cuspidal ell modular representations of p adic classical groups for a classical group over a non archimedean local field of odd residual characteristic p we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p as representations induced from a cuspidal type we also give a fundamental step towards the classification of cuspidal representations identifying when certain cuspidal types induce to equivalent representations this result is new even in the case of complex representations finally we prove that the representations induced from more general types are quasi projective a crucial tool for extending the results here to arbitrary irreducible representations

intertwining and supercuspidal types for p adic classical groups let f be a non archimedean local field of residual characteristic different from 2 and let g be a unitary symplectic or orthogonal group considered as the fixed point subgroup in gl n f of an involution s we generalize the notion of a simple character for which was introduced by bushnell and kutzko annals of mathematics studies 129 princeton university press 1993 to define semisimple characters given a semisimple character for fixed by s we transfer it to a character for g and calculate its intertwining if the torus associated to is maximal compact we obtain supercuspidal representations of g which are new if the torus is split only over a wildly ramified extension

incompressible smoothed particle hydrodynamics for free surface flows a generalised diffusion based algorithm for stability and validations for impulsive flows and propagating waves the incompressible smoothed particle hydrodynamics isph method with projection based pressure correction has been shown to be highly accurate and stable for internal flows and importantly for many problems the pressure field is virtually noise free in contrast to the weakly compressible sph approach xu et al 2009 31 however for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels a new algorithm is presented which remedies this issue giving stable and accurate solutions to both internal and free surface flows generalising the particle shifting approach of xu et al 2009 31 the algorithm is based upon fick s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability the algorithm is validated against analytical solutions for an internal flow at higher reynolds numbers than previously the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times the method is then validated for progressive regular waves with paddle motion defined by linear theory the accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels the test cases are thought to provide a more thorough quantitative validation than previously undertaken

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

index concepts for linear mixed systems of differential algebraic and hyperbolic type equations for many technical systems the use of a refined network modeling approach leads to hyperbolic type initial boundary value problems of partial differential algebraic equations pdaes the boundary conditions of these systems are governed by time dependent differential algebraic equations daes that couple the pdae system with the network elements that are modeled by daes in time only in order to classify these systems we extend some index notions that have already been introduced to treat parabolic type problems a perturbation index is considered that reflects the sensitivity of the mixed system to slight perturbations in the right hand side of the pdaes as well as in the input signals of the dae systems and initial values in order to make an a posteriori analysis of semidiscretization in space and time we introduce additionally a space and a method of lines mol index here one is especially interested in whether the semidiscretized systems properly reflect the properties of the underlying systems we will show that these indices may detect an artificial sensitivity with respect to perturbations e g if the semidiscretization does not consider the information transport along the characteristics

a conservative immersed interface method for large eddy simulation of incompressible flows we propose a conservative second order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered cartesian grid the method is based on a finite volume discretization of the incompressible navier stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained a level set technique is used for description and tracking of the interface geometry so that an extension of the method to moving boundaries and flexible walls is straightforward numerical stability is ensured for small cells by a conservative mixing procedure discrete conservation and sharp representation of the fluid solid interface render the method particularly suitable for large eddy simulations of high reynolds number flows accuracy second order grid convergence and robustness of the method is demonstrated for several test cases inclined channel flow at re 20 flow over a square cylinder at re 100 flow over a circular cylinder at re 40 re 100 and re 3900 as well as turbulent channel flow with periodic constrictions at re 10 595

a differentiation index for partial differential algebraic equations a differentiation index for nonlinear partial differential algebraic equations is presented determination of the differentiation index with respect to a direction in the space of independent variables uncovers all equations that must be satisfied by cauchy data on the hyperplane orthogonal to that direction this index is thus a generalization of the differentiation index of differential algebraic equations the motivation for this work is consistent initialization of partial differential algebraic systems the analysis is demonstrated through several examples including some taken from fluid dynamics and chemical engineering

pressure boundary conditions for computing incompressible flows with sph in smoothed particle hydrodynamics sph methods for fluid flow incompressibility may be imposed by a projection method with an artificial homogeneous neumann boundary condition for the pressure poisson equation this is often inconsistent with physical conditions at solid walls and inflow and outflow boundaries for this reason open boundary flows have rarely been computed using sph in this work we demonstrate that the artificial pressure boundary condition produces a numerical boundary layer that compromises the solution near boundaries we resolve this problem by utilizing a rotational pressure correction scheme with a consistent pressure boundary condition that relates the normal pressure gradient to the local vorticity we show that this scheme computes the pressure and velocity accurately near open boundaries and solid objects and extends the scope of sph simulation beyond the usual periodic boundary conditions

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

unified semi analytical wall boundary conditions applied to 2 d incompressible sph this work aims at improving the 2 d incompressible sph model isph by adapting it to the unified semi analytical wall boundary conditions proposed by ferrand et al 10 the isph algorithm considered is as proposed by lind et al 25 based on the projection method with a divergence free velocity field and using a stabilising procedure based on particle shifting however we consider an extension of this model to reynolds averaged navier stokes equations based on the k e turbulent closure model as done in 10 the discrete sph operators are modified by the new description of the wall boundary conditions in particular a boundary term appears in the laplacian operator which makes it possible to accurately impose a von neumann pressure wall boundary condition that corresponds to impermeability the shifting and free surface detection algorithms have also been adapted to the new boundary conditions moreover a new way to compute the wall renormalisation factor in the frame of the unified semi analytical boundary conditions is proposed in order to decrease the computational time we present several verifications to the present approach including a lid driven cavity a water column collapsing on a wedge and a periodic schematic fish pass our results are compared to finite volumes methods using volume of fluids in the case of free surface flows we briefly investigate the convergence of the method and prove its ability to model complex free surface and turbulent flows the results are generally improved when compared to a weakly compressible sph model with the same boundary conditions especially in terms of pressure prediction

construction of tame supercuspidal representations the notion of depth is defined by moy prasad mp2 the notion of a generic character will be defined in 9 when g gln or g is the multiplicative group of a central division algebra of dimension n with n p 1 our generic characters are just the generic characters in my where the definition is due to kutzko moreover in these cases our construction literally specializes to howe s construction as formulated in my and it is known that the construction yields all supercuspidal representations my hm notice that the initial datum in our construction consists of very simple objects linear characters and supercuspidal representations of depth zero the latter are well understood by the work of moy prasad and morris see 3 by the work of howe irreducible supercuspidal representations of gln f with n p 1 are parametrized by certain characters of e as e varies through

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

index and characteristic analysis of linear pdae systems automatable analyses of the index and well posedness of two general classes of linear pdaes are presented for use in equation based dynamic simulation packages these analyses determine whether a problem possesses a unique solution trajectory the potential effect of noise in the initial and boundary conditions on the calculated solution and the index of the model equations measures of the degeneracy of the system rather than a differentiation index bound the order of derivatives of forcing functions that appear in the solution

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

semisimple types for p adic classical groups we construct for any symplectic unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic a type for each bernstein component of the category of smooth representations using bushnell kutzko s theory of covers moreover for a component corresponding to a cuspidal representation of a maximal levi subgroup we prove that the hecke algebra is either abelian or a generic hecke algebra on an infinite dihedral group with parameters which are at least in principle computable via results of lusztig in an appendix we make a correction to the proof of a result of the second author that every irreducible cuspidal representation of a classical group as considered here is irreducibly compactly induced from a type

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

fast free surface detection and level set function definition in sph solvers the present paper proposes a novel algorithm to detect the free surface in particle simulations both in two and three dimensions since the proposed algorithms are based on sph interpolations their implementation does not require complex geometrical procedures thus the free surface detection can be easily embedded in sph solvers without a significant increase of the cpu time throughout this procedure accurate normal vectors to the free surface are made available then it is possible to define a level set function algorithm which is presented in detail the latter allows in depth analyses of three dimensional free surface simulations by using standard visualization tools including internal features of the flow the algorithms proposed for detecting free surface particles and defining the level set function are validated on simple and complex two and three dimensional flow simulations the usefulness of the proposed procedures to post process and analyze complex flows are illustrated on realistic examples

the supercuspidal representations of p adic classical groups let g be a unitary symplectic or special orthogonal group over a locally compact non archimedean local field of odd residual characteristic we construct many new supercuspidal representations of g and bushnell kutzko types for these representations moreover we prove that every irreducible supercuspidal representation of g arises from our constructions

supercuspidal representations an exhaustion theorem let be a reductive adic group we prove that all supercuspidal representations of arise through yu s construction subject to certain hypotheses on depending on as a corollary under the same hypotheses we see that any supercuspidal representation is compactly induced from a representation of an open subgroup which is compact modulo the center

a new class of discretization methods for the solution of linear differential algebraic equations with variable coefficients we discuss new discretization methods for linear differential algebraic equations daes with variable coefficients we introduce numerical methods to compute the local invariants of such daes that were introduced by the authors in a previous paper p kunkel and v mehrmann j comput appl math 56 1994 pp 225 251 using these quantities we are able to determine numerically global invariances like the strangeness index which generalizes the differentiation index for daes that in particular include undetermined solution components based on these methods we then obtain regularization schemes which allow us to employ general solution methods the new methods are tested on a number of numerical examples

semisimple characters for p adic classical groups let g be a unitary symplectic or orthogonal group over a non archimedean local field of residual characteristic different from 2 considered as the fixed point subgroup in a general linear group of an involution following previous work of bushnell and kutzko and of the author we generalize the notion of a semisimple character for and for g in particular following the formalism of bushnell and henniart we show that these semisimple characters have certain functorial properties finally we show that any positive level supercuspidal representation of g contains a semisimple character

comparisons of weakly compressible and truly incompressible algorithms for the sph mesh free particle method in the smoothed particle hydrodynamics sph discretisation method for the navier stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption wcsph this includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the wcsph mach number and explicit method this paper presents comparisons of a semi implicit and truly incompressible sph isph algorithm with the classical wcsph method showing how some of the problems encountered in wcsph have been resolved by using isph to simulate incompressible flows mathematical models are presented before describing sph formalism several standard boundary conditions are introduced and special attention is given to tracking the surface particles the lid driven cavity flow re 400 and 1000 is performed as a benchmarking test a bluff body test case a square cylinder in a closed channel re d 20 and 100 based on the cylinder diameter shows that pressure fields extracted from wcsph are very unreliable whereas isph predict pressures and forces in closer agreement with classical finite volume cfd methods dam breaking cases with dry or wet beds downstream are then presented to highlight free surface flow and rapid dynamics effects the wcsph and isph results are generally verified with reference data from experiment and or another numerical method all the comparisons show improvement with isph and good agreement in general

on the hecke algebra of a type for unramified p adic unitary groups abstract let f be a non archimedean local field of odd residue characteristic equipped with a galois involution with fixed field f 0 and let g be a symplectic group over f or an unramified unitary group over f 0 for a simple type j p p in g which is a g cover associated to a certain simple stratum we show that the corresponding hecke algebra h g p is generic

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