dissipative issue of high order shock capturing schemes with non convex equations of state it is well known that closed with a non convex equation of state eos the riemann problem for the euler equations allows non standard waves such as split shocks sonic isentropic compressions or rarefaction shocks to occur loss of convexity then leads to non uniqueness of entropic or lax solutions which can only be resolved via the liu oleinik criterion equivalent to the existence of viscous profiles for all admissible shock waves this suggests that in order to capture the physical solution a numerical scheme must provide an appropriate level of dissipation a legitimate question then concerns the ability of high order shock capturing schemes to naturally select such a solution to investigate this question and evaluate modern as well as future high order numerical schemes there is therefore a crucial need for well documented benchmarks a thermodynamically consistent c non convex eos that can be easily introduced in eulerian as well as lagrangian hydrocodes for test purposes is here proposed along with a reference solution for an initial value problem exhibiting a complex composite wave pattern the bizarrium test problem two standard lagrangian numerical approaches both based on a finite volume method are then reviewed vnr and godunov type schemes and evaluated on this riemann problem in particular a complete description of several state of the art high order godunov type schemes applicable to general eoss is provided we show that this particular test problem reveals quite severe when working on high order schemes and recommend it as a benchmark for devising new limiters and or next generation highly accurate schemes

conservative rezoning remapping for general quadrilateral meshes a classic problem in lagrangian numerical hydrodynamics is the conservative transfer of quantities from an old distorted mesh to a new mesh the same problem arises whenever the mesh is changed as for example in adaptive mesh techniques this transfer of information is an interpolation process which is frequently called rezoning or remapping the general problem of conservative rezoning from one arbitrary mesh to another may be formulated as follows m sub k integral integral integral sub v sub k rho r dv that is we compute the mass m sub k of each cell of the new mesh by integrating the known density distribution in the old mesh over the cell volume v sub k a direct intregation is generally prohibitive we show however that is is possible to convert this integral to a surface integral by the appropriate use of the divergence theorem thus greatly reducing the complexity of the problem for two dimensional generall quadrilateral meshes the resulting method is exact and particularly simple

improved mean square error estimate for the lms transversal equalizer with narrowband interference when the least mean square lms algorithm is used to adapt an adaptive transversal equalizer that is subject to strong narrowband interference a so called non wiener or nonlinear effect takes place this results in the mean square error mse performance of the adaptive equalizer being better than that of the fixed wiener filter of equivalent structure reuter and zeidler proposed a transfer function based approach to provide an estimate of the mse performance of the equalizer in such an environment we have recently shown that the mean of the lms weights in this adaptive equalizer problem shifts away from the wiener filter solution as a result we propose an mse model for the lms equalizer that is an improvement over the existing reuter zeidler model the new model uses the same transfer function based approach but incorporates the shift in the mean of the weights numerical simulations are provided to illustrate the improvement

generalized geometric cluster algorithm for fluid simulation we present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids the connection with well known cluster algorithms for lattice spin models is discussed and an explicit full cluster decomposition is derived for a particle configuration in a fluid we investigate a number of basic properties of the geometric cluster algorithm including the dependence of the cluster size distribution on density and temperature practical aspects of its implementation and possible extensions are discussed the capabilities and efficiency of our approach are illustrated by means of two example studies

graphical representations for ising systems in external fields a graphical representation based on duplication is developed that is suitable for the study of ising systems in external fields two independent replicas of the ising system in the same field are treated as a single four state ashkin teller model bonds in the graphical representation connect the ashkin teller spins for ferromagnetic systems it is proved that ordering is characterized by percolation in this representation the representation leads immediately to cluster algorithms some applications along these lines are discussed

the time line interpolation method for large time step godunov type schemes abstract this paper describes the use of the time line interpolation procedure for the design of large time step godunov type schemes for systems of hyperbolic conservation laws in one dimension these schemes are based on a specific procedure to characterize the left and right states of the riemann problems at the cell interfaces when the courant number associated with the waves exceeds unity to do so the time line interpolation technique is used constant and linear reconstruction techniques are presented sonic or critical points are seen to be a source of difficulty in the algorithm and an appropriate treatment is proposed the algorithms are applied to the linear advection equation to the inviscid burgers equation and to the set of hyperbolic conservation laws that describe shallow water flow in one dimension these simulations show the superiority of the linear time reconstruction over the use of a constant time reconstruction when the linear reconstruction technique is used the modulus of the amplification factor of the scheme is equal to unity for all wave numbers inducing oscillations in the computed profile owing to the phase error the introduction of a slope limiter allows these oscillations to be eliminated but yields numerical diffusion thus restricting the range of applications of the scheme

the generalized riemann problem for reactive flows abstract a generalized riemann problem is introduced for the equations of reactive non viscous compressible flow in one space dimension initial data are assumed to be linearly distributed on both sides of a jump discontinuity the resolution of the singularity is studied and the first order variation in time of flow variables is given in exact form

iterative analysis of the steady state weight fluctuations in lms type adaptive filters an iterative method is proposed for the analysis of the steady state weight fluctuations in an lms type adaptive fir filter without the widely used independence assumption a power series of the weight error correlation matrix is derived in terms of the stepsize some new effects are observed e g a decrease of the weight fluctuations along the tapped delay line

a second order godunov type scheme for compressible fluid dynamics abstract a second order accurate scheme for the integration in time of the conservation laws of compressible fluid dynamics is presented two related versions are proposed one lagrangian and the second direct eulerian they both share the common ingredient which is a full analytic solution for the time derivatives of flow quantities at a jump discontinuity assuming initial nonvanishing slopes on both sides while this solution is an extension of the solution to the classical riemann problem the resulting schemes are second order extensions of godunov s methods in both cases they are very simple to implement in computer codes several numerical examples are shown where the only additional mechanism is a simple monotonicity algorithm

a particle level set based sharp interface cartesian grid method for impact penetration and void collapse an eulerian sharp interface cartesian grid method is developed for the numerical simulation of the response of materials to impact shocks and detonations the mass momentum and energy equations are solved along with evolution equations for deviatoric stresses and equivalent plastic strain these equations are cast in eulerian conservation law form the mie gruneisen equation of state is used to obtain pressure and the material is modeled as a johnson cook solid the eno scheme is employed to capture shocks in combination with a hybrid particle level set technique to evolve sharp immersed boundaries the numerical technique is able to handle collisions between multiple materials and can accurately compute the dynamics of the immersed boundaries results of calculations for axisymmetric taylor bar impact and penetration of a tungsten rod into steel plate show good agreement with moving finite element solutions and experimental results qualitative agreement with theory is shown for the void collapse phenomenon in an impacted material containing a spherical void

numerical defects of the hll scheme and dissipation matrices for the euler equations the harten lax van leer scheme is popularly used in the cfd community however oscillations are observed from shock tube problems for stiffened gases when the adiabatic index is greater than 3 to understand this phenomenon the dissipation effect of the scheme is evaluated quantitatively in terms of dissipation matrices we have proven and numerically demonstrated that lack of positive definiteness is the root of numerical defects

a free lagrange augmented godunov method for the simulation of elastic plastic solids a lagrangian finite volume godunov scheme is extended to simulate two dimensional solids in planar geometry the scheme employs an elastic perfectly plastic material model implemented using the method of radial return and either the stiffened gas or osborne equation of state to describe the material the problem of mesh entanglement common to conventional two dimensional lagrangian schemes is avoided by utilising the free lagrange method the lagrangian formulation enables features convecting at the local velocity such as material interfaces to be resolved with minimal numerical dissipation the governing equations are split into separate subproblems and solved sequentially in time using a time operator split procedure local riemann problems are solved using a two shock approximate riemann solver and piecewise linear data reconstruction is employed using a muscl based approach to improve spatial accuracy to illustrate the effectiveness of the technique numerical simulations are presented and compared with results from commercial fixed connectivity lagrangian and smooth particle hydrodynamics solvers autodyn 2d the simulations comprise the low velocity impact of an aluminium projectile on a semi infinite target the collapse of a thick walled beryllium cylinder and the high velocity impact of cylindrical aluminium and steel projectiles on a thin aluminium target the analytical solution for the collapse of a thick walled cylinder is also presented for comparison

efficient solution algorithms for the riemann problem for real gases a procedure for constructing solutions to the riemann problem for gas dynamics with a general convex equation of state is given approximate procedures involving a local parametrization of the equation of state are introduced in order to calculate numerical fluxes in conservative finite difference schemes this leads to difference schemes which are as accurate and almost as fast as the analogous schemes for polytropic gases numerical results in one and two space variables are presented

a general non iterative riemann solver for godunov s method abstract godunov s method is characterized by the use of a riemann problem solution to resolve discontinuities at the interface between cells the major drawback of this method is the difficulty and the high cost of solving the nonlinear riemann problem exactly especially for materials with complex equations of state this paper describes a simplified and noniterative approximate riemann solver which is characterized by only two material dependent parameters for a given material these parameters are the local speed of sound and a parameter which is directly related to the shock density ratio in the limit of strong shocks these parameters are conveniently obtained from a linear fit to the experimental data for the shock hugoniot in various materials the approximate riemann solver retains the essential quadratic nonlinearity which enables it to deal with the whole range of cases from weak sound waves to strong shocks

a new nodal solver for the two dimensional lagrangian hydrodynamics we describe a cell centered godunov type scheme for the lagrangian hydrodynamic equations on general unstructured meshes with nodal fluxes the nodal solver only depends on the angular repartition of the physical variables around the node and not on the length of the edges the scheme verifies a weak consistency property numerical results are compared to eucclhyd and glace schemes which are also cell centered schemes with node based fluxes for lagrangian hydrodynamics

sinusoidal interference rejection analysis of an lms adaptive feedforward controller with a noisy periodic reference this paper applies a new vector subspace model to determine the non wiener solutions of the lms algorithm when the reference input is an arbitrary noisy periodic signal the lms weights are modeled as a deterministic time varying mean plus a zero mean fluctuating part for the mean weight each harmonic component of the periodic reference is shown to excite only a two dimensional 2 d subspace of the n dimensional tap weight space the fluctuating part of the weight is due to the reference noise that excites the full n dimensional space the power spectrum of the error is computed using the correlation function of the weight fluctuations the error is shown to be primarily the sum of a white noise and the canceled periodic residual for an independent noise vector model when the effects of the tapped delay line are incorporated in the model the noise becomes colored with a spectrum centered about the canceled sinusoidal frequency this weight model significantly simplifies the understanding of the non wiener behavior and can be applied to active noise cancellation problems when filters appear in the cancellation loop

system size dependence of the autocorrelation time for the swendsen wang ising model abstract we present monte carlo simulation results of the autocorrelation time for the swendsen wang method for the simulation of the ising model we have calculated the exponential and the integrated autocorrelation time at the critical point t c of the two dimensional ising model our results indicate that both autocorrelation times depend logarithmically on the linear system size l instead of a power law the simulations were carried out on the parallel computer of the condensed matter theory group at the university of mainz

application of the grp scheme to open channel flow equations the grp generalized riemann problem scheme originally conceived for gasdynamics is reformulated for the numerical integration of the shallow water equations in channels of rectangular cross section variable width and bed profile including a friction model for the fluid channel shear stress this scheme is a second order analytic extension of the first order godunov scheme based on time derivatives of flow variables at cell interfaces resulting from piecewise linear data reconstruction in cells the second order time integration is based on solutions to generalized riemann problems at cell interfaces thus accounting for the full governing equations including source terms the source term due to variable bed elevation is treated in a well balanced way so that quiescent flow is exactly replicated this is done by adopting the surface gradient method sgm several problems of steady or unsteady open channel flow are considered including the terms corresponding to variable channel width and bed elevation as well as to shear stress at the fluid channel interface using the manning friction model in all these examples remarkable agreement is obtained between the numerical integration and the exact or accurate solutions

proper complex random processes with applications to information theory the covariance of complex random variables and processes when defined consistently with the corresponding notion for real random variables is shown to be determined by the usual complex covariance together with a quantity called the pseudo covariance a characterization of uncorrelatedness and wide sense stationarity in terms of covariance and pseudo covariance is given complex random variables and processes with a vanishing pseudo covariance are called proper it is shown that properness is preserved under affine transformations and that the complex multivariate gaussian density assumes a natural form only for proper random variables the maximum entropy theorem is generalized to the complex multivariate case the differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum if and only if the random vector is proper gaussian and zero mean the notion of circular stationarity is introduced for the class of proper complex random processes a discrete fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain an application of the theory is presented

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

riemann solvers for perfect and near perfect gases the equations for the riemann problem for a perfect gas or constant covolume equation of state are rewritten in terms of three similarity parameters and a weak dependence on the ratio of specific heats of the gases these parameters are used to demonstrate the errors in the solutions of existing linearized riemann solvers and to develop a new solver that has the simplicity of the linearized solvers but that is more accurate among nonlinear solvers the two expansion approximation is shown to be very accurate except for flows involving strong shock waves an equivalent two shock approximation is developed that is very accurate for converging flows it is combined with the two expansion approximation to give an approximation that has a bounded error for all initial conditions more accurate or exact solutions to the riemann problem require iterative methods faster exact solvers are obtained by using the new approximations as starting values by reformulating the iteration technique for faster convergence and by using a look up table to speed up part of the calculation average solution times are reduced to about two thirds of the previously fastest method nomenclature a speed of sound b covolume constant eq 9 c velocity proportional to speed of sound eqs 8 and 9 du velocity similarity parameter eq 15 e error function eq 33 g 2y y 1 eq 3 g 7 1 eq 2

finite size calculations on the three dimensional ising model abstract recent numerical results for the critical behaviour of the three dimensional ising model based on finite size calculations show significant discrepancies we review possible sources of systematic deviations and strategies to avoid these or to track them down we present some new finite size results for the binder cumulant obtained by means of a perturbation expansion and by cluster monte carlo methods

simultaneous analysis of several models in the three dimensional ising universality class we investigate several three dimensional lattice models believed to be in the ising universality class by means of monte carlo methods and finite size scaling these models include spin 1 models with nearestneighbor interactions on the simple cubic and on the diamond lattice for the simple cubic lattice we also include models with third neighbor interactions of varying strength and some equivalent neighbor models also included are a spin 1 model and a hard core lattice gas separate analyses of the numerical data confirm the ising like critical behavior of these systems on this basis we analyze all these data simultaneously such that the universal parameters occur only once this leads to an improved accuracy the thermal magnetic and irrelevant exponents are determined as y t51 5868 3 y h52 4816 1 and y i520 821 5 respectively the binder ratio is estimated as q5 m 2 2 m 4 50 62 341 4

rigorous lower bound on the dynamic critical exponents of the swendsen wang algorithm we prove the rigorous lower bound z sw v for the dynamic critical exponent of the swendsen wang algorithm for two dimensional q state potts models with q 2 3 4 this implies z sw 0 2 5 1 we present numerical data indicating that z sw 0 55 0 03 0 89 0 05 for q 3 4 95 confidence limits statistical errors only the discrepancy for q 4 appears to be caused by multiplicative logarithmic corrections

interface tracking for axisymmetric flows a front tracking method for inviscid gas dynamics is presented the key constructions and algorithms used in the code are described and the interrelations between shock capturing interface dynamics computational geometry grid construction and parallelism are discussed for the code as a whole validation is carried out by comparing the single mode bubble velocity for rayleigh taylor instability with theoretical models and experimental results the calculations are validated by mesh refinement studies and by the comparison of the asymptotic limit of the minimum radius r rm min rightarrow infty to a pure planar computation in two dimensions

cluster algorithm for hard spheres and related systems in this paper we present a cluster algorithm for the simulation of hard spheres and related systems in this algorithm a copy of the configuration is rotated with respect to a randomly chosen pivot point the two systems are then superposed and clusters of overlapping spheres in the joint system are isolated each of these clusters can be flipped independently a process which generates non local moves in the original configuration a generalization of this algorithm which works perfectly well at small density can be made to work successfully at densities around the solid liquid transition point in the two dimensional hard sphere system

real gas flows in a duct a numerical scheme is presented for the solution of the euler equations of compressible flow of a real gas in a single spatial coordinate this include flow in a duct of variable cross section as well as flow with cylindrical or spherical symmetry and can prove useful when testing codes for the two dimensional equations governing compressible flow of a real gas the scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock

a high order cell centered lagrangian scheme for compressible fluid flows in two dimensional cylindrical geometry the goal of this paper is to present high order cell centered schemes for solving the equations of lagrangian gas dynamics written in cylindrical geometry a node based discretization of the numerical fluxes is obtained through the computation of the time rate of change of the cell volume it allows to derive finite volume numerical schemes that are compatible with the geometric conservation law gcl two discretizations of the momentum equations are proposed depending on the form of the discrete gradient operator the first one corresponds to the control volume scheme while the second one corresponds to the so called area weighted scheme both formulations share the same discretization for the total energy equation in both schemes fluxes are computed using the same nodal solver which can be viewed as a two dimensional extension of an approximate riemann solver the control volume scheme is conservative for momentum total energy and satisfies a local entropy inequality in its first order semi discrete form however it does not preserve spherical symmetry on the other hand the area weighted scheme is conservative for total energy and preserves spherical symmetry for one dimensional spherical flow on equi angular polar grid the two dimensional high order extensions of these two schemes are constructed employing the generalized riemann problem grp in the acoustic approximation many numerical tests are presented in order to assess these new schemes the results obtained for various representative configurations of one and two dimensional compressible fluid flows show the robustness and the accuracy of our new schemes

solution of the generalized riemann problem for advection reaction equations we present a method for solving the generalized riemann problem for partial differential equations of the advection reaction type the generalization of the riemann problem here is twofold firstly the governing equations include nonlinear advection as well as reaction terms and secondly the initial condition consists of two arbitrary but infinitely differentiable functions an assumption that is consistent with piecewise smooth solutions of hyperbolic conservation laws the solution procedure local and valid for sufficiently small times reduces the solution of the generalized riemann problem of the inhomogeneous nonlinear equations to that of solving a sequence of conventional riemann problems for homogeneous advection equations for spatial derivatives of the initial conditions we illustrate the approach via the model advection reaction equation the inhomogeneous burgers equation and the nonlinear shallow water equations with variable bed elevation

shock induced martensitic phase transitions critical stresses riemann problems and applications in this paper we develop a theory for phase transitions in solids under shock loading this theory applies in particular to a class of experiments which as a result of solid to solid phase transitions give rise to certain characteristic patterns consisting of two shock like waves we show that the single assumption that stresses in a phase cannot lie beyond its transition boundaries leads to a complete model for the physical systems at hand this model is different from others proposed in the literature it does not make use of kinetic relations and it accounts for the observed wave histories without parameter fitting the first part of this paper focuses on the basic mathematical description of our model and it presents solutions to the complete set of riemann problems which could arise as a result of dynamic interactions including the basic two wave structures mentioned above in the second part of the paper we use our riemann solver to construct general solutions for the piecewise constant initial value problems usually arising in experiment and we specialize our solutions to two widely studied polymorphic phase changes the graphite diamond transition and the transition in iron we show that in the presence of well accepted quations of state for the pure phases our model leads to close quantitative agreement with a wide range of experimental results possible sources of disagreement in certain fine features are also discussed interestingly in some cases our theory predicts sequences of events which differ from those generally accepted in particular our model predicts a variety of regimes for the iron experiments which previous theoretical investigations had not surmised and it indicates the existence of certain unexpected transformation domains in the graphite systems

remark on the generalized riemann problem method for compressible fluid flows the generalized riemann problem grp method was proposed for compressible fluid flows based on the lagrangian formulation m ben artzi j falcovitz a second order godunov type scheme for compressible fluid dynamics j comput phys 55 1 1984 1 32 and a direct eulerian version was developed in m ben artzi j li g warnecke a direct eulerian grp scheme for compressible fluid flows j comput phys 28 2006 19 43 by using the concept of riemann invariants the central feature of the grp method is the resolution of centered rarefaction waves in this note we show how to use the concept of riemann invariants in order to resolve the rarefaction waves in the lagrangian coordinate system and result in the grp scheme

a two dimensional unstructured cell centered multi material ale scheme using vof interface reconstruction we present a new cell centered multi material arbitrary lagrangian eulerian ale scheme to solve the compressible gas dynamics equations on two dimensional unstructured grid our ale method is of the explicit time marching lagrange plus remap type namely it involves the following three phases a lagrangian phase wherein the flow is advanced using a cell centered scheme a rezone phase in which the nodes of the computational grid are moved to more optimal positions a cell centered remap phase which consists of interpolating conservatively the lagrangian solution onto the rezoned grid the multi material modeling utilizes either concentration equations for miscible fluids or the volume of fluid vof capability with interface reconstruction for immiscible fluids the main original feature of this ale scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the lagrangian one in this formalism the rezoned grid is defined as a convex combination between the lagrangian grid and the grid resulting from condition number smoothing this convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the cauchy green tensor over the lagrangian phase regarding the cell centered remap phase we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the lagrangian cells the first one is a simplified swept face based method whereas the second one is a cell intersection based method our multi material ale methodology is assessed through several demanding two dimensional tests the corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme

a comparison of first and second order rezoned and lagrangian godunov solutions abstract in this paper we present solutions from a godunov type algorithm to a selection of hydrodynamics test problems included in this selection are implosions in planar cylindrical and spherical coordinates piston problems with a variety of mesh configurations including the difficult saltzman problem interacting blast waves and a spherical expansion on a rectangular mesh these solutions have been obtained using caveat a three dimensional arbitrary lagrangian eulerian ale hydrodynamics code that employs a godunov method of solution with an approximate riemann solver first and second order solutions are presented for most of the problems and rezoned and lagrangian solutions to the implosion noh problem are compared

a contribution to the numerical prediction of unsteady flows methods based on flux differe nce splitting are investigated with reference to the prediction of unsteady compressible flows they combine the feature of taking into account the wake like nature of these flows and the capability of correctly capturing shock waves two recently proposed approaches and a third one suggested here are compared for one dimensional flow with particular reference to the means of operating the splitting they are extended to the cases of variable area ducts and a general transformation of the independent variables firstand second order accurate schemes are presented and procedures for the computation at the boundaries are shown finally numerical experiments are reported and discussed

riemann solvers for water hammer simulations by godunov method the water hammer phenomenon can be described by a 2 2 system of hyperbolic partial differential equations pdes numerical solution of these pdes using finite volume schemes is investigated herein the underlying concept of the godunov scheme is the riemann problem that must be solved to provide fluxes between the computational cells the presence of the kinetic terms in the momentum equation determines the existence of shock and rarefaction waves which influence the design of the riemann solver approximation of the expressions for the riemann invariants and jump relationships can be used to derive first and second order approximate non iterative solvers the first order approximate solver is almost 2000 times faster than the exact one but gives inaccurate predictions when the densities and celerities are low the second order approximate solver gives very accurate solutions and is 300 times faster than the exact iterative one detailed indications are provided in the appendices for the practical implementation of the riemann solvers described herein copyright 2000 john wiley sons ltd

thermodynamical effects and high resolution methods for compressible fluid flows one of the fundamental differences of compressible fluid flows from incompressible fluid flows is the involvement of thermodynamics this difference should be manifested in the design of numerical schemes unfortunately the role of entropy expressing irreversibility is often neglected even though the entropy inequality as a conceptual derivative is verified for some first order schemes in this paper we refine the grp solver to illustrate how the thermodynamical variation is integrated into the design of high resolution methods for compressible fluid flows and demonstrate numerically the importance of thermodynamic effects in the resolution of strong waves as a by product we show that the grp solver works for generic equations of state and is independent of technical arguments

derivative riemann solvers for systems of conservation laws and ader methods in this paper we first briefly review the semi analytical method e f toro v a titarev solution of the generalized riemann problem for advection reaction equations proc roy soc london 458 2018 2002 271 281 for solving the derivative riemann problem for systems of hyperbolic conservation laws with source terms next we generalize it to hyperbolic systems for which the riemann problem solution is not available as an application example we implement the new derivative riemann solver in the high order finite volume ader advection schemes we provide numerical examples for the compressible euler equations in two space dimensions which illustrate robustness and high accuracy of the resulting schemes

numerical solution to rarefaction or shock wave duct area change interaction conclusion it may be said that vt rj prescribed by eq 5 gives the best correlation with measurement for k and further substantiates the claim of so and hwang1 that the solution eqs 3 7 represents the best solution for self preserving turbulent round jets furthermore eqs 3 7 also represent the solutions for incompressible heated round jets if the turbulent prandtl number prt is assumed to be constant then eq 3 with the exponent r 2 i2 replaced by ri2pr vn2 becomes the solution of the temperature equation since eqs 1 and 2 are equally applicable for incompressible heated round jets eqs 8 11 also represent solutions for such flows therefore the present results are just as valid for nonisothermal round jets

non wiener mean weight behavior of lms transversal equalizers with sinusoidal interference the least mean square lms algorithm is generally expected to operate near the corresponding wiener filter solution an important exception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference for this application the steady state lms equalizer behavior does not correspond to that of the fixed wiener equalizer the mean of its weights is different from the wiener weights and its mean square error performance may be significantly better than the wiener performance assuming a large interference to signal ratio isr we present the solution for the mean of the lms weight vector in steady state based on the butterweck expansion of the weight update equation the analytical results are valid for all mean square stable step sizes simulation results are included to support the analytical results and show that the analytical results predict the simulation results accurately over a wide range of isr

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

nonlinear effects in lms adaptive equalizers an adaptive transversal equalizer based on the least mean square lms algorithm operating in an environment with a temporally correlated interference can exhibit better steady state mean square error mse performance than the corresponding wiener filter this phenomenon is a result of the nonlinear nature of the lms algorithm and is obscured by traditional analysis approaches that utilize the independence assumption current filter weight vector assumed to be statistically independent of the current data vector to analyze this equalizer problem we use a transfer function approach to develop approximate analytical expressions of the lms mse for sinusoidal and autoregressive interference processes we demonstrate that the degree to which lms may outperform the corresponding wiener filter is dependent on system parameters such as signal to noise ratio snr signal to interference ratio sir equalizer length and the step size parameter

a general topology godunov method we describe a numerical technique for solving 2 dimensional compressible multimaterial problems using a general topology mesh multimaterial problems are characterized by the presence of interfaces whose shapes may become arbitrarily complex in the course of dynamic evolution computational methods based on more conventional fixed connectivity quadrilateral meshes do not have adequate flexibility to follow convoluted interface shapes and frequently fail due to excessive mesh distortion the present method is based on a mesh of arbitrary polygonal cells because this mesh is dual to a triangulation its topology is unrestricted and it is able to accommodate arbitrary boundary shapes additionally this mesh is able to quickly and smoothly change local mesh resolution thus economizing on the number of mesh cells and it is able to improve mesh isotropy because in a region of uniform mesh the cells tend to become regular hexagons the underlying algorithms are based on those of the caveat code these consist of an explicit finite volume cell centered arbitrary lagrangian eulerian ale technique coupled with the godunov method which together are readily adaptable to a general topology mesh several special techniques have been developed for this extension to a more general mesh they include an interface propagation scheme based on huygens construction a near lagrangian mesh rezoning algorithm that minimizes advection while enhancing mesh regularity an efficient global remapping algorithm that is capable of conservatively transferring quantities from one general mesh to another and various mesh restructering algorithms such as mesh reconnection smoothing and point addition and deletion

a cell centered lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two dimensional cylindrical geometry we develop a new cell centered control volume lagrangian scheme for solving euler equations of compressible gas dynamics in cylindrical coordinates the scheme is designed to be able to preserve one dimensional spherical symmetry in a two dimensional cylindrical geometry when computed on an equal angle zoned initial grid unlike many previous area weighted schemes that possess the spherical symmetry property our scheme is discretized on the true volume and it can preserve the conservation property for all the conserved variables including density momentum and total energy several two dimensional numerical examples in cylindrical coordinates are presented to demonstrate the performance of the scheme in terms of symmetry accuracy and non oscillatory properties

computation of reactive duct flows in external fields abstract a grp scheme is introduced for the numerical integration of the euler system of equations of compressible reactive flow in a duct of variable cross section subject to an external potential the grp generalized riemann problem scheme is based on an analytic solution of the grp at jump discontinuities it is a second order scheme generalizing the first order godunov scheme having the property of high resolution of shocks and other discontinuities some numerical examples are considered including an infinite spherical reflected shock a spherical blast wave and gas collapse under an external potential

high dimensional lattice gases we investigate the critical behaviour of hard core lattice gases in four five and six dimensions by means of monte carlo simulations in order to suppress critical slowing down we use a geometrical cluster monte carlo algorithm in particular nearest neighbour exclusion lattice gases on simple hypercubic lattices are investigated these models undergo ising like ordering transitions where the majority of the lattice gas particles settle on one of two sublattices a finite size scaling analysis of the simulation data confirms that these lattice gases display classical critical behaviour the results agree with the renormalization predictions at and above the upper critical dimensionality in particular the predicted value of the binder cumulant is confirmed

the simple cubic lattice gas with nearest neighbour exclusion ising universality abstract the lattice gas with nearest neighbour exclusion on the simple cubic lattice is studied by means of statistically accurate monte carlo simulations with an efficient cluster algorithm our results for critical exponents are y h 2 47 1 and y t 1 60 2 these results agree well with the three dimensional ising universality class we explain the discrepancy with an earlier study the critical activity is z c 1 0559 1 the size distribution of the clusters indicates that the percolation threshold of the cluster formation process of the monte carlo algorithm coincides with the critical point

a lagrangian staggered grid godunov like approach for hydrodynamics much research in lagrangian staggered grid hydrodynamics sgh has focused on explicit viscosity models for adding dissipation to a calculation that has shocks the explicit viscosity is commonly called artificial viscosity recently researchers have developed hydrodynamic algorithms that incorporate approximate riemann solutions on the dual grid 28 29 35 30 2 3 this approach adds dissipation to the calculation via solving a riemann like problem in this work we follow the works of 28 29 35 30 and solve a multidirectional riemann like problem at the cell center the riemann like solution at the cell center is used in the momentum and energy equations the multidirectional riemann like problem used in this work differs from previous work in that it is an extension of the cell centered hydrodynamics cch nodal solution approach in 7 incorporating the multidirectional riemann like problem from 7 into sgh has merits such as the ability to resist mesh instabilities like hourglass null modes and chevron null modes the approach is valid for complex multidimensional flows with strong shocks numerical details and test problems are presented

ising universality in three dimensions a monte carlo study we investigate three ising models on the simple cubic lattice by means of monte carlo methods and finite size scaling these models are the spin 1 2 ising model with nearest neighbour interactions a spin 1 2 model with nearest neighbour and third neighbour interactions and a spin 1 model with nearest neighbour interactions the results are in accurate agreement with the hypothesis of universality analysis of the finite size scaling behaviour reveals corrections beyond those caused by the leading irrelevant scaling field we find that the correction to scaling amplitudes are strongly dependent on the introduction of further neighbour interactions or a third spin state in a spin 1 ising model these corrections appear to be very small this is very helpful for the determination of the universal constants of the ising model the renormalization exponents of the ising model are determined as yt 1 587 2 yh 2 4815 15 and yi 0 82 6 the universal ratio q m2 2 m4 is equal to 0 6233 4 for periodic systems with cubic symmetry the critical point of the nearest neighbour spin 1 2 model is kc 0 2216546 10

brain venous haemodynamics neurological diseases and mathematical modelling a review behind medicine m is physiology p behind physiology is physics p and behind physics is always mathematics m for which i expect that the symmetry of the quadruplet mppm will be compatible with the characteristic bias of hyperbolic partial differential equations a theme of this paper i start with a description of several idiopathic brain pathologies that appear to have a strong vascular dimension of which the most prominent example considered here is multiple sclerosis the most common neurodegenerative disabling disease in young adults other pathologies surveyed here include retinal abnormalities transient global amnesia transient monocular blindness meniere s disease and idiopathic parkinson s disease it is the hypothesised vascular aspect of these conditions that links medicine to mathematics through fluid mechanics in very complex networks of moving boundary blood vessels the second part of this paper is about mathematical modelling of the human cardiovascular system with particular reference to the venous system and the brain a review of a recently proposed multi scale mathematical model then follows consisting of a one dimensional hyperbolic description of blood flow in major arteries and veins coupled to a lumped parameter description of the remaining main components of the human circulation derivation and analysis of the hyperbolic equations is carried out for blood vessels admitting variable material properties and with emphasis on the venous system a much neglected aspect of cardiovascular mathematics veins unlike their arterial counterparts are highly deformable even collapsible under mild physiological conditions we address mathematical and numerical challenges regarding the numerical analysis of the hyperbolic pdes we deploy a modern non linear finite volume method of arbitrarily high order of accuracy in both space and time the ader methodology in vivo validation examples and brain haemodynamics computations are shown we also point out two preliminary but important new findings through the use of mathematical models namely that extracranial venous strictures produce chronic intracranial venous hypertension and that augmented pressure increases the blood vessel wall permeability

numerical simulation of two phase flow in pipes using godunov method the partial differential equations that describe two phase flows in pipes are highly non linear due to the strong dependence between pressure and wave celerity the possible appearance of shock waves makes godunov schemes very attractive for they can handle such discontinuities automatically fluxes at the cell interfaces are computed by solving a riemann problem to do so an approximate state non iterative solver designed in a previous study is used the treatment of boundary conditions uses an iterative procedure existing approximations for the sound celerity under the isothermal assumption are generalized to other situations a comparison between the isothermal and the adiabatic assumptions shows that such assumptions play an important role in the behaviour of the solution finally numerical results obtained using the first order godunov method on representative test cases are presented and the need for higher order reconstruction techniques is acknowledged copyright 2001 john wiley sons ltd

an approach for treating contact surfaces in lagrangian cell centered hydrodynamics a new method is presented for modeling contact surfaces in lagrangian cell centered hydrodynamics cch the contact method solves a multi directional riemann like problem at each penetrating or touching node along the contact surface the velocity of a penetrating or touching node and the corresponding forces are explicitly calculated using the riemann like nodal solver the contact method works with material strength and allows surfaces to impact slide and separate results are presented for several test problems involving both gases and materials with strength the new contact surface approach extends the modeling capabilities of cch

dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we study the dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we find that the li sokal bound on the autocorrelation time int const xc h holds along the self dual curve of the symmetric ashkin teller model and is almost but not quite sharp the ratio int c h appears to tend to infinity either as a logarithm or as a small power 0 05 p 0 12 in an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time

formulations of artificial viscosity for multi dimensional shock wave computations in this paper we present a new formulation of the artificial viscosity concept physical arguments for the origins of this term are given and a set of criteria that any proper functional form of the artificial viscosity should satisfy is enumerated the first important property is that by definition a viscosity must always be dissipative transferring kinetic energy into internal energy and must never act as a false pressure the artificial viscous force should be galilean invariant and vary continuously as a function of the criterion used to determine compression and expansion and remain zero for the latter case these requirements significantly constrain the functional form that the artificial viscous force can have in addition an artificial viscosity should be able to distinguish between shock wave and adiabatic compression and not result in spurious entropy production when only the latter is present it must therefore turn off completely for self similiar motion where only a uniform stretching and or a rigid rotation occurs an additional important but more subtle condition where the artificial viscosity should produce no effect is along the direction tangential to a convergent shock front since the velocity is only discontinuous in the normal direction our principal result is the development of a new formulation of an edge centered artificial viscosity that is to be used in conjunction with a staggered spatial placement of variables that meets all of these standards and without the need for problem dependent numerical coefficients that have in the past made the artificial viscosity method appear somewhat arbitrary our formulation and numerical results are given with respect to two spatial dimensions but all of our arguments carry over directly to three dimensions a central feature of our development is the implementation of simple advection limiters in a straightforward manner in more than one dimension to turn off the artificial viscosity for the above mentioned conditions and to substantially reduce its effect when strong velocity gradients are absent

cluster dynamics and universality of ising lattice gases abstract lattice gases with nearest neighbour exclusion are studied by means of monte carlo simulations with an efficient cluster algorithm the critical dynamics is consistent with a dynamical exponent z 0 in the case of wolff like cluster updates for square and simple cubic lattices in the studied range of lattice sizes we find the critical activity z c 0 72020 4 for the body centred cubic lattice the critical exponents y h 2 475 8 and y t 1 61 6 disagree with an earlier study but they do agree with the known values for the three dimensional ising universality class

boundary condition treatment in 2 2 systems of propagation equations numerical modelling of the water hammer phenomenon involves solving a 2 2 system of propagation equations numerically in the present paper this system is solved using the piecewise parabolic method ppm scheme a higher order extension of the godunov method to reach high order discretization accuracy the ppm scheme uses six points in space to solve the advection equation hence treatment of boundary conditions which proves to be of importance to water hammer modelling is not straightforward several options for the handling of boundary conditions are presented herein and only one combination among nine is shown to provide good results this shows that even very accurate numerical schemes may be of poor help in problem solving if boundary conditions are not handled properly results given by the ppm scheme are compared with those given by other solution techniques method of characteristics moc proving the superior accuracy efficiency relations used by the ppm over the usual approximations of the moc 1998 john wiley sons ltd

the non interacting hard square lattice gas ising universality the critical exponents of the non interacting hard square lattice gas model are determined by means of series analysis and finite size scaling the series analysis leads to results for the exponents that are consistent with the expected ising universal values a scaling analysis is performed on different types of numerical finite size data obtained by means of the transfer matrix method the results support ising universality a procedure based on conformal invariance reproduces the known ising temperature and magnetic exponents within 10 6 furthermore we estimate the critical density of the hard square model as rho c 0 367 743 000 5

arbitrary high order discontinuous galerkin schemes based on the grp method for compressible euler equations combined with the discontinuous galerkin dg framework the generalized riemann problem grp method is applied to design a grp dg scheme with high order accuracy for compressible euler equations since numerical fluxes with second order accuracy in time are derived by the grp method the reconstruction steps for physical variables in the new scheme are halved compared with the traditional runge kutta discontinuous galerkin rk dg scheme the numerical results are also improved due to more introduced physical information several numerical examples verify the validity of the proposed schemes