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Constrained minimization for monotonic reconstruction

Description: The authors present several innovations in a method for monotonic reconstructions. It is based on the application of constrained minimization techniques for the imposition of monotonicity on a reconstruction. In addition, they present extensions of several classical TVD limiters to a genuinely multidimensional setting. In this case the linear least squares reconstruction method is expanded upon. They also clarify data dependent weighting techniques used with the minimization process.
Date: August 20, 1996
Creator: Rider, W.J. & Kothe, D.B.
Partner: UNT Libraries Government Documents Department

A comparison of interface tracking methods

Description: In this Paper we provide a direct comparison of several important algorithms designed to track fluid interfaces. In the process we propose improved criteria by which these methods are to be judged. We compare and contrast the behavior of the following interface tracking methods: high order monotone capturing schemes, level set methods, volume-of-fluid (VOF) methods, and particle-based (particle-in-cell, or PIC) methods. We compare these methods by first applying a set of standard test problems, then by applying a new set of enhanced problems designed to expose the limitations and weaknesses of each method. We find that the properties of these methods are not adequately assessed until they axe tested with flows having spatial and temporal vorticity gradients. Our results indicate that the particle-based methods are easily the most accurate of those tested. Their practical use, however, is often hampered by their memory and CPU requirements. Particle-based methods employing particles only along interfaces also have difficulty dealing with gross topology changes. Full PIC methods, on the other hand, do not in general have topology restrictions. Following the particle-based methods are VOF volume tracking methods, which are reasonably accurate, physically based, robust, low in cost, and relatively easy to implement. Recent enhancements to the VOF methods using multidimensional interface reconstruction and improved advection provide excellent results on a wide range of test problems.
Date: March 27, 1995
Creator: Kothe, D.B. & Rider, W.J.
Partner: UNT Libraries Government Documents Department

Dynamical modeling of surface tension

Description: In a recent review it is said that free-surface flows ``represent some of the difficult remaining challenges in computational fluid dynamics``. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace`s equation by an equivalent volume force. Here, we describe how CSF might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin. This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin are discussed.
Date: August 1, 1996
Creator: Brackbill, J.U. & Kothe, D.B.
Partner: UNT Libraries Government Documents Department

FLIP (fluid-implicit-particle): A low-dissipation, particle-in-cell method for fluid flow

Description: Since convective transport is the largest source of computational diffusion, FLIP (fluid-implicit-particle) eliminates convection, and uses instead a Lagrangian formulation. In FLIP, as in PIC, particles represent the fluid: a grid is used only to calculate interactions among particles. FLIP is an adaptation to fluid flows of the implicit moment method for plasma simulation. The particles carry coordinates, momentum, mass and energy; everything necessary to describe the fluid. Using the particle data, Lagrangian moment equations solved on a grid advance the particle variables from time step to time step. An adaptive grid and implicit time differencing extend the method to singular and low-speed flows. Aspects of FLIP's properties are illustrated by calculations of the Rayleigh-Taylor instability, an unstable, subsonic stream, and a supersonic jet. The results demonstrate FLIP's applicability to the many problems where low dissipation is crucial to correct modeling. 21 refs.
Date: January 1, 1987
Creator: Brackbill, J.U.; Kothe, D.B. & Ruppel, H.M.
Partner: UNT Libraries Government Documents Department

A parallel, volume-tracking algorithm for unstructured meshes

Description: Many diverse areas of industry benefit from the use of volume of fluid methods to predict the movement of materials. Casting is a common method of part fabrication. The accurate prediction of the casting process is pivotal to industry. Mold design and casting is currently considered an art by industry. It typically involves many trial mold designs, and the rejection of defective parts is costly. Failure of cast parts, because residual stresses reduce the part`s strength, can be catastrophic. Cast parts should have precise geometric details that reduce or eliminate the need for machining after casting. Volume of fluid codes will help designers predict how the molten metal fills a mold and where ay trapped voids remain. Prediction of defects due to thermal contraction or expansion will eliminate defective, trial mold designs and speed the parts to market with fewer rejections. Increasing the predictability and therefore the accuracy of the casting process will reduce the art that is involved in mold design and parts casting. Here, recent enhancements to multidimensional volume-tracking algorithms are presented. Illustrations in two dimensions are given. The improvements include new, local algorithms for interface normal constructions and a new full remapping algorithm for time integration. These methods are used on structured and unstructured grids.
Date: October 1, 1996
Creator: Mosso, S.J.; Swartz, B.K.; Kothe, D.B. & Ferrell, R.C.
Partner: UNT Libraries Government Documents Department

JTpack90: A parallel, object-based, Fortran 90 linear algebra package

Description: The authors have developed an object-based linear algebra package, currently with emphasis on sparse Krylov methods, driven primarily by needs of the Los Alamos National Laboratory parallel unstructured-mesh casting simulation tool Telluride. Support for a number of sparse storage formats, methods, and preconditioners have been implemented, driven primarily by application needs. They describe the object-based Fortran 90 approach, which enhances maintainability, performance, and extensibility, the parallelization approach using a new portable gather/scatter library (PGSLib), current capabilities and future plans, and present preliminary performance results on a variety of platforms.
Date: March 1, 1997
Creator: Turner, J.A.; Kothe, D.B. & Ferrell, R.C.
Partner: UNT Libraries Government Documents Department

A high resolution finite volume method for efficient parallel simulation of casting processes on unstructured meshes

Description: We discuss selected aspects of a new parallel three-dimensional (3-D) computational tool for the unstructured mesh simulation of Los Alamos National Laboratory (LANL) casting processes. This tool, known as {bold Telluride}, draws upon on robust, high resolution finite volume solutions of metal alloy mass, momentum, and enthalpy conservation equations to model the filling, cooling, and solidification of LANL castings. We briefly describe the current {bold Telluride} physical models and solution methods, then detail our parallelization strategy as implemented with Fortran 90 (F90). This strategy has yielded straightforward and efficient parallelization on distributed and shared memory architectures, aided in large part by new parallel libraries {bold JTpack9O} for Krylov-subspace iterative solution methods and {bold PGSLib} for efficient gather/scatter operations. We illustrate our methodology and current capabilities with source code examples and parallel efficiency results for a LANL casting simulation.
Date: March 1, 1997
Creator: Kothe, D.B.; Turner, J.A.; Mosso, S.J. & Ferrell, R.C.
Partner: UNT Libraries Government Documents Department

High resolution finite volume parallel simulations of mould filling and binary alloy solidification on unstructured 3-D meshes

Description: The Los Alamos National Laboratory (LANL) is currently developing a new casting simulation tool (known as Telluride) that employs robust, high-resolution finite volume algorithms for incompressible fluid flow, volume tracking of interfaces, and solidification physics on three-dimensional (3-D) unstructured meshes. Their finite volume algorithms are based on colocated cell-centered schemes that are formally second order in time and space. The flow algorithm is a 3-D extension of recent work on projection method solutions of the Navier-Stokes (NS) equations. Their volume tracking algorithm can accurately track topologically complex interfaces by approximating the interface geometry as piecewise planar. Coupled to their fluid flow algorithm is a comprehensive binary alloy solidification model that incorporates macroscopic descriptions of heat transfer, solute redistribution, and melt convection as well as a microscopic description of segregation. The finite volume algorithms, which are efficient, parallel, and robust, can yield high-fidelity solutions on a variety of meshes, ranging from those that are structured orthogonal to fully unstructured (finite element). The authors discuss key computer science issues that have enabled them to efficiently parallelize their unstructured mesh algorithms on both distributed and shared memory computing platforms. These include their functionally object-oriented use of Fortran 90 and new parallel libraries for gather/scatter functions (PGSLib) and solutions of linear systems of equations (JTpack90). Examples of their current capabilities are illustrated with simulations of mold filling and solidification of complex 3-D components currently being poured in LANL foundries.
Date: June 1, 1997
Creator: Reddy, A.V.; Kothe, D.B. & Lam, K.L.
Partner: UNT Libraries Government Documents Department

Accurate and robust methods for variable density incompressible flows with discontinuities

Description: We are interested in the solution of incompressible flows which are characterized by large density variations, interfacial physics, arbitrary material topologies and strong vortical content. The issues present in constant density incompressible flow are exacerbated by the presence of density discontinuities. A much greater premium requirement is placed the positivity of computed quantities The mechanism of baroclinc vorticity generation exists ({gradient}p x {gradient}p) to further complicate the physics.
Date: September 1996
Creator: Rider, W. J.; Kothe, D. B. & Puckett, E. G.
Partner: UNT Libraries Government Documents Department

Advanced three-dimensional Eulerian hydrodynamic algorithm development

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 purpose of this project is to investigate, implement, and evaluate algorithms that have high potential for improving the robustness, fidelity and accuracy of three-dimensional Eulerian hydrodynamic simulations. Eulerian computations are necessary to simulate a number of important physical phenomena ranging from the molding process for metal parts to nuclear weapons safety issues to astrophysical phenomena such as that associated with a Type 2 supernovae. A number of algorithmic issues were explored in the course of this research including interface/volume tracking, surface physics integration, high resolution integration techniques, multilevel iterative methods, multimaterial hydrodynamics and coupling radiation with hydrodynamics. This project combines core strengths of several Laboratory divisions. The project has high institutional benefit given the renewed emphasis on numerical simulations in Science-Based Stockpile Stewardship and the Accelerated Strategic Computing Initiative and LANL`s tactical goals related to high performance computing and simulation.
Date: November 1, 1998
Creator: Rider, W.J.; Kothe, D.B. & Mosso, S.
Partner: UNT Libraries Government Documents Department

Convergence and accuracy of kernel-based continuum surface tension models

Description: Numerical models for flows of immiscible fluids bounded by topologically complex interfaces possessing surface tension inevitably start with an Eulerian formulation. Here the interface is represented as a color function that abruptly varies from one constant value to another through the interface. This transition region, where the color function varies, is a thin O(h) band along the interface where surface tension forces are applied in continuum surface tension models. Although these models have been widely used since the introduction of the popular CSF method [BKZ92], properties such as absolute accuracy and uniform convergence are often not exhibited in interfacial flow simulations. These properties are necessary if surface tension-driven flows are to be reliably modeled, especially in three dimensions. Accuracy and convergence remain elusive because of difficulties in estimating first and second order spatial derivatives of color functions with abrupt transition regions. These derivatives are needed to approximate interface topology such as the unit normal and mean curvature. Modeling challenges are also presented when formulating the actual surface tension force and its local variation using numerical delta functions. In the following they introduce and incorporate kernels and convolution theory into continuum surface tension models. Here they convolve the discontinuous color function into a mollified function that can support accurate first and second order spatial derivatives. Design requirements for the convolution kernel and a new hybrid mix of convolution and discretization are discussed. The resulting improved estimates for interface topology, numerical delta functions, and surface force distribution are evidenced in an equilibrium static drop simulation where numerically-induced artificial parasitic currents are greatly mitigated.
Date: December 1, 1998
Creator: Williams, M.W.; Kothe, D.B. & Puckett, E.G.
Partner: UNT Libraries Government Documents Department

Low-speed flow hydrodynamics

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 objective of this project was the inception and development of a new casting simulation tool that is founded in modern, high-order numerical algorithms, accurate physical models, and advanced computational science constructs needed to execute efficiently on parallel architectures. This project has therefore led to the development and application of a new simulation tool (known as Telluride) for the modeling of casting processes used in the manufacture of metal alloy components needed for various Department of Energy (DOE) and Defense Programs (DP) projects. As a result of the efforts undertaken in this project, Telluride can now model key foundry processes in the DOE/DP and in industry. Successes realized over the course of this project have secured funding for further Telluride development by the DOE Accelerated Strategic Computing Initiative (ASCI) Program.
Date: August 1, 1997
Creator: Cerutti, J.H.; Kothe, D.B. & Mosso, S.J.
Partner: UNT Libraries Government Documents Department

Volume tracking of interfaces having surface tension in two and three dimensions

Description: Solution algorithms are presented for tracking interfaces with piecewise linear (PLIC) volume-of-fluid (VOF) methods on fixed (Eulerian) two-dimensional (2-D) structured and three-dimensional (3-D) structured and unstructured grids. We review the theory of volume tracking methods, derive appropriate volume evolution equations, identify and present solutions to the basic geometric functions needed for interface reconstruction and volume fluxing, and provide detailed algorithm templates for modern 2-D and 3-D PLIC VOF interface tracking methods. We discuss some key outstanding issues for PLIC VOF methods, namely the method used for time integration of fluid volumes (operator splitting, unsplit, Runge-Kutta, etc.) and the estimation of interface normals. We also present our latest developments in the continuum surface force (CSF) model for surface tension, namely extension to 3-D and variable surface tension effects. We identify and focus on key outstanding CSF model issues that become especially critical on fine meshes with high density ratio interfacial flows, namely the surface delta function approximation, the estimation of interfacial curvature, and the continuum surface force scaling and/or smoothing model. Numerical results in two and three dimensions are used to illustrate the properties of these methods.
Date: March 1, 1996
Creator: Kothe, D.B.; Rider, W.J.; Mosso, S.J.; Brock, J.S. & Hochstein, J.I.
Partner: UNT Libraries Government Documents Department

Multiscale simulations of alloy phase stability

Description: First principles, atomic scale and continuum level models are combined to predict thermodynamic properties of alloys and stability of phases. Many-body interactions, as well as vacancies, defects, and non-stoichiometry are included in the modeling process and the structural stability of hypothetical phases is evaluated. The resulted thermodynamic functions and phase diagrams are integrated in a casting simulation computer program. The process of relating microscopic modeling results to the macroscopic heat transfer and phase equilibrium calculations is detailed to emphasize the self-consistency of the approach and to identify the potential sources of errors. The sequence: data acquisition, modeling, prediction experimental validation, is illustrated for several recent results in actinide based alloys.
Date: January 1, 2002
Creator: Stan, M. (Marius); Baskes, M. I. (Michael I.); Valone, S. M. (Steven M.); Chen, S. P. (Shao-Ping) & Kothe, D. B. (Douglas B.)
Partner: UNT Libraries Government Documents Department

Sensitivity analysis of a nonlinear Newton-Krylov solver for heat transfer with phase change.

Description: Development of a complex metal-casting computer model requires information about how varying the problem parameters affects the results (metal flow and solidification). For example, we would like to know how the last point to solidify or the cooling rate at a given location changes when the physical properties of the metal, boundary conditions, or mold geometry are changed. As a preliminary step towards a complete sensitivity analysis of a three-dimensional casting simulation, we examine a one-dimensional version of a metal-alloy phase-change conductive-heat-transfer model by means of Automatic Differentiation (AD). This non-linear 'Jacobian-free' method is a combination of an outer Newton-based iteration and an inner conjugate gradient-like (Krylov) iteration. The implicit solution algorithm has enthalpy as the dependent variable from which temperatures are determined. We examine the sensitivities of the difference between an exact analytical solution for the final temperature and that produced by this algorithm to the problem parameters. In all there are 17 parameters (12 physical constants such as liquid density, heat capacity, and thermal conductivity, 2 initial and boundary condition parameters, the final solution time, and 2 algorithm tolerances). We apply AD in the forward and reverse mode and verify the sensitivities by means of finite differences. In general, the finite-difference method requires at least N+1 computer runs to determine sensitivities for N problem parameters. By forward and reverse, we mean the direction through the solution and in time and space in which the derivative values are obtained. The forward mode is typically more efficient for determining the sensitivity of many responses to one or a few parameters, while the reverse mode is better suited for sensitivities of one or a few responses with respect to many parameters. The sensitivities produced by all the methods agreed to at least three significant figures. The forward and reverse AD code ...
Date: January 1, 2002
Creator: Henninger, Rudolph J.; Knoll, D. A. (Dana A.); Kothe, D. B. (Douglas B.) & Lally, B. R. (Bryan R.)
Partner: UNT Libraries Government Documents Department

RIPPLE: A new model for incompressible flows with free surfaces

Description: A new free surface flow model, RIPPLE, is summarized. RIPPLE obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology. The key innovation is the Continuum Surface Force (CSF) model which represents surface tension as a (strongly) localized volume force. Other features include a high-order momentum advection model, a volume-of-fluid free surface treatment, and an efficient two-step projection solution method. RIPPLE'S unique capabilities are illustrated with two example problems: low-gravity jet-induced tank flow, and the collision and coalescence of two cylindrical rods. 17 refs., 7 figs.
Date: January 1, 1991
Creator: Kothe, D.B. & Mjolsness, R.C.
Partner: UNT Libraries Government Documents Department