limitations of traditional finite volume discretizations for unsteady computational fluid dynamics traditional finite volume methods are popular in the field of refined subsonic flow simulation althrough a degree of confidence has been established in existing algorithms for accurate steady state simulations at least for laminar flows a dubiety still pervades unsteady simulations the traditional finite volume approach is typified by patankar s simple algorithm an approach and terminology for discretizing the equations of fluid flow heat transfer and associated transport processes this methodology althrough adequate for steady state simulations is ineffective for unsteady state problems with significant convective effects the computational fluid dynamics community has largely adopted leonard s suggestion for steady subsonic flow modeling since patankar s discretization can be readily quickened by simply changing the interpolation functions for the face values the same approach is not readily extendable to unsteady simulations it performs progressively worse as the courant number increases beyond 1 countering the only reason for using it in preference to the computationally cheaper explicit methods

finite groups of chain difference one a finite group g is said to have chain difference one if the lengths of any two unrefinable subgroup chains of g differ by at most one finite simple groups of chain difference one were classified by b brewster et al 1993 j algebra160 179 191 using the classification of finite simple groups we give an more elementary proof of this result in particular we give an elementary proof that a minimal counterexample has dihedral or semidihedral sylow 2 subgroups

accuracy characteristics of traditional finite volume discretizations for unsteady computational fluid dynamics recently manson et al demonstrated the shortcoming of traditional finite volume approaches typified by patankar s simple algorithm for discretizing the equations of fluid flow heat transfer and associated transport processes they were able to show for one severe test case low spatial resolution and zero diffusion that traditional finite volume approaches are ineffective for unsteady state problems with significant convective effects they are ineffective because there exists a time step limitation even for implicit methods which is imposed by accuracy constraints rather than stability constraints the objective of the present paper is to show that the poor performance of these methods in that paper was not simply due to the severity of the test case this paper will demonstrate the same inadequacy prevails for a range of spatial resolutions and non zero diffusion cases this knowledge is already documented but its significance still seems to elude the cfd community who persist with traditional discretizations for unsteady advection 7 refs 5 figs

lp and bmo bounds of weighted hardy littlewood averages abstract this paper characterizes those nonnegative functions defined on 0 1 for which the weighted hardy littlewood average u f 0 1 f t t dt is bounded on either l p r n p 1 or bmo r n meanwhile the corresponding operator norms are worked out

the norm inequalities for the weighted cesaro mean operators this paper gives some necessary and sufficient conditions for the weighted cesaro mean operators to be bounded on herz spaces the corresponding new operator norm inequalities are obtained

on the subgroup structure of classical groups in this paper we establish a result on the subgroup structure of classical groups over algebraically closed elds and use this to give a new proof of a fundamental theorem of m aschbacher on subgroups of nite classical groups let v be a nite dimensional vector space over an algebraically closed eld k and let g be one of the classical algebraic groups sl v sp v or so v our result is a reduction theorem concerning the subgroups of g we de ne a certain collection c of natural proper subgroups of g and prove that any closed nite or in nite subgroup of g either lies in a member of c or is roughly speaking a simple group acting irreducibly on v aschbacher s result is an analogous reduction theorem for subgroups of nite classical groups we obtain this as a relatively easy consequence of our main result by taking xed points under the action of a frobenius morphism using a standard process involving lang s theorem the proof of the main result uses elementary linear algebra together with a few basic facts from the theory of algebraic groups various complications which arise in the nite group setting in as become much more straightforward in the algebraic group setting in particular questions involving extension elds do not occur and issues of conjugacy are easily settled when we descend to nite invent math 134 427 453 1998

a comparison of hybrid and quadratic upstream differencing in high reynolds number elliptic flows abstract numerical computations have been performed of various two dimensional elliptic flows at high reynolds number with a view to assessing the relative merits of the widely used hybrid i e upwind central interpolation and the recently proposed quadratic upstream interpolation of leonard known as quick the latter scheme possesses less intrinsic stability than hybrid differencing by selectively evaluating some of the convective elements at a previous iteration level however satisfactorily rapid convergence has been obtained it is concluded from the flows tested that the extra computational effort per node required for quick over the hybrid difference scheme is more than repaid by the greater numerical accuracy that results

constructing an entropy stable upwind scheme for compressible fluid flow computations a relationship between entropy processes and numerical upwinding is examined in the context of computational gasdynamics a discretized form of the entropy inequality is constructed at the integration point where convection diffusion modeling occurs in finite volume methods conventional upwinding schemes may violate the local form of the second law of thermodynamics but a modified upwinding scheme uses additional momentum constraints and pressure terms to provide a positive entropy production rate the second law is seen as an important quantitative measure of nonphysical numerical results as well as a sound basis for error analysis applications to converging diverging nozzle and blunt body flow problems demonstrate the promising performance of the overall numerical algorithm

grid convergence error analysis for mixed order numerical schemes new developments are presented in the area of grid convergence error analysis and error estimation for mixed order numerical schemes a mixed order scheme is defined here as a numerical method where the order of the local truncation error varies either spatially e g at a shock wave or for different terms in the governing equations e g first order convection with second order diffusion the case examined herein is the mach 8 laminar flow of a perfect gas over a sphere cone geometry this flowfield contains a strong bow shock wave where the formally second order numerical scheme is reduced to first order via a flux limiting procedure the mixedorder error analysis method allows for non monotone behavior in the solutions variables as the mesh is refined non monotonicity in the local solution variables is shown to arise from a cancellation of first and second order error terms for the present case the proposed error estimator which is based on the mixed order analysis is shown to provide good estimates of the actual error furthermore this error estimator nearly always provides conservative error estimates in the sense that the actual error is less than the error estimate for the case examined

regular article on a class of pade finite volume methods a class of pade finite volume methods providing an improved spectral resolution is presented and compared with well known methods the formulation is based on the sliding averages of the variables and allows the computation of derivatives of all orders using the fourier analysis these methods are examined with respect to i order of accuracy ii spectral resolution iii boundary conditions and iv stability

a computational strategy for the regularized 13 moment equations with enhanced wall boundary conditions the challenge of modeling low speed rarefied gas flow in the transition regime is well known in this paper we propose a numerical solution procedure for the regularized 13 moment equations within a finite volume framework the stress and heat flux equations arising in the method of moments are transformed into the governing equations for the stress and heat flux deviators based on their first order approximation to model confined flows a complete set of wall boundary conditions for the 13 moment equations are derived based on the maxwell wall boundary model this has been achieved by expanding the molecular distribution function to fourth order accuracy in hermite polynomials empirical correction factors are introduced into the boundary conditions and calibrated against direct simulation monte carlo data the numerical predictions obtained from the regularized 13 moment equations and the navier stokes fourier equations are compared with data generated using the direct simulation monte carlo method for planar couette flow for a range of wall velocities and knudsen numbers 0 012 1 0 the results indicate that the regularized 13 moment equations are in good qualitative agreement with the direct simulation monte carlo data the results also highlight limitations that are caused by the use of a first order expansion of the third moment

implicit method for incompressible flow calculations in three dimensional ducts and cascades a method is presented for the numerical solution of the incompressible navier stokes equations in three dimensional ducts and cascades both laminar and turbulentows are resolved the latter through the k turbu lence model the method is based on an elliptic formulation which consists of the sequential solution of the mean ow and the turbulence equations through an approximate factorization technique the cost of factorization is minimized through the formation and inversion of a single matrix for all but the continuity equations the conti nuity constraint is enforced by means of thepressure correction technique forwhich a moreef cient variant of the approximate factorization scheme is employed the method exhibitsgood convergence characteristics asdepicted from the analyzed three dimensional problems the prediction capabilities of this method are demonstrated by analyzing thelaminarowin a three dimensional bend and theturbulentowin a linearcompressorcascade with zero and nonzero tip clearance for cascadeow problems with nonzero tip clearances a variant of the present method accommodating multiple patched subdomains is devised

about riesz transforms on the heisenberg groups see also m1 subsequently several other proofs have been given of probabilistic b ba see also g v or analytic d r p nature also p a meyer has given in m2 a similar result in the gaussian setting the aim of this work is to prove analogous inequalities for the family of heisenberg groups h n instead of the family of euclidean spaces r n the euclidean proofs do not adapt to the non commutative situation of h however our method is reminiscent of some ideas of the proofs by duoandikoetxearubio de francia d r and pisier p a new feature is however the central r6te played by the heat kernel and our proof heavily relies on its explicit expression in h n given by gavean g and hulanicki h let us recall finally that apart from any question of uniformity the boundedness of the riesz transforms on every nilpotent lie group is a well known issue see l v

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

hausdorff operators on the power weighted hardy spaces abstract in this paper we study the high dimensional hausdorff operators on the power weighted hardy spaces we establish their sharp boundedness on power weighted hardy spaces and local hardy spaces particularly our results solve an open question posted by liflyand in 16

local mesh refinement within a multi block structured grid scheme for general flows abstract a multi level flow adaptive mesh refinement strategy has been formulated and implemented within a structured grid multiblock scheme for 2d laminar transitional and turbulent recirculating flow although the locally refined irregular grid portions are organised as block structured patches within coarse grid blocks a special data structure allows high storage economy to be achieved issues of particular interest in the study include the performance of different flow adaptation sensors based on solution properties and error and the response of the solution accuracy to inter grid interpolation practices based on bi linear bi quadratic and compact interpolation the effectiveness of the local refinement strategy especially in terms of cpu and memory resources is examined by reference to four test cases ranging from an analytically prescribed scalar field over a square domain to a transitional flow over a highly loaded compressor blade the study demonstrates that cpu and memory savings with a three level refinement for the compressor blade case are of order 70 and 90 respectively relative to the requirements of globally fine grids returning similar accuracy levels

semi implicit second order schemes for numerical solution of level set advection equation on cartesian grids abstract a new parametric class of semi implicit numerical schemes for a level set advection equation on cartesian grids is derived and analyzed an accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial lax wendroff procedure and numerical von neumann stability analysis the obtained semi implicit scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one dimensional scheme that is not the case for analogous fully explicit or fully implicit schemes a further improvement is obtained by using so called corner transport upwind extension in two dimensional case the extended semi implicit scheme with a specific velocity dependent value of is 3rd order accurate in space and time for a constant advection velocity and it is unconditional stable according to the numerical von neumann stability analysis for the linear advection equation in general

a finite volume method with linearisation in time for the solution of advection reaction diffusion systems the numerical solution in one space dimension of advection reaction diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models this work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest the basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method the resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations

the length and depth of compact lie groups let g be a connected lie group an unrefinable chain of g is defined to be a chain of subgroups g g 0 g 1 cdots g t 1 where each g i is a maximal connected subgroup of g i 1 in this paper we introduce the notion of the length respectively depth of g defined as the maximal respectively minimal length of such a chain and we establish several new results for compact groups in particular we compute the exact length and depth of every compact simple lie group and draw conclusions for arbitrary connected compact lie groups g we obtain best possible bounds on the length of g in terms of its dimension and characterize the connected compact lie groups that have equal length and depth the latter result generalizes a well known theorem of iwasawa for finite groups more generally we establish a best possible upper bound on dim g in terms of the chain difference of g which is its length minus its depth

a consistently formulated quick scheme for fast and stable convergence using finite volume iterative calculation procedures abstract previous applications of quick for the discretization of convective transport terms in finite volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme instead earlier formulations have been established numerically by trial and error the new formulation for quick presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance careful testing performed for the wall driven square enclosure flow configuration shows that the consistently derived version of quick is more stable and converges faster than any of the formulations previously employed this testing includes the relative evaluation of boundary conditions approximated by second and third order finite difference schemes as well as calculations performed at higher reynolds numbers than previously reported

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

boundedness of multidimensional hausdorff operators on h1 rn abstract in this paper we consider the h 1 boundedness of multidimensional hausdorff operators defined by h a f x r n u f a u x d u where l l o c 1 r n a u a i j u i j 1 n is an n n matrix and each a i j u is a measurable function of u let b i j 1 n b i j for the matrix b b i j u i j 1 n we prove that h a is bounded from the hardy space h 1 to itself if r n u det a 1 u ln 1 a 1 u n det a 1 u d u our result improves known results in addition we show that the above condition is optimal in the size condition

stable numerical method applying a total variation diminishing scheme for incompressible flow to solve incompressible navier stokes equations a stable finite difference method applying a total variation diminishing tvd upwind scheme originally designed for compressible flow is proposed the validity and the receptivity of this method employing such a tvd scheme for application to incompressible flow analysis are investigated by the evaluation of the accuracy stability and convergence rate using the generalized implicit simplified marker and cell smac solution method combined with the tvd scheme three dimensional developing entry flows through a square curved duct are calculated and compared with available experimental data and some computational results obtained by quadratic upstream interpolations for the convective kinematics quick schemes as well as by third order upwind schemes

an assessment of flow oriented schemes for reducing false diffusion un facteur limitatif important dans la modelisation precise des problemes d ecoulement est la representation numerique des termes de convection dans les equations de navier stokes revue des differentes methodes d approximation des termes de convection pour reduire les erreurs de fausse diffusion dans le contexte des methodes de differences finies et de volumes finis

a lagrangian stochastic modeling framework for multi phase flow in porous media many of the complex physical processes relevant for compositional multi phase flow in porous media are well understood at the pore scale level in order to study co 2 storage in sub surface formations however it is not feasible to perform simulations at these small scales directly and effective models for multi phase flow description at darcy scale are needed unfortunately in many cases it is not clear how the micro scale knowledge can rigorously be translated into consistent macroscopic equations here we present a new methodology which provides a link between lagrangian statistics of phase particle evolution and darcy scale dynamics unlike in finite volume methods the evolution of lagrangian particles representing small fluid phase volumes is modeled each particle has a state vector consisting of its position velocity fluid phase information and possibly other properties like phase composition while the particles are transported through the computational domain according to their individual velocities the properties are modeled via stochastic processes honoring specified lagrangian statistics note that the conditional expectations of the particle velocities are different for different fluid phases the goal of this paper is to present the general framework for this alternative modeling approach various one and two dimensional numerical experiments demonstrate that with appropriate stochastic rules the particle solutions are consistent with a standard two phase darcy flow formulation in the end we demonstrate how to model non equilibrium phenomena within the stochastic particle framework which will be the main focus of the future work

the length and depth of algebraic groups let g be a connected algebraic group an unrefinable chain of g is a chain of subgroups g g 0 g 1 cdots g t 1 where each g i is a maximal connected subgroup of g i 1 we introduce the notion of the length respectively depth of g defined as the maximal respectively minimal length of such a chain working over an algebraically closed field we calculate the length of a connected group g in terms of the dimension of its unipotent radical r u g and the dimension of a borel subgroup b of the reductive quotient g r u g in particular a simple algebraic group of rank r has length dim b r which gives a natural extension of a theorem of solomon and turull on finite quasisimple groups of lie type we then deduce that the length of any connected algebraic group g exceeds frac 1 2 dim g we also study the depth of simple algebraic groups in characteristic zero we show that the depth of such a group is at most 6 this bound is sharp in the positive characteristic setting we calculate the exact depth of each exceptional algebraic group and we prove that the depth of a classical group over a fixed algebraically closed field of positive characteristic tends to infinity with the rank of the group finally we study the chain difference of an algebraic group which is the difference between its length and its depth in particular we prove that for any connected algebraic group g with soluble radical r g the dimension of g r g is bounded above in terms of the chain difference of g

the p adic weighted hardy cesaro operator and an application to discrete hardy inequalities abstract this paper aims to investigate the boundedness of the p adic analog of the weighted hardy cesaro operator u s f z p f s t t d t on weighted lebesgue spaces and weighted bmo spaces in each case we obtain the corresponding operator norms u s in particular these results have a surprising relevance to discrete hardy inequalities on the real field we prove a reverse bmo hardy inequality and give a necessary condition on so that the commutator of u s is bounded on l r q p n with symbols in bmo q p n

multivariate hausdorff operators on the spaces lp rn abstract the operators h indicated in the title are characterized by a finite borel measure on r n a borel measurable function c on r n and an n n a e nonsingular matrix a whose entries are also borel measurable functions on r n and h f is defined by means of a lebesgue stieltjes integral with respect to we give simple sufficient conditions in order that these operators be bounded on the lebesgue spaces l p r n for some 1 p these sufficient conditions are exact even in the well known special cases of the cesaro and copson operators we also determine the hausdorff operator h which is adjoint to h in a certain sense we reveal interrelations among these operators and the fourier transform of a function f in l 1 r n on closing we present further special hausdorff operators

simple accurate and efficient revisions to maccormack and saulyev schemes high peclet numbers abstract stream water quality modeling often involves numerical methods to solve the dynamic one dimensional advection dispersion reaction equations adre there are numerous explicit and implicit finite difference schemes for solving these problems and two commonly used schemes are the maccormack and saulyev schemes this paper presents simple revisions to these schemes that make them more accurate without significant loss of computation efficiency using advection dominated high peclet number problems as test cases performances of the revised schemes are compared to performances of five classic schemes forward time centered space ftcs backward time centered space btcs crank nicolson and the traditional maccormack and saulyev schemes all seven of the above numerical schemes were tested against analytical solutions for pulse and step inputs of mass to a steady flow in a channel and performances were considered with respect to stability accuracy and computational efficiency results indicated that both the modified saulyev and the maccormack schemes which are named the saulyevc and maccormackc schemes respectively greatly improved the prediction accuracy over the original ones the computation efficiency in terms of cpu time was not impacted for the saulyevc scheme the maccormackc scheme demonstrated increased time consumption but was still much faster than implicit schemes

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

quasiconformal mappings on the heisenberg group on etudie les applications conformes et quasi conformes sur le groupe de heisenberg la metrique invariante a gauche naturelle sur cet espace est non isotrope sous des dilatations et ne peut se decrire par une metrique de riemann ceci engendre de nouveaux phenomenes

a semi lagrangian finite volume method for newtonian contraction flows a new finite volume method for solving the incompressible navier stokes equations is presented the main features of this method are the location of the velocity components and pressure on different staggered grids and a semi lagrangian method for the treatment of convection an interpolation procedure based on area weighting is used for the convection part of the computation the method is applied to flow through a constricted channel and results are obtained for reynolds numbers based on half the flow rate up to 1000 the behavior of the vortex in the salient corner is investigated qualitatively and quantitatively and excellent agreement is found with the numerical results of dennis and smith proc roy soc london a 372 1980 pp 393 414 and the asymptotic theory of smith j fluid mech 90 1979 pp 725 754

incorporation of point sources in numerical transport schemes numerical experiments with the stone brian numerical transport scheme for a continuous point source injection into steady uniform flow show that substantial oscillations can be generated upstream of the fixed steep front at the source location these occur because this scheme does not possess the transportive property oscillations are most severe when the point source massflow is all allocated to a single grid node in which case they can lead to gross mass conservation errors if the upstream boundary condition is not specified carefully incorporation of point sources in schemes that lack the transportive property is not trivial

a new numerical approach to solve an elliptic equation a new numerical approach to solve an elliptic partial differential equation that originates from the governing equations of steady state fluid flow and heat transfer is presented the elliptic partial differential equation is transformed by introducing an exponential function to eliminate the convection terms in the equation a fourth order central differencing scheme and a second order central differencing scheme are used to numerically solve the transformed elliptic partial differential equation analytical solutions of this equation are also given comparisons are made between the analytical solutions the numerical results using the present schemes and those using the four classical differencing schemes namely the first order upwind scheme hybrid scheme power law scheme and exponential scheme the comparisons illustrate that the proposed algorithm performs better than the four classical differencing schemes

evaluation of a bounded high resolution scheme for combustor flow computations the present paper is concerned with the application of a high resolution scheme for a finite volume discretization method the capability of the chosen scheme is evaluated for the numerical simulation of three dimensional flowfields special emphasis lies in the calculation of the processes in the mixing zone of gas turbine combustors thus numerical results are compared with detailed measurements of velocity and temperature in a model mixing zone the velocity field as well as the temperature field strongly depend on the scheme used for the discretization of the momentum and energy equations the proposed high resolution scheme and the well known quick scheme yield similar results which are superior to those obtained with the simple upwind scheme for the simulation of turbulent transport the standard fc model is employed the effect of numerical diffusion caused by the usual upwind discretization of the convective transport of a and e is assessed by the application of the high resolution scheme of the discretization of the a and e equations as a result it is found that the velocity and temperature fields are insensitive to the scheme that is applied for the discretization of the a and e equations

hardy space estimates of hausdorff operators on the heisenberg group abstract this is a continuation of a series of works about hausdorff operator on hardy spaces in the setting of the heisenberg group in this paper we obtain the boundedness from lebesgue spaces to hardy spaces for fractional hausdorff operators and their compositions with riesz transforms we also establish the boundedness for two kinds of special hausdorff operators the hausdorff poisson operator and the hausdorff gauss operator on hardy spaces

assessment of finite difference approximations for the advection terms in the simulation of practical flow problems abstract an assessment of seven discretization schemes for the advection terms of the transport equation to reduce numerical diffusion in practical flow problems has been established the schemes have been evaluated using three test cases for laminar flow problems the test cases consist of the transport of a scalar step in a uniform velocity field two interacting parallel streams and a slot jet the performance of the schemes is evaluated for advection dominated flows in transient and steady state solutions the considered schemes include four that have not been evaluated before for practical flow problems in general schemes which produced less numerical diffusion suffered from more numerical dispersion or oscillations two bounding techniques considered in the study were effective in significantly elliminating numerical dispersion

an efficient immersed boundary treatment for complex moving object an efficient immersed boundary treatment for simulation of flexible moving body immersed in fluid is presented the level set signed distance function is used to indicate body surface a simple mapping strategy is proposed to avoid costly signed distance re initialization computations the strategy is efficient for both rigid and deformable structures and can be extended to 3 d case easily with the use of signed distance function reconstruction of flow variables on a body surface can be easily implemented through linear bilinear or quadratic interpolation in order to suppress the pressure oscillations caused by the role conversion of forcing points and fluid points a modified interpolation scheme is presented by introducing a dynamic weight term to the fluid point together with local grid refinement and using larger time step the pressure oscillations can be effectively diminished by the modified interpolation scheme the proposed method is validated by 2 d numerical simulations on a uniform flow past a fixed cylinder in line and transversely oscillating cylinders a flapping wing a 3 d simulation on a uniform flow past a rectangle plane with an initial attack angle and a moving anguilliform swimmer present numerical results are compared with other cfd solutions as well as experimental results

strongly singular convolution operators on the heisenberg group we consider the l2 mapping properties of a model class of strongly singular integral operators on the heisenberg group hn these are convolution operators on hn whose kernels are too singular at the origin to be of calderon zygmund type this strong singularity is compensated for by introducing a suitably large oscillation our results are obtained by utilizing the group fourier transform and uniform asymptotic forms for laguerre functions due to erdelyi

generalized poincare embeddings and weighted hardy operator on qpα q spaces abstract the poincare embeddings w 1 n r n bmo r n and the john nirenberg inequality in bmo r n are classical results in modern analysis and partial differential equations this paper studies the generalized poincare embeddings and the john nirenberg inequality in q p q r n spaces furthermore for the weighted hardy operator u and its adjoint v this paper gives sufficient and necessary conditions on weight function to ensure the boundedness of them on q p q r n spaces

numerical simulation of filamentary discharges with parallel adaptive mesh refinement direct simulation of filamentary gas discharges like streamers or dielectric barrier micro discharges requires the use of an adaptive mesh the objective of this paper is to develop a strategy which can use a set of grids with suitable local refinements for the continuity equations and poisson s equation in 2d and 3d geometries with a high order discretization the advantages of this approach are presented with a filamentary discharge simulation in plane plane geometry in nitrogen within the diffusion drift approximation

a new subgroup lattice characterization of finite solvable groups abstract we show that if g is a finite group then no chain of modular elements in its subgroup lattice l g is longer than a chief series also we show that if g is a nonsolvable finite group then every maximal chain in l g has length at least two more than the chief length of g thereby providing a converse of a result of j kohler our results enable us to give a new characterization of finite solvable groups involving only the combinatorics of subgroup lattices namely a finite group g is solvable if and only if l g contains a maximal chain x and a chain m consisting entirely of modular elements such that x and m have the same length

on the properties of discrete spatial filters for cfd the spatial filtering of variables in the context of computational fluid dynamics cfd is a common practice most of the discrete filters used in cfd simulations are locally accurate models of continuous operators however when filters are adaptative i e the filter width is not constant or meshes are irregular discrete filters sometimes break relevant global properties of the continuous models they are based on for example the principle of maxima and minima reduction or conservation are eventually infringed in this paper we analyze the properties of analytic continuous convolution filters and extract those we consider to define filtering then we impose the accomplishment of these properties on explicit discrete filters by means of constraints three filters satisfying the derived conditions are deduced and compared to common differential discrete cfd filters on synthetic fields tests on the developed discrete filters show the fulfillment of the imposed properties in particular the problem of maxima and minima generation is resolved for physically relevant cases the tests are conducted on the basis of the eigenvectors of graph laplacian matrices of meshes thus insight into the relations between filtering and oscillation growth on general meshes is provided further tests on singularity fields and on isentropic vortices have also been conducted to evaluate the performance of filters on basic cfd fields results confirm that imposing the proposed conditions makes discrete filters properties consistent with those of the continuous ones

third order upwind finite element computation of the incompressible navier stokes equations part i computation of flow around rectangular cylinders abstract aerodynamic behaviours of two dimensional unsteady flows around rectangular cylinders are numerically investigated by third order upwind finite element computation of the incompressible navier stokes equations a turbulence model such as the two equation model is not incorporated in the computational scheme so that the rectangular cylinders at depth breadth ratios from 0 7 to 4 to be considered are located in a uniform flow it is found that the numerical results of flows around the rectangular cylinders obtained by using the third order upwind finite element scheme are in good agreement with other computational and experimental results

a finite volume formulation for transient convection and diffusion equations with unstructured distorted grids and its applications in fluid flow simulations with a collocated variable arrangement abstract this paper describes a finite volume method for simulating transport processes governed by convection diffusion type equations the formulation is based on a cell centred unstructured grid with an edge based data structure discretisation is independent of control volume or cell shape by using a surface vector decomposition at the midpoint of the interface between cells along with a deferred correction approach any cross diffusion due to grid skewness can be readily accounted for when discretising the diffusive flux for modelling fluid flow processes a collocated arrangement of variables is employed so that a single coefficient matrix applies for the momentum equations of each velocity component to avoid checkerboard oscillation arising from pressure velocity decoupling occurring under the collocated variable arrangement when a pressure based solution algorithm is employed a novel pseudo flux interpolation method is proposed for unstructured grids ensuring that the solution is both under relaxation factor and time step for transient calculation independent the methodology can be formulated within a framework whereby either a coupled or a decoupled solution algorithm can be employed the features and advantages of the method are demonstrated by solution of the navier stokes equations for two benchmark flow problems

a comparison of higher order bounded convection schemes this paper presents a comparison of recently developed four higher order bounded convection schemes soucup hlpa smarter and lppa which employ different characteristics in a normalized variable diagram all the schemes are formulated on a non uniform non orthogonal grid and their relative performances are compared through applications to the several test problems the results of numerical experiments show that all the tested bounded schemes resolve the boundedness problem retaining the accuracy of the higher order scheme the hlpa smarter and lppa schemes result in nearly the same solution behaviours and the soucup scheme is shown to be relatively more diffusive than the other three bounded schemes

boundedness of hausdorff operators on real hardy spaces h1 over locally compact groups abstract results of liflyand and collaborators on the boundedness of hausdorff operators on the hardy space h 1 over finite dimensional real space are generalized to the case of locally compact groups that are spaces of homogeneous type special cases and examples of compact lie groups homogeneous groups in particular the heisenberg group and finite dimensional spaces over division rings are considered in conclusion we solve for the space l 2 an open question on compactness of a hausdorff operator posed by liflyand

linearity for actions on vector groups abstract let k be an arbitrary field let g be a smooth linear algebraic group over k and let u be a vector group over k on which g acts by automorphisms of algebraic groups the action of g on u is said to be linear if there is a g equivariant isomorphism of algebraic groups u lie u suppose that g is connected and that the unipotent radical of g is defined over k if the g module lie u is simple we show that the action of g on u is linear if g acts by automorphisms on a connected split unipotent group u we deduce that u has a filtration by g invariant closed subgroups for which the successive factors are vector groups with a linear action of g when g is connected and the unipotent radical of g is defined and split over k this verifies an assumption made in earlier work of the author on the existence of levi factors on the other hand for any field k of positive characteristic we show that if the category of representations of g is not semisimple there is an action of g on a suitable vector group u which is not linear

estimates of weighted hardy littlewood averages on the p adic vector space abstract in the p adic vector space q p n we characterize those non negative functions defined on z p w q p 0 w p 1 for which the weighted hardy littlewood average u f z p f t t d t is bounded on l r q p n 1 r and on bmo q p n also in each case we find the corresponding operator norm u