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Turbulent diffusion of small particles

Description: The diffusion of small, spherical, rigid particles suspended in an incompressible turbulent fluid, but not interacting with each other, was studied. As a stochastic process, the turbulent fluid velocity field is assumed to be homogeneous, isotropic and stationary. Assuming the Stokes regime, a particle of equation of motion is used which includes only the effects of Stokes drag and a virtual mass force and an exact solution is found for the particle velocity correlation function, for all times and initial conditions, in terms of a fluid velocity correlation function measured along the motion of the particle. This shows that for times larger than a certain time scale, the particle velocity correlation becomes stationary. The effect of small shears in the fluid velocity was considered, under the additional restrictions of a certain high frequency regime for the turbulence. The shears convected past the particle much faster than the growth of the boundary layer. New force terms due to the presence of such shears are calculated and incorporated into the equation of motion. A perturbation solution to this equation is constructed, and the resultant particle velocity correlation function and diffusion coefficient are calculated. To lowest order, the particle diffusivity is found to be unaltered by the presence of small mean flow shears. The last model treated is one in which particles traverse a turbulent fluid with a large mean velocity. Among other restrictions, linearized form drag is assumed. The diffusion coefficient for such particles was calculated, and found to be much smaller than the passive scalar diffusion coefficient. This agrees within 5 percent with the experimental results of Snyder and Lumley.
Date: November 1, 1977
Creator: Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Calculations of cratering experiments with the bedded crack model

Description: The physical models upon which the BCM (bedded crack model) is based are described. Calculations of a cratering event in the Colony Oil Shale mine in Colorado are presented. The process of crater formation is outlined based on computer simulations. The BCM is a statistical model which describes fracture in terms of the growth of microcracks. (DMC)
Date: January 1, 1981
Creator: Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Numerical simulation of fracture

Description: A constructive model for brittle, and quasi-brittle materials is described. The Bedded Crack Model contains a microphysical description of fracture based on Griffith theory. The effect of cracks on material properties is described by effective modulus theory. Underlying the model is a statistical framework in which the evolution in time of a statistical distribution of cracks is calculated. The theory upon which the model is based is described. The model is implemented in a finite difference computer code. Our model is contrasted with the phenomenologic models usually found in computer codes. A computational simulation of the strain rate dependence of failure stress is presented and compared with laboratory data. A simulation of a gas gun experiment is presented, and the mechanism of spall described.
Date: January 1, 1983
Creator: Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Criterion for quasibrittle crack growth

Description: An expression to predict the onset of growth of a crack in a quasibrittle material is derived. An energy criterion essentially equivalent to the first two laws of thermodynamics is employed. The criterion is applied to the elastic-plastic crack of Olesiak and Wnuk (1968). 12 references, 3 figures. (ACR)
Date: January 1, 1984
Creator: Margolin, L.G. & Smith, B.W.
Partner: UNT Libraries Government Documents Department

A method for treating hourglass patterns

Description: Hourglassing is a problem frequently encountered in numerical simulations of fluid and solid dynamics. The problem arises because certain volume-preserving distortions of cell shape produce no restoring forces. The result is an unrestricted drifting mode in the velocity field that leads to severe distortions of the computational mesh. These distortions cause large errors in the numerical approximations of the equations of motion. The drift may also allow adjacent vertices to get very close to each other. This results in the computational time step based on a Courant stability condition to become very small, effectively halting the calculation. We describe a mathematical formalism that identifies and selectively damps the hourglass patterns. The damping is constructed to preserve the physical aspects of the solution while maintaining a reasonable computational mesh. We further describe the implementation of our scheme in a 2D hydro code, and show the relative improvement in the results of six different test problems that we calculated.
Date: January 1, 1987
Creator: Margolin, L.G. & Pyun, J.J.
Partner: UNT Libraries Government Documents Department

Algorithm for the computation of nonlinear electron thermal conduction on an arbitrarily shaped, two-dimensional domain

Description: A numerical algorithm is described for computing coupled heat and hydrodynamic flow on an arbitrarily shaped, time-varying domain. The algorithm extends the ICED-ALE method, for the computation of hydrodynamic motion using an arbitrary Eulerian-Lagrangian mesh, to include electron thermal conduction. Appropriate difference equations in conservation form are developed, and the Dufort-Frankel scheme is adapted to advance these equations in time. Results are presented which illustrate the application of the algorithm to the two-dimensional hydrodynamic motion induced by illuminating spherical and thin foil targets with a single laser beam.
Date: October 1, 1977
Creator: Brackbill, J.U. & Margolin, L.G.
Partner: UNT Libraries Government Documents Department

DPDC (double-pass donor cell): A second-order monotone scheme for advection

Description: We are developing a new, second-order, monotone scheme for advection. DPDC (i.e., double-pass donor cell) is based on Smolarkiewicz' simple, positive definite method. Both schemes are multipass methods in which upstream approximations to the truncation error are subtracted from the equations. We describe two significant improvements to Smolarkiewicz' method. First, we use a local gauge transformation to convert the method from being positive definite to the stronger condition of being monotone. Second, we analytically approximate the sum of the corrections of all the passes to use in a single corrective pass. This increases the accuracy of the method, but does not increase the order of accuracy. We compare DPDC with van Leer's method for advection of several different pulses in a constant velocity field. 5 refs., 4 figs.
Date: September 26, 1988
Creator: Beason, C W & Margolin, L G
Partner: UNT Libraries Government Documents Department

Design analysis of liquid metal pipe supports

Description: Design guidelines pertinent to liquid metal pipe supports are presented. The numerous complex conditions affecting the support stiffness and strength are addressed in detail. Topics covered include modeling of supports for natural frequency and stiffness calculations, support hardware components, formulas for deflection due to torsion, plate bending, and out-of-plane flexibility. A sample analysis and a discussion on stress analysis of supports are included. Also presented are recommendations for design improvements for increasing the stiffness of pipe supports and which were utilized in the FFTF system.
Date: February 1, 1979
Creator: Margolin, L.L. & LaSalle, F.R.
Partner: UNT Libraries Government Documents Department

Numerical model for simulating dynamic processes in rocks

Description: A constitutive model for porous, brittle rocks that includes both compaction and fracture is presented. The model is microphysical in that inelasticity is directly related to the mechanics of crack growth and also to the plastic collapse of spherical pores. The model is suitable for computing and has been implemented in a two-dimensional stress wave code. The paper describes a mechanical model of pore collapse, the role of effective moduli in combining the effects of the pores and the cracks in a consistent fashion, and the importance of self-consistent corrections to the moduli in the calculation of spall. 12 references, 1 figure. (ACR)
Date: January 1, 1985
Creator: Margolin, L.G. & Smith, B.W.
Partner: UNT Libraries Government Documents Department

Numerical simulation of fracture

Description: The Bedded Crack Model (BCM) is a constitutive model for brittle materials. It is based on effective modulus theory and makes use of a generalized Griffith criterion for crack growth. It is used in a solid dynamic computer code to simulate stress wave propagation and fracture in rock. A general description of the model is given and then the theoretical basis for it is presented. Some effects of finite cell size in numerical simulations are discussed. The use of the BCM is illustrated in simulations of explosive fracture of oil shale. There is generally good agreement between the calculations and data from field experiments.
Date: January 1, 1982
Creator: Margolin, L.G. & Adams, T.F.
Partner: UNT Libraries Government Documents Department

Momentum-control volumes for finite-difference codes

Description: We consider the integration of the Navier-Stokes equations in finite-difference codes. We first describe the surface-integral technique using momentum-control volumes. Then we focus on the problem of the spherical expansion of a gas. We analyze the difference equations to see why the numerical calculation does not preserve spherical symmetry. Then we propose general, yet simple, techniques for reducing the errors that break the symmetry. We proceed to show numerical results to demonstrate the utility of our techniques. Finally, we consider questions of accuracy and stability of the integration of nonuniform meshes.
Date: January 1, 1983
Creator: Margolin, L.G. & Nichols, B.D.
Partner: UNT Libraries Government Documents Department

Gradient scaling for nonuniform meshes

Description: This paper is concerned with the effect of nonuniform meshes on the accuracy of finite-difference calculations of fluid flow. In particular, when a simple shock propagates through a nonuniform mesh, one may fail to model the jump conditions across the shock even when the equations are differenced in manifestly conservative fashion. We develop an approximate dispersion analysis of the numerical equations and identify the source of the mesh dependency with the form of the artificial viscosity. We then derive an algebraic correction to the numerical equations - a scaling factor for the pressure gradient - to essentially eliminate the mesh dependency. We present several calculations to illustrate our theory. We conclude with an alternate interpretation of our results. 14 refs., 5 figs.
Date: January 1, 1985
Creator: Margolin, L.G.; Ruppel, H.M. & Demuth, R.B.
Partner: UNT Libraries Government Documents Department

Multiscale science for science-based stockpile stewardship

Description: This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The goal of this project has been to develop and apply the methods of multi scale science to the problems of fluid and material mixing due to instability and turbulence, and of materials characterization. Our specific focus has been on the SBSS (science-based stockpile stewardship) issue of assessing the performance of a weapons with off-design, aged, or remanufactured components in the absence of full-scale testing. Our products are physics models, based on microphysical principles and parameters, and suitable for implementation in the large scale design and assessment codes used in the nuclear weapons program.
Date: December 1, 2000
Creator: Margolin, L. & Sharp, D.
Partner: UNT Libraries Government Documents Department

A RATIONALE FOR IMPLICIT TURBULENCE MODELING

Description: We present a rationale for the success of nonoscillatory finite volume (NFV) difference schemes in modeling turbulent flows without need of subgrid scale models. Our exposition focuses on certain truncation terms that appear in the modified equation of one particular NFV scheme, MPDATA. We demonstrate that these truncation terms have physical justification, representing the modifications to the governing equations that arise when one considers the motion of finite volumes of fluid over finite intervals of time.
Date: April 1, 2001
Creator: MARGOLIN, L. G. & RIDER, W. J.
Partner: UNT Libraries Government Documents Department

Forward in time methods for global climate research. Final report

Description: Purpose is to demonstrate feasibility and utility of nonoscillatory forward-in-time (NFT) methods formodeling the global dynamics of the atmosphere and oceans. This includes development of new algorithms, construction of numerical models, and testing these models. One aspect of the research is to compare two variants of NFT methods, one based on Eulerian approximations and the other based on semi-Lagrangian approximations.
Date: May 1, 1996
Creator: Margolin, L.G. & Smolarkiewicz, P.K.
Partner: UNT Libraries Government Documents Department

On "spurious" eddies

Description: Recently several papers have appeared in the CFD literature, proposing an idealized instability problem as a benchmark for discriminating among numerical algorithms for two-dimensional Navier-Stokes flows. The problem is a double shear layer simulated at coarse resolution and with a prescribed interface perturbation. A variety of second-order accurate schemes have been tested, with all results falling into one of two solution patterns - one pattern with two eddies and the other with three eddies. In the literature, there is no fast-and-firm rule to predict the results of any particular algorithm. However it is asserted that the two-eddy solution is correct. Our own research has led to two conclusions. First, the appearance of the third eddy is tied up with small details of the truncation error; we illustrate this point by prescribing small changes that lead to reversal of the appearance/disappearance of the third eddy in several schemes. Second, we discuss the realizability of the two solutions and suggest that the three-eddy solution is the more physical. Overall, we conclude that this problem is a poor choice of benchmark to discriminate among numerical algorithms.
Date: January 1, 2001
Creator: Drikakis, D. (Dimitris); Margolin, L. G. & Smolarkiewicz, P. K. (Piotr K.)
Partner: UNT Libraries Government Documents Department

Summary of accomplishments and research on forward-in-time differencing for shallow fluid flows on the sphere. Final technical report

Description: This past year the authors have continued the development of their 3D grid point model. The general model is nonhydrostatic, is written in nonorthogonal terrain following coordinates, and consistently incorporates either Eulerian or semi-Lagrangian differencing. The non-hydrostatic formulation will be particularly useful when the grid size is small enough to resolve nonhydrostatic processes--for example: convective instabilities, and internal gravity wave dynamics in deep sheared atmospheres. However, the authors have also found that the nonhydrostatic formulation has numerical advantages on coarser grids, such as a better conditioning of the Laplacian matrix that must be inverted. In addition, use of the nonhydrostatic equations allows consistency as the mesh is refined, or when using nested grids. The authors have used this model as a vehicle to compare the advantages of Eulerian and semi-Lagrangian methods. They have incorporated more options into different versions of the basic model. They have implemented a fairly sophisticated subgrid scale turbulence parameterization in the basic model and performed a number of LES studies of planetary boundary layers to calibrate the model. In order to further improve the efficiency of the model, they have developed a new method for treating systems with a variety of time scales. Traditional strategies, including split explicit methods, semi-implicit methods, and mode splitting, all have some inaccuracies and/or stability problems. The new method, which they have named the method of averages (MOA), is based on three steps. To validate the method, they built a 2D shallow water model of an ocean basin.
Date: April 2, 1998
Creator: Smolarkiewicz, P. & Margolin, L.
Partner: UNT Libraries Government Documents Department

MPDATA: A positive definite solver for geophysical flows

Description: This article is a review of MPDATA, a class of methods for the numerical simulation of advection based on the sign-preserving properties of upstream differencing. MPDATA was designed originally as an inexpensive alternative to flux-limited schemes for evaluating the transport of nonnegative thermodynamic variables (such as liquid water or water vapour) in atmospheric models. During the last decade, MPDATA has evolved from a simple advection scheme to a general approach for integrating the conservation laws of geophysical fluids on micro-to-planetary scales. The purpose of this paper is to summarize the basic concepts leading to a family of MPDATA schemes, review the existing MPDATA options, as well as to demonstrate the efficacy of the approach using diverse examples of complex geophysical flows.
Date: March 1, 1997
Creator: Smolarkiewicz, P.K. & Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Forward-in-Time Differencing for Fluids: Nonhydrostatic Modeling of Rotating Stratified Flow on a Mountainous Sphere

Description: Traditionally, numerical models for simulating planetary scale weather and climate employ the hydrostatic primitive equations-an abbreviated form of Navier-Stokes equations that neglect vertical accelerations and use simplified inertial forces. 1 Although there is no evidence so far that including nonhydrostatic effects in global models has any physical significance for large scale solutions, there is an apparent trend in the community toward restoring Navier-Stokes equations (or at least their less constrained forms) in global models of atmospheres and oceans. The primary motivation for this is that the state-of-the-art computers already admit resolutions where local nonhydrostatic effects become noticeable. Other advantages include: the convenience of local mesh refinement; better overall accuracy; insubstantial computational overhead relative to hydrostatic models; universality and therefore convenience of maintaining a single large code; as well as conceptual simplicity and mathematical elegancy--features important for education. The few existing nonhydrostatic global models differ in analytic formulation and numerical design, reflecting their different purposes and origins. Much of our present research improves the design of a high-performance numerical model for simulating the flows of moist (and precipitating), rotating, stratified fluids past a specified time-dependent irregular lower boundary. This model is representative of a class of nonhydrostatic atmospheric codes employing the an elastic equations of motion in a terrain-following curvilinear framework, and contains parallel implementations of semi-Lagrangian and Eulerian approximations selectable by the user. The model has been employed in a variety of applications; the quality of results suggest that modern nonoscillatory forward-in-time (NFT) methods are superior to the more traditional centered-in-time-and-space schemes, in terms of accuracy, computational efficiency, flexibility and robustness.
Date: March 31, 1999
Creator: Smolarkiewicz, P.K.; Grubisic, V. & Margolin, L.G.
Partner: UNT Libraries Government Documents Department

Semi-Lagrangian shallow water modeling on the CM-5

Description: We discuss the parallel implementation of a semi-Lagrangian shallow-water model on the massively parallel Connection Machine CM-5. The four important issues we address in this article are (i) two alternative formulations of the elliptic problem and their relative efficiencies, (ii) the performance of two successive orders of a generalized conjugate residual elliptic solver, (iii) the time spent in unstructured communication -- an unavoidable feature of semi-Lagrangian schemes, and (iv) the scalability of the algorithm.
Date: September 1, 1995
Creator: Nadiga, B.T.; Margolin, L.G. & Smolarkiewicz, P.K.
Partner: UNT Libraries Government Documents Department