Showing papers on "Eulerian path published in 1987"

Greedy algorithm and symmetric matroids

Abstract: Symmetric matroids are set systems which are obtained, in some sense, by a weakening of the structure of a matroid. These set systems are characterized by a greedy algorithm and they are suitable for dealing with autodual properties of matroids. Applications are given to the eulerian tours of 4-regular graphs and the theory ofg-matroids.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Abstract: Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

An Efficient Two‐Time‐Level Semi‐Lagrangian Semi‐Implicit Integration Scheme

Abstract: The semi-implicit semi-Lagrangian integration technique enables numerical weather prediction models to be run with much longer timesteps than permitted by a semi-implicit Eulerian scheme. the choice of timestep can then be made on the basis of accuracy rather than stability requirements. to realize the full potential of the technique, it is important to maintain second-order accuracy in time; this has previously been achieved by applying it in the context of a three-time-level integration scheme. In this paper we present a two-time-level version of the technique which yields the same level of accuracy for half the computational effort. Unlike other efficient two-time-level schemes, ours does not rely on operator splitting. We apply this scheme to a variable-resolution barotropic finite-element regional model with a minimum gridlength of 100 km, using timesteps of up to three hours. the results are verified against a control run with uniformly high resolution, and are shown to be of similar accuracy to those of a semi-implicit Eulerian integration with a timestep of 10 minutes.

Semi-Lagrangian advection on a Gaussian grid

Abstract: The treatment of advection is related to the stability, accuracy and efficiency of models used in numerical weather prediction. In order to remain stable, conventional Eulerian advection schemes must respect a Courant-Friedrichs-Lewy (CFL) criterion, which limits the size of the time step that can be used in conjunction with a given spatial resolution. In recent years, tests with gridpoint models have shown that semi-Lagrangian schemes permit the use of large time steps (roughly three to six times those permitted by the CFL criterion for the corresponding Eulerian models), without reducing the accuracy of the forecasts. This leads to improved model efficiency, since fewer steps are needed to complete the forecast. Can similar results be achieved in spectral models? This paper examines the semi-Lagrangian treatment of advection on the Gaussian grid used in spectral models. Interpolating and noninterpolating versions of the semi-Lagrangian scheme are applied to the problem of solid body rotation on...

Consistency conditions for random‐walk models of turbulent dispersion

Abstract: Random‐walk models have long been used to calculate the dispersion of passive contaminants in turbulence. When applied to nonstationary and inhomogeneous turbulence, the model coefficients are functions of the Eulerian turbulence statistics. More recently the same random‐walk models have been used as turbulence closures in the evolution equation for the Eulerian joint probability density function (pdf) of velocity. There are, therefore, consistency conditions relating the coefficients specified in a random‐walk model of dispersion and the Eulerian pdf calculated using the same random‐walk model. It is shown that even if these conditions are not satisfied, the dispersion model does not violate the second law of thermodynamics: all that is required to avoid a second‐law violation is that the mean pressure gradient be properly incorporated. It is also shown that for homogeneous turbulence the consistency conditions are satisfied by a linear Gaussian model; and that for inhomogeneous turbulence they are satisfied by a nonlinear Gaussian model.

Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

Abstract: A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating MHD flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

On Beat Wave Excitation of Relativistic Plasma Waves

Abstract: The beat wave excitation process is examined analytically in the Eulerian fluid description. The effects of plasma drifts, harmonics, pump rise time, frequency mismatch, phenomenological damping, plasma inhomogeneities, and two dimensions are discussed. The consistency between the Eulerian and Lagrangian fluid descriptions is verified.

Digraph decompositions and Eulerian systems

Abstract: The theory of digraph decompositions introduced by W. Cunningham and the theory of isotropic systems introduced by the author are unified. A basic combinatorial tool is the operation of local complementation at a vertex of a digraph, a generalization of the similar operation already known for simple graphs. This allows us to unify in a single class the semibrittle digraphs characterized by W. Cunningham and to devise a more efficient algorithm for searching for a split of a digraph.

Numerical Methods for Solving the Transport Equation

Abstract: The depth-averaged transport equation, which governs the spread of thermal and chemical pollutants in coastal seas, is described. Methods of numerical solutions based on Eulerian and Lagrangian approaches are outlined. For testing numerical methods a number of exact solutions for special cases and suitable error measures are given. An example of their use in testing three finite difference methods for solving the one-dimensional transport equation is given.

Enumeration of labelled threshold graphs and a theorem of frobenius involving eulerian polynomials

Abstract: We enumerate labelled threshold graphs by the number of vertices, the number of isolated vertices, and the number of distinct vertex-degrees and we give the exact asymptotics for the number of labelled threshold graphs withn vertices. We obtain the appropriate generating function and point out a combinatorial interpretation relating its coefficients to the Stirling numbers of the second kind. We use these results to derive a new proof of a theorem of Frobenius expressing the Eulerian polynomials in terms of the Stirling numbers.

Further developments in a nonlinear theory of water waves for finite and infinite depths

Abstract: This paper is a companion to an earlier one (Green & Naghdi 1986, Phil. Trans. R. Soc. Lond . A 320, 37-70 (1986)) and deals with certain aspects of a nonlinear waterwave theory and its applications to waters of infinite and finite depths. A new procedure is used to establish a 1-1 correspondence between the lagrangian and eulerian formulations of the integral balance laws of a general thermomechanical theory of directed fluid sheets, as well as their associated jump conditions in the presence of any number of directors. (Such a correspondence between lagrangian and eulerian formulations was previously possible in the special case of a single constrained director.) These results are valid for both compressible and incompressible (not necessarily inviscid) fluids. Applications are then made to special cases of the general theory (including the jump conditions) for incompressible inviscid fluids of infinite depth (with two directors) and of finite depth (with three directors) and the nature of the results are illustrated with particular reference to a wedge-like boat.

Stress dependency on ultrasonic wave propagation velocity

Abstract: The theory of wave propagation in a stressed solid was applied to the measurement of ultrasonic wave propagating velocity through tensile specimens of carbon steels containing 0.2 to 0.5% C, and Murnaghan's third order elastic constants of both Eulerian and Lagrangian formulation were obtained for those steels. They were ten times as large as the second order elastic constants, and values of the Eulerian constantn in them largely changed with composition of specimens. It was found that there was a simple relation between the Eulerian and Lagmngkn third order elastic constants.

Lagrangian and Eulerian Representations of Metasomatic Alteration of Minerals

Abstract: Both Lagrangian and Eulerian formulations of fluid flow coupled to fluid/rock interaction provide complete descriptions of metasomatic processes based on a continuum representation of porous media. The Eulerian method is an inherently transient description of advective and diffusive/dispersive transport referred to a reference frame that is fixed with respect to the rock mass. The Lagrangian method, applicable to flowing systems, is referred to a frame of reference that is fixed relative to the moving fluid. Applied to a single packet of fluid, the Lagrangian formulation is equivalent to the open system reaction path formulation of mass transfer, and results in a steady state description of metasomatic processes for surface controlled mineral dissolution rates. Numerical finite difference calculations describing the alteration of microcline and quartz at 100°C due to combined infiltration and diffusion based on the Eulerian formulation, are compared with results obtained from a single Lagrangian fluid packet. Following a transient period during which mineral reaction products pyrophyllite and kaolinite precipitate and redissolve, the Eulerian calculation results in the formation of a steady state which coincides with the reaction path of a single Lagrangian fluid packet. The steady state involves only the minerals gibbsite and muscovite, and extends throughout a spatial region which advances downstream from the inlet of the porous medium. The position of the gibbsite-muscovite boundary is stationary and independent of the porosity of the porous medium for constant surface area. With increasing time, the steady state configuration must eventually be destroyed as the abundance of microcline decreases with a consequent decrease in surface area and therefore dissolution rate. Nonetheless, the lifetime of the steady state is orders of magnitude longer than the time required to achieve a steady state regime. These observations suggest that the time evolution of a geochemical system may be approximated by a sequence of steady states, each corresponding to different surface areas, positions of alteration zones, porosity and permeability. In the latter case reaction fronts propagate at nonzero, retarded velocities in response to steady fluid flow, while in the former case they may be essentially stationary for long periods of time. The Lagrangian and Eulerian representations are generalized to incorporate geochemical systems characterized by primary and secondary porosities. Because the Lagrangian approach is computationally much faster than the Eulerian method, it is of considerable practical importance.

Measurements of the Vertical Acceleration in Wind Waves

Abstract: Recent theoretical studies of the accelerations in regular gravity waves of finite steepness have shown striking differences between the Eulerian and the Lagrangian accelerations (those measured by fixed instruments or freely floating instruments, respectively). In the present paper, attention is directed to field observations of accelerations in random seas. Two sets of data are analyzed, representing Eulerian and Lagrangian measurements. The Eulerian accelerations are found to be notably asymmetric, with maximum downwards accelerators exceeding −1.6g. The Lagrangian acceleration histograms are narrower and more symmetric, in general. As might be expected, the acceleration variance is highly sensitive to the high-frequency cutoff, in both types of data.

A combined Eulerian-Lagrangian analysis for computation of two-phase flows

Abstract: A combined Eulerian-Lagrangian analysis, which combines a linearized block implicit Navier-Stokes analysis for the continuous phase with a Lagrangian analysis for the motion of the droplet phase to simulate evaporating two-phase flows, has been developed. A unique aspect of this analysis is that the Lagrangian equations for the droplet motion have been transformed into the Eulerian computational space using coordinate transformation resulting in better computational efficiency. Use of the present implicit procedure for the continuous phase makes it possible to efficiently use a locally highly refined mesh. The coupling of the continuous phase and the droplet phase analyses is such that it allows the use of convergence acceleration techniques for steady-state problems, as well as making it possible to simulate transient flows. A rapidly evaporating two-phase flow caused by spray of liquid nitrogen in gaseous nitrogen has been used as a test problem to demonstrate the computer code using this analysis.

A Lagrangian-Eulerian approach to modeling hydrogeochemical transport of multi-component systems

Abstract: For advection-dominated hydrogeochemical transport problems, negative concentration can occur especially in sharp front cases when traditional numerical methods of finite element or finite difference are used to solve the governing equations. Negative concentration, in addition to being illogical, also gives two undesired effects. It can easily tumble into nonconvergent solutions or existing chemical equilibrium models are unable to deal with negative concentrations. A Lagrangian-Eulerian approach is employed to overcome the problems of negative concentration. In this approach, one adopts a Lagrangian viewpoint when dealing with the advective terms and an Eulerian viewpoint when dealing with all other terms in the hydrogeochemical transport equations. However, in general the fictitious Lagrangian particles will not coincide with the grid nodes. Thus, the accuracy of the advective step is contingent on the means by which a concentration value of a fictitious particle is approximated by that of the node values surrounding the particle. It is shown that a linear interpolation is equivalent to the upstream weighting scheme with the Courant number less than or equal to one. Other nonlinear interpolations are explored to increase the accuracy in the Lagrangian step of dealing with the advection terms. Several examples are used to demonstrate the utilitymore » and versatility of the Lagrangian-Eulerian approach to solving hydrogeochemical transport problems. 9 refs.« less

Prospects for Eulerian CFD analysis of helicopter vortex flows

Abstract: The applicability of current finite-volume CFD algorithms based on the Euler equations to the vortex flow over a helicopter in forward flight is investigated analytically. The general characteristics of the flow are reviewed; existing Euler, Navier-Stokes, perturbation, high-order, and adaptive methods are briefly characterized; and a novel Eulerian/Lagrangian approach with entropy and vorticity corrections is presented in detail. Numerical results for simple convection of a finite-core Lamb vortex moving downstream with its axis perpendicular to the flow are presented in graphs, and the possibility of extending the method to three-dimensional, viscous, and shock flows is discussed.

On the Eulerian source-receptor relationship

Abstract: A new approach is proposed to delineate the source-receptor relationship in an Eulerian model. A small, unique oscillatory signal is superimposed on each emission source in the airshed. At receptor sites the concentration time series are analyzed by a Fourier transform to give the amplitudefrequency spectrum. Distinct peaks found in the spectrum are identified at the emission frequencies. The amplitude of the spectrum at the source frequency represents the individual contribution from that emitter. Various atmospheric transport and diffusion models are solved to show the effects of different physical and chemical processes on the oscillatory signals. Both analytical and numerical solutions are used to demonstrate the performance of the method.

Comprehensive modeling of turbulent particulate flows using Eulerian and Lagrangian schemes

Abstract: This paper addresses turbulent particle dispersion and modulation effects in dilute gas-particle turbulent flows using the Eulerian and Lagrangian modeling approaches. Gradient diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangian formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. For the particle size and loading considered, the turbulence transport equations must be modified to account for the modulation effects. Models are proposed for both Eulerian and Lagrangian schemes. Comparisons and predictions are made in fully developed gas-solid pipe flow and confined coaxial jets laden with particles. For the monodispersed system investigated, Eulerian approach is less expensive and gives more consistent results than the Lagrangian approach. The Lagrangian technique should be further developed to eliminate current inherent inconsistencies especially with regard to the symmetry boundary condition.

Two-dimensional dynamic graphs and their vlsi applications

Abstract: This thesis deals with problems related to the design of highly regular VLSI chips. We treat these problems from both a practical and theoretical point of view. The first part of the thesis deals with the optimization of leaf cells either isolated or embedded in regular arrays. We develop what we call the critical-path optimization method for finding locally optimal cells in large arrays, with the criterion of speed and power consumption. Experimental results are given for the optimization of an array multiplier consisting of identical one-bit full adders. In order to make the optimization of very large array multipliers practical, we develop what we call the canonical configuration method. This method generates the critical path of any large array multiplier from the critical paths which appear in some array of fixed size. This allows us to optimize any large array multiplier in time independent of the size of the array. The second part of the thesis deals with theoretical aspects of the problems and techniques of the first part. A two-dimensional dynamic graph is a locally-finite, infinite graph comprised of identical finite graphs at every integer orthogonal grid point in the Euclidean plane and edges which connect these finite graphs in a regular pattern. First, we solve the acyclicity problem for dynamic graphs by using a semiring defined on the set of convex polygons with respect to two operations: vector summation and convex hull of the union. Second, we study problems of planarity testing, weak connectivity, finding an Eulerian path, and testing 2-colorability of dynamic graphs. Instead of solving these problems for infinite dynamic graphs, we reduce these to problems for finite graphs by making use of regularity. Finally, we investigate the longest path problem for dynamic graphs. We re-define the canonical configuration in terms of dynamic graphs and investigate why and when the canonical configuration becomes practical.

Advection-Dispersion with Adaptive Eulerian-Lagrangian Finite Elements

Abstract: Advection-dispersion is generally solved numerically with methods that treat the problem from one of three perspectives. These are described as the Eulerian reference, the Lagrangian reference or a combination of the two that will be referred to as Eulerian-Lagrangian. Methods that use the Eulerian-Lagrangian approach incorporate the computational power of the Lagrangian treatment of advection with the simplicity of the fixed Eulerian grid. A modified version of a relatively new adaptive Eulerian-Lagrangian finite element method is presented for the simulation of advection-dispersion. In the vicinity of steep concentration fronts, moving particles are used to define the concentration field. A modified method of characteristics called single-step reverse particle tracking is used away from steep concentration fronts. An adaptive technique is used to insert and delete moving particles as needed during the simulation. Dispersion is simulated by a finite element formulation that involves only symmetric and diagonal matrices. Based on preliminary tests on problems with analytical solutions, the method seems capable of simulating the entire range of Peclet numbers with Courant numbers well in excess of 1.

The transformation from Eulerian to Lagrangian coordinates for solutions with discontinuities

Abstract: We demonstrate the equivalence of Eulerian and Lagrangian coordinates for weak, discontinuous solutions in one space dimension. This transformation also induces a one to one correspondence between the convex extensions, or "entropy functions" of the system of conservation laws in either coordinate system. Such entropy functions are of interest in the theory of compensated compactness, and our results imply the equivalence of some of the elements of that theory in either coordinate system.