from the space time discretization numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method

threshold computation and cryptographic security threshold machines are turing machines whose acceptance is determined by what portion of the machine s computation paths are accepting paths probabilistic machines are turing machines whose acceptance is determined by the probability weight of the machine s accepting computation paths in 1975 simon proved that for unbounded error polynomial time machines these two notions yield the same class pp perhaps because simon s result seemed to collapse the threshold and probabilistic modes of computation the relationship between threshold and probabilistic computing for the case of bounded error has remained unexplored in this paper we compare the bounded error probabilistic class bpp with the analogous threshold class bpppath and more generally we study the structural properties of bpppath we prove that rm bpp path contains both np bpp and p rm np log and that rm bpp path is contained in p rm sigma 2 p log rm bpp np and pp we conclude that unless the polynomial hierarchy collapses bounded error threshold computation is strictly more powerful than bounded error probabilistic computation we also consider the natural notion of secure access to a database an adversary who watches the queries should gain no information about the input other than perhaps its length we show for both bpp and bpppath that if there is any database for which this formalization of security differs from the security given by oblivious database access then p neq pspace it follows that if any set lacking small circuits can be securely accepted then p neq pspace

reductions among polynomial isomorphism types abstract a set a is polynomial many one reducible to a set b a is karp reducible to b if there is a polynomially computable function f such that for all x x a iff f x b arbitrary sets a and b are of the same polynomial many one degree if each is polynomial many one reducible to the other a and b are polynomially isomorphic if the function f can be taken one to one onto and polynomially invertible in classical recursive function theory all many one complete sets are recursively isomorphic berman and hartmanis have observed that all known np complete sets are polynomially isomorphic berman and hartmanis have observed that all known np complete sets are polynomially isomorphic and have conjectured that all np complete sets complete under karp reducibility are isomorphic in this paper we show that not just the complete degree but every polynomial many one degree consists either of a single isomorphism type or else contains infinitely many isomorphism types densely ordered under one one size increasing polynomially invertible reductions and also contains infinitely many isomorphisms types which are incomparable under one one invertible reductions in fact we show that every countable partial ordering can be embedded in any such many one degree we also exhibit polynomial degrees which have infinitely many isomorphism types no examples are known of degrees consisting of a single isomorphism type

efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method abstract radial basis function interpolation is often employed in mesh deformation algorithms for unstructured meshes for example in fluid structure interaction or design optimization problems this is known to be a robust methodology that results in high quality deformed meshes the applicability of this method to large problems is currently hampered by its prohibitive computational cost however which is caused by the need to solve a dense system of equations the computation time grows as o n b 3 if a direct solver is employed for the solution where n b denotes the number of boundary nodes in the mesh while alternative iterative solvers often suffer from an unfavorable convergence behavior in this paper we present the inverse fast multipole method as a novel fast approximate direct solver with a computational cost scaling as o n b the linear complexity is achieved by transforming the dense system into an extended sparse system along with the compression of certain matrix blocks into low rank factorizations the solver is inexact although the error can be controlled and made as small as needed a low accuracy solver can hence be used as an efficient preconditioner in an iterative scheme numerical benchmarks are presented demonstrating that the proposed approach enhances the computational efficiency of mesh deformation algorithms based on radial basis function interpolation significantly without jeopardizing their robustness and quality

oscillation constants for euler type differential equations involving the p t laplacian abstract this paper deals with the oscillation problem for the nonlinear differential equation x p t 2 x t p t x p t 2 x 0 where is a positive parameter and p t 1 is a nondecreasing and smooth function some non oscillation criteria are given for this equation the obtained results are the best possible in a certain sense we use the riccati technique and the function sequence technique moreover we propose a conjecture concerning the oscillation problem for this equation in the case when p t tends to infinity as t

a fictitious domain approach for a mixed finite element method solving the two phase stokes problem with surface tension forces abstract in this article we study a mixed finite element formulation for solving the stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor on an interface that splits the domain into two subdomains equality of velocities is assumed at the interface the interface conditions are taken into account with multipliers a suitable lagrangian functional is introduced for deriving a weak formulation of the problem a specificity of this work is the consideration of the interface with a fictitious domain approach the latter is inspired by the xfem approach in the sense that cut off functions are used but it is simpler to implement since no enrichment by singular functions is provided in that context getting convergence for the dual variables defined on the interface is non trivial for that purpose an augmented lagrangian technique stabilizes the convergence of the multipliers which is important because their value would determine the dynamics of the interface in an unsteady framework theoretical analysis is provided where we show that a discrete inf sup condition independent of the mesh size is satisfied for the stabilized formulation this guarantees optimal convergence rates that we observe with numerical tests the capacity of the method is demonstrated with robustness tests and with an unsteady model tested for deformations of the interface that correspond to ellipsoidal shapes in dimension 2

a computational framework for free surface fluid flows accounting for surface tension abstract this work is concerned with the simulation of incompressible newtonian fluid flow problems with free surfaces in the presence of surface tension the computational framework presented is based on the stabilised velocity pressure finite element method the movement and deformation of the computational domain are accounted for by employing the arbitrary lagrangian eulerian ale description of the fluid kinematics the numerical model is extended to incorporate surface tension effects a novel partitioned solution procedure is developed based on the newton raphson methodology which incorporates full linearisation of the overall incremental problem several numerical examples are provided to demonstrate the efficiency of the methodology

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

singular solutions of nonlinear differential equations with p t laplacian abstract this paper deals with the singular solutions of the nonlinear differential equation a t x p t 2 x b t x q t 2 x involving p t laplacian sufficient conditions are given for the existence and the nonexistence of singular solutions of the first second kind in addition we study the existence of proper solutions and the coexistence of proper solutions and singular solutions of the second kind finally some examples are given to illustrate our results

optimal low order finite element methods for incompressible flow abstract in this paper we consider the characterization of optimal stabilisation parameters associated with mixed finite element approximations of stokes flow we show how the optimal parameter in terms of the approximating power of the method is related to the parameter value which minimises the condition number of the associated schur complement system for the pressure field we illustrate the tightness of our abstract theoretical results in the cases of the q 1 p 0 quadrilateral and p 1 p 1 triangular elements

an ale based iterative cbs algorithm for non isothermal non newtonian flow with adaptive coupled finite element and meshfree method this paper presents a generalized scheme of the fractional step algorithm using characteristic based split cbs in ale framework for the numerical simulation of incompressible non isothermal non newtonian fluid flows and applies it combined with the adaptive coupled finite element and meshfree method for spatial discretizations to the polymer injection molding process based on the idea to discretize the material time derivative instead of the spatial time derivative the characteristic galerkin method is derived in a more general way and is used to discretize the non newtonian momentum and the energy conservation equations an iterative procedure which makes the conservation equations satisfied in an implicit sense is introduced into the scheme to enhance its stability in the time domain numerical experiments with the power law fluid model demonstrate and validate the performance and the capability of the proposed scheme

finite element approximation of some degenerate monotone quasilinear elliptic systems in this paper we examine the continuous piecewise linear finite element approximation of the following system given bf f equiv f j and bf g equiv g j find bf u equiv u j j 1 to r with r 1 or 2 such that nabla cdot k z nabla bf u z nabla bf u z bf f z quad z in omega subset r 2 quad bf u partial omega bf g partial omega where nabla bf u equiv partial u j partial z i 1 leq i leq 2 1 leq j leq r and k is a given matrix on omega times r 2 times r we characterize a class of matrices k for which we prove error bounds for this discretization for sufficiently regular solutions bf u achievable at least for some model problems our bounds improve on existing results in the literature it is shown that for a notable subclass of k for which only suboptimal error bounds have been previously derived the piecewise linear finite element approximation of this problem will converge

finite element approximation of the p cdot laplacian we study a priori estimates for the p cdot laplace dirichlet problem mathrm div vert nabla mathbf v vert p cdot 2 nabla mathbf v mathbf f we show that the gradients of the finite element approximation with zero boundary data converge with rate o h alpha if the exponent p is alpha holder continuous the error of the gradients is measured in the so called quasi norm i e we measure the l 2 error of vert nabla mathbf v vert frac p 2 2 nabla mathbf v

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

truly monolithic algebraic multigrid for fluid structure interaction the coupling of flexible structures to incompressible fluids draws a lot attention during the last decade many different solution schemes have been proposed in this contribution we concentrate on strong coupling fluid structure interaction by means of monolithic solution schemes therein a newton krylov method is applied to the monolithic set of nonlinear equations such schemes require good preconditioning to be efficient we propose two preconditioners that apply algebraic multigrid techniques to the entire fluid structure interaction system of equations the first is based on a standard block gauss seidel approach where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem the second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields the resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

robust algorithms a different approach to oracles abstract a new notion of an oracle machine being helped by an oracle set is introduced it is required that the oracle machine is robust i e it always computes the same set independent of the oracle the main result states that the class of sets that can be computed by deterministic polynomial time algorithms being helped by some oracle set is exactly np co np some connections to probabilistic classes are also investigated

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

an arbitrary lagrangian eulerian finite element approach for fluid structure interaction phenomena the present contribution is concerned with the design of a family of consistent fluid structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations the characterization of the moving fluid structure interface is realized by means of the arbitrary lagrangian eulerian technique the spatial discretization is performed with the finite element method whereby either a first order upwind scheme or the classical second order upwind petrov galerkin technique are used to discretize the linearized fluid equations while the standard bubnov galerkin method is applied to the structural equations in order to streamline coupling the structure is discretized in a velocity based fashion the temporal discretization of both the fluid and the structural equations is embedded in the generalized framework by making use of classical newmark approximations in time to quantify the sources of error of the proposed algorithms systematic studies in terms of the one dimensional piston model problem are presented copyright 2003 john wiley sons ltd

numerical simulation of bubble rising in viscous liquid an improved numerical algorithm for front tracking method is developed to simulate the rising of a bubble in quiescent viscous liquid due to buoyancy in the new numerical algorithm volume correction is introduced to conserve the bubble volume while tracking the bubble s rising and deforming and volume flux conservation based simple algorithm is adopted to solve the navier stokes equation for fluid flow using finite volume method the new front tracking algorithm is validated systematically by simulating single bubble rising and deforming in quiescent viscous liquid under different flow regimes the simulation results are compared with the experimental measurement in terms of terminal bubble shape and velocity the simulation results demonstrate that the new algorithm is robust in the flow regimes with larger ranges of reynolds number re 200 bond number bo 200 density ratio r l r b 1000 and viscosity ratio m l m b 500 the new front tracking algorithm is also applied to investigate bubble rising and deforming behaviour in the various flow regimes of air bubble water solution system under effects of reynolds number bond number density ratio viscosity ratio as well as the bubble initial shape which have been explored previously by experiments the predicted bubble shape and terminal velocity agree well with the experimental results hence the new modelling algorithm expands the conventional front tracking method to more realistic and wider applications

improved volume conservation in the computation of flows with immersed elastic boundaries this paper introduces a recipe for the construction of a finite difference divergence operator the coefficients of which are completely determined once an interpolation scheme has been chosen substitution of this divergence operator for the previously used divergence based on central differences makes a dramatic improvement in the overall volume conservation that is observed in an immersed boundary computation this improvement is particularly important for computations in which an elastic boundary separates chambers containing fluid at substantially different pressures a situation which is prominent in cardiac fluid dynamics during the contraction of the ventricles

a moving mesh interface tracking method for 3d incompressible two phase flows an interface tracking method using an unstructured moving mesh has been developed for simulating three dimensional incompressible and immiscible two phase flows the interface mesh is moved in a lagrangian fashion a local mesh adaptation method is used to capture the changing interface curvature maintain good mesh quality and deal with large deformation the interface is of zero thickness so the jump and continuity conditions across the interface are implemented directly without any smoothing of the properties of the two fluids this is theoretically beneficial compared to other methods that allow the fluids properties to continuously vary in an interface region the curvature for interfacial tension calculation is geometrically computed by a least squares parabola fitting method a mesh separation scheme for interfacial flows is employed to handle topological transition the numerical technique is tested and validated by several cases which include a two layer couette flow an oscillating droplet surrounded by gas and a droplet in shear flow the results obtained from numerical simulations are found to be in excellent agreement with analytical solutions and experimental results a collapsing ligament in a quiescent gas flow and a modulated jet pinching are simulated to show the robustness of the method

quasi norm error bounds for the finite element approximation of a non newtonian flow we consider the finite element approximation of a non newtonian flow where the viscosity obeys a general law including the carreau or power law for sufficiently regular solutions we prove energy type error bounds for the velocity and pressure these bounds improve on existing results in the literature a key step in the analysis is to prove abstract error bounds initially in a quasi norm which naturally arises in degenerate problems of this type

convergence analysis for incompressible generalized newtonian fluid flows with nonstandard anisotropic growth conditions we study equations to describe incompressible generalized newtonian fluids where the extra stress tensor satisfies a nonstandard anisotropic asymptotic growth condition an implicit finite element discretization and a simple fully practical fixed point scheme with proper thresholding criterion are proposed and convergence toward weak solutions of the limiting problem is shown computational experiments are included which motivate nontrivial fluid flow behavior

numerical simulation of 3d bubbles rising in viscous liquids using a front tracking method the rise of bubbles in viscous liquids is not only a very common process in many industrial applications but also an important fundamental problem in fluid physics an improved numerical algorithm based on the front tracking method originally proposed by tryggvason and his co workers has been validated against experiments over a wide range of intermediate reynolds and bond numbers using an axisymmetric model j hua j lou numerical simulation of bubble rising in viscous liquid j comput phys 22 2007 769 795 in the current paper this numerical algorithm is further extended to simulate 3d bubbles rising in viscous liquids with high reynolds and bond numbers and with large density and viscosity ratios representative of the common air water two phase flow system to facilitate the 3d front tracking simulation mesh adaptation is implemented for both the front mesh on the bubble surface and the background mesh on the latter mesh the governing navier stokes equations for incompressible newtonian flow are solved in a moving reference frame attached to the rising bubble specifically the equations are solved using a finite volume scheme based on the semi implicit method for pressure linked equations simple algorithm and it appears to be robust even for high reynolds numbers and high density and viscosity ratios the 3d bubble surface is tracked explicitly using an adaptive unstructured triangular mesh the numerical model is integrated with the software package paramesh a block based adaptive mesh refinement amr tool developed for parallel computing paramesh allows background mesh adaptation as well as the solution of the governing equations in parallel on a supercomputer further peskin distribution function is applied to interpolate the variable values between the front and the background meshes detailed sensitivity analysis about the numerical modeling algorithm has been performed the current model has also been applied to simulate a number of cases of 3d gas bubbles rising in viscous liquids e g air bubbles rising in water simulation results are compared with experimental observations both in aspect of terminal bubble shapes and terminal bubble velocities in addition we applied this model to simulate the interaction between two bubbles rising in a liquid which illustrated the model s capability in predicting the interaction dynamics of rising bubbles

kiva 4 the kiva family of codes was developed to simulate the thermal and fluid processes taking place inside an internal combustion engine in this latest version of this open source code kiva 4 the numerics have been generalized to unstructrured meshes this change required modifications to the lagrangian phase of the computations the pressure solution and fundamental changes in the fluxing schemes of the rezoning phase this newest version of the code inherits all the droplet phase capabilities and physical sub models of previous versions the integration of the gas phase equations with moving solid boundaries continues to employ the successful arbitrary lagrangian eulerian ale methodology its new unstructured capability facilitates grid construction in complicated geometries and affords a higher degree of flexibility the numerics of the code emphasizing the new additions are described various computational examples are performed demonstrating the new capabilities of the code