Showing papers on "Eulerian path published in 1981"

Lagrangian and Eulerian Time-Scale Relations in the Daytime Boundary Layer

Abstract: Lagrangian (neutral balloon) and Eulerian (tower and aircraft) turbulence observations were made in the daytime mixed layer near Boulder, Colorado. Average sampling time was ∼25 min. Average Lagrangian time scale is ∼70 s and average ratio of Lagrangian to Eulerian time scales (β = TL/TE) is about 1.7. The ratio β is inversely proportional to turbulence intensity i. These data support the formula β = 0.7/i. Lagrangian time scale for the vertical component of turbulence at heights above ∼100 m is given by the formula TL = 0.17zi/σμ where zi is mixing depth. This formula is valid for the horizontal components of turbulence at all heights in the mixed layer. Lagrangian spectra in the inertial subrange are best represented by the formula Fr(n) = 0.2ϵn−2.

A canonical transformation relating the lagrangian and eulerian description of ideal hydrodynamics

Abstract: We derive by means of a canonical transformation the variational principle of Seliger and Whitham for the Eulerian description of ideal hydrodynamics from the more familiar variational principle that yields the equations of motion of an ideal fluid in the Lagrangian description.

Variational Principle for Two-Dimensional Incompressible Hydrodynamics and Quasigeostrophic Flows

Abstract: A new variational principle is derived through the construction of the action in terms of a new set of canonical coordinates. The main advantage of this set of coordinates is that they contain exclusively information concerning the Eulerian description of the flow.

SALE-3D: a simplified ALE computer program for calculating three-dimensional fluid flow

Abstract: This report presents a simplified numerical fluid-dynamics computing technique for calculating time-dependent flows in three dimensions. An implicit treatment of the pressure equation permits calculation of flows far subsonic without stringent constraints on the time step. In addition, the grid vertices may be moved with the fluid in Lagrangian fashion or held fixed in an Eulerian manner, or moved in some prescribed manner to give a continuous rezoning capability. This report describes the combination of Implicit Continuous-fluid Eulerian (ICE) and Arbitrary Lagrangian-Eulerian (ALE) to form the ICEd-ALE technique in the framework of the Simplified-ALE (SALE-3D) computer program, for which a general flow diagram and complete FORTRAN listing are included. Sample problems show how to modify the code for a variety of applications. SALE-3D is patterned as closely as possible on the previously reported two-dimensional SALE program.

A numerical comparison between Lagrangian and Eulerian rainfall statistics

Abstract: Air trajectories and precipitation data are used to estimate certain parameters characterizing the duration and intensity of precipitation events and the length of the intervening dry periods. The results seem to indicate that the magnitudes of these parameters differ only moderately whether they be estimated in an Eulerian or a Lagrangian frame of reference. DOI: 10.1111/j.2153-3490.1981.tb01747.x

A fractional volume of fluid method for free boundary dynamics

Abstract: The volume of fluid (VOF) technique is presented as a simple and efficient means for numerically treating free boundaries embedded in a calculational mesh of Eulerian or Arbitrary-Lagrangian-Eulerian cells. It is particularly useful because it uses a minimum of stored information, treats intersecting free boundaries automatically, and can be readily extended to three-dimensional calculations.

On Eulerian and Lagrangean Objectivity in Continuum Mechanics

Abstract: In continuum mechanics the commonly—used definition of objectivity (or frame-indifference) of a tensor field does not distinguish between Eulerian, Lagrangean and two—point tensor fields. This paper highlights the distinction and provides a definition of objectivity which reflects the different transformation rules for Eulerian, Lagrangean and twopoint tensor fields under an observer transformation. The notion of induced objectivity is introduced and its implications examined.

The Eulerian- and Lagrangian-mean flows induced by stationary, dissipating planetary waves

Abstract: The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating planetary waves are discussed by employing a simple channel model on a beta-plane It is assumed that the wave is excited by the bottom undulation and dissipated by Newtonian cooling with relaxation time alpha and by Rayleigh friction with (lambda)(alpha), lambda being constant Three cases where lambda is equal to one are discussed: (1) the basic zonal wind U sub 0 and the dissipation rate alpha are both constant; (2) U sub 0 varies with height while alpha is constant; and (3) U sub 0 and alpha both vary with height In case (1), the Eulerian- and the Lagrangian-mean fields are shown to depend on the difference between the dissipation scale-height and the density scale-height In case (2) and case (3), it is shown that the results for case (1) are modified under slightly more realistic situations

Hull/EPIC3 Linked Eulerian/Lagrangian Calculation in Three Dimension

Abstract: : This report documents a demonstration calculation performed to evaluate the three-dimensional Eulerian/Lagrangian linked hydrocode developed under this contract. The calculation consists of a staballoy rod impacting an armor plate at obliquity 65 degrees and velocity 1 km/sec. Calculational results compared favorably with experimental data. The linked calculation was completed with the use of about nine total CDC 7600 computer hours as compared to the estimated 25 hours if the calculation had been run with only the Eulerian code. (Author)

ICECO-CEL: A Coupled Eulerian-Lagrangian Code for Analyzing Primary System Response in Fast Reactors

Abstract: This report describes a coupled Eulerian-Lagrangian code, ICECO-CEL, for analyzing the response of the primary system during hypothetical core disruptive accidents. The implicit Eulerian method is used to calculate the fluid motion so that large fluid distortion, two-dimensional sliding interface, flow around corners, flow through coolant passageways, and out-flow boundary conditions can be treated. The explicit Lagrangian formulation is employed to compute the response of the containment vessel and other elastic-plastic solids inside the reactor containment. Large displacements, as well as geometrical and material nonlinearities are considered in the analysis. Marker particles are utilized to define the free surface or the material interface and to visualize the fluid motion. The basic equations and numerical techniques used in the Eulerian hydrodynamics and Lagrangian structural dynamics are described. Treatment of the above-core hydrodynamics, sodium spillage, fluid cavitation, free-surface boundary conditions and heat transfer are also presented. Examples are given to illustrate the capabilities of the computer code. Comparisons of the code predictions with available experimental data are also made.

On the momentum of Eulerian phonons

Abstract: For a one-dimensional dispersive medium the linear momentum of a phonon is discussed in both the Lagrangian and the Eulerian picture, i.e. with the use of substantial (material) and local coordinates, respectively. As phonons are usually considered as solutions of the linearized equations of motion, in the Eulerian picture the linear momentum of a phonon is only defined up to linear terms in the fields. To obtain results relevant towards higher order in the fields, one has to solve the nonlinear equations of motion. This is done to obtain expressions for the linear momentum up to terms quadratic in the fields.

On the influence of shape and dimensions of particles on the properties of the modified

Abstract: Almtr~--It is considered Hariow's particle-in-cell method modification which consists in the use of finite-size particles for two-dimensioual gasdynamics computations. The algorithm for computation of motion of finite size particles is described. It is shown that the use of finite size particles can lead to the local violation of the approximation of original differential equations. However the quantities obtained by averaging the numerical solution over certain spatial subdomains approximate the conservation laws. It is shown that if the characteristic particle dimensions tend to zero, then the modified particle-in-cell method passes to the original Harlow's method. Results of numerical experiments are given to illustrate the properties of the modified particle-in-cell method. At present the finite-difference shock-smoothing techniques are intensively used for the numerical modeling of multidimensional gas flows with discontinuities. Despite a wide spectrum of existing sbock-smoothing schemes it is still difficult to choose a method being the most appropriate for the solution of a specific class of problems. To a great extent this is caused by the fact that we often do not know some important properties of the numerical techniques already elaborated. One of the efficient methods for the numerical modeling of flows of continuous media is the particle-in-cell method (PIC-metbod) proposed by Harlow more than 20 yr ago (1-7). The use of Lagrangian particles in Harlow's method renders this method to be especially versatile when solving problems with large relative displacements and big deformations of a medium. At the same time the discrete representation of a continuum as a set of a finite number of point particles just causes the undersirable effect in Harlow's method: a transition of the particle from one Eulerian computational cell to another one leads to the jump change in the quantities of Eulerian cells sought for (mass, momentum, etc.). Let N be the average number of particles per cell. Suppose that the average number of particles along each of the coordinate directions x, y is equal to ~/N for a cell. Then it is easy to show that the amplitude of statistical fluctuations caused by the discrete character of particles is proportional to I/x/N, see also (8). Thus, this amplitude can be diminished by a significant increase in the average number of particles N. According to the estimates of the work(9), a number of machine words which are to be stored at each time step when using Harlow's method is proportional to (4+ 3N). Moreover, one should take into account the increase in needed machine time as N-*oo. For the purpose of weakening the effect of discrete density in the PIC-method it was proposed in(10) to consider the finite size particles. The two algorithms realizing this idea in the one-dimensional case were presented in detail in (11). The algorithm for computation of two-dimensional flows by PIC-method for the case when the particles have the shape of a circle ("circular particles") is described in (12). Some results of the two-dimensional computations of high-velocity impact problems using the method of circular particles are presented in (12, 13). In the work(14), a case is considered when the particles have the shape of a square whose dimensions coincide with the ones of a cell of the Eulerian computing mesh. Some discussions of a general character on the use of the form parameters of particles in the two-dimensional case are presented in (15) without consideration of specific algorithms. Note that the dimensions and shape of each particle may be, generally speaking, the functions of the time and the spatial coordinates. This circumstance does seem quite useful if