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The Legacy of Group T-3
(taken from LA-UR-1426 by Norman L.
Johnson)
Feel free to browse through the entire history or click on the area of
interest:
- Introduction
- Early History of Group T-3 (1958-68)
Abstract
The early history is presented of the prolific development
of CFD methods in the Fluid Dynamics Group (T-3) at Los Alamos National
Laboratory in the years from 1958 to the late 1960s. Many of the currently
used numerical methods: PIC, MAC, vorticity-stream-function, ICE, ALE
methods and the k-e method for turbulence- originated during this
time. The rest of the paper summarizes the current research in T-3 for
CFD, turbulence and solids modeling. The research areas include reactive
flows, multimaterial flows, multiphase flows and flows with spatial discontinuities.
Also summarized are modern particle methods and techniques developed for
large scale computing on massively parallel computing platforms and distributed
processors.
1. Introduction
At times in history there often comes together a unique confluence of
people and events that can change the development of history. In many
ways the early development of Computational Fluid Dynamics (CFD) methods
at Los Alamos National Laboratory, and in particular in the Fluid Dynamics
Group, in the late 50s and through the 60s was such an example, a rare
integration of unique computational resources, people and applications.
Arguably, a critical factor was the creation of the worlds largest computer
resources for programs of national interest that were available for exploration
into alternative CFD methods. But equally, the presence of Francis H.
Harlow with his prolific creativity, which continues to this day, and
his colleagues were also a rare occurrence. Even though the laboratory
programs at the time needed robust simulations of multimaterial, compressible
flows, all applications were fair game because of the almost total absence
of CFD codes at the time.
The purpose of the present work is two-fold: to review the early days
of the development of CFD methods in the Fluid Dynamics group (T-3) at
Los Alamos National Laboratory (at that time called Los Alamos Scientific
Laboratory and hereafter referred to as Los Alamos) and to summarize the
current research in T-3, as an invitation to the reader to inquire about
more information as warranted.
Although this review focuses on the work from T-3, there is significant
work that has been done over the years in other parts of the laboratory,
some in collaboration with T-3, or, more often, as independent work. The
author makes apologies for the myopic view of CFD at Los Alamos and is
the first to recognize the direct contributions of colleagues in other
parts of the Laboratory and the contribution of the Laboratory as a whole,
in providing one of the premiere research facilities in the world.
2. Early History of Group T-3 (1958-68)
In the early years of the Fluid Dynamics Group (T-3) in
the Theoretical Division at Los Alamos, the problems of interest were
multiple materials under high compression, in which solids behave like
fluids. The standard approach in the 50s to numerical modeling of deforming
materials was a Lagrangian treatment with staggered primary variables
(thermodynamic variables at the element centers, kinematic variables at
the vertices or nodes). The Lagrangian method satisfied the need for an
accurate interfacial treatment, but severely suffered from mesh distortions
under the large shearing deformations and instabilities. Typical simulations
at the time had to be halted when the mesh entangled and painstakingly
"remeshed" by hand, and then the simulation continued.
PIC: Particle-In-Cell
In this time of great need, the PIC method was proposed
and developed by Harlow in 1957 [Evans et al.][Harlow,
1957]. The original PIC code used mass particles that carried
material position, mass, and species information on a two-dimensional
(2D), uniform, Eulerian mesh. It treated transient, compressible flows
of multiple materials with no restrictions on interfacial deformation.
It was also the first of the T-3 codes that used the technique of solution
phases: the division of the computational cycle into a Lagrangian and
Eulerian (remap or rezone) phase. Fig. 1-1 shows a result from an early
PIC calculation. A large number of particles per element - 16 was
found to be best in 2D - were required to reduce the inherent fluctuations
of the method (this is discussed in more detail in the FLIP section
3.3 below) and, consequently, the method was memory intensive, particularly
for the computers of the time (IBM 701 and 704). While the PIC
scheme for fluid flow had limited application outside of Los Alamos except
for plasma simulations, the T-3 PIC method did find significant
use in the Soviet Union as the "Large Particle" technique. The
PIC method has had a major resurgence almost three decades later
in the development of FLIP (see section 3.3).
Fig. 1-1. A shock passing though two gases with a stepped interface, with
a density ratio of 2 (the lighter gas is shown) [47]. The PIC particles
and mesh are not illustrated.
Formation and Style of Group
T-3
The success of the PIC method in solving the truly
unsolvable problems of the time made the idea of forming a dedicated fluid
dynamics group attractive. With the support of Stan Ulam and Conrad Longmire,
the Fluid Dynamics Group (T-3) was created in the Theoretical Division
in 1958, with Harlow as its first Group Leader. Harlow remained group
leader until 1973. T-3 started out with seven core members, and grew to
13 members by 1963, 15 members by 1970, and 25 by 1990. Although the group
was largely funded by weapons research money in these early years and
weapons applications remained the main area of application, the atmosphere
of the late fifties and sixties was one of free exploration of CFD techniques
for solving a wide variety of applications, including incompressible,
free-surface flows.
The rest of this introduction focuses on the specific techniques that
were developed; these were developed with a common approach, a certain
style that was characteristic to T-3. The techniques were developed under
the collaboration of typically a programmer and a theorist. The involvement
of a skilled programmer was essential, because each code pushed the limits
of the current computer capability. The necessity for large computers
precluded much of the use of this work outside of Los Alamos in the early
60s. Computer codes for each new method were written from scratch and
were not intended to be exported. But, as the 60s progressed, the T-3
techniques were widely applied across the country. The development of
codes for use outside Los Alamos came much later.
FLIC: Fluid-In-Cell
To address the particle fluctuations and the large memory
requirements of the PIC method, the FLIC method was developed under Harlow's
direction by Gentry, Martin and Daly [Gentry
et al, 1966]. The FLIC method treated compressible flows of a single
material on a 2D, uniform, Eulerian mesh, in which all the state variables
were co-located at the cell center. The technique fluxed material across
cell boundaries in the now-typical Eulerian fashion. Not surprisingly,
the method suffered from stability problems from poorly coupled momentum
and pressure fields, which plagued the co-located variable methods for
the next three decades. The method included the capability to treat arbitrarily
shaped objects by using a piece-wise linear representation of a solid
boundary in the regular mesh - a precursor to the later fractional area/volume
formulation.
Vorticity and Stream Function
Method
Fromms work was the first and only foray away from primitive
variables in T-3 of velocity and pressure, and developed the first treatment
of strongly contorting incompressible flows in the world: the vorticity-stream-function
method for 2D, transient, incompressible flows in 1963 by Fromm and Harlow
[Fromm et al, 1963]. Fromm's ideas of a
"Phase-Error Correction" method anticipated monotonicity-preserving
methods currently popular. The origin of this idea has been largely forgotten.
MAC: Marker-And-Cell
To treat incompressible, free surface flows, the MAC
method was developed by Harlow and Welch [Harlow
et al, 1965] as a variation of the PIC method but treating
applications that extended beyond those addressed by the vorticity-stream-function
method. The MAC method was the first successful technique for incompressible
flows. Particles were used as markers to locate the material in the mesh
and, consequently, to define the location of the free-surface. The MAC
method had the advantage of a more compact finite difference stencil and
tight coupling between the pressure and velocity fields. To treat the
fluid incompressibility, a solution to the Poisson equation for the pressure
was used. This was in contrast to later methods that solved the coupled
velocity-pressure equations, as discussed by Viecelli [Viecelli,
1969]. Although the solution of Poisson's equation was numerically
simple, the specification of the velocity boundary conditions were not
straightforward. There was some controversy at the time about the relative
stability of the MAC method, and this was resolved in the now-classic
paper by Hirt [Hirt, 1968], in which he
showed that the MAC method is unstable with centered momentum advection
unless the viscosity is sufficiently large. This work was the precursor
of the modern truncation error subtraction analysis. This controversy
illustrated the T-3 approach: the development was always on the physics,
with limited application of mathematical analysis of, e.g., convergence
and stability properties. The MAC method is still in use and has
profited from the added efficiency of modern conjugate gradient schemes
for solving the Poisson equation.
ICE: Implicit-Continuous-Fluid-Eulerian
Also in the late 60s, an all-speed code was developed,
and called the ICE method [Amsden, 1968][Harlow
et al, 1970]. The ICE method was the first approach that removed
the Courant stability limitation based on the fluid sound speed. Originally,
the method had a fully nonlinear implicitness, which is often replaced
by a modern linear implicitness - a more simple approach, but with the
same stability properties in the limit of zero Mach number. In the limit
of zero Mach number, the ICE scheme reduces to the MAC scheme.
SOLA and Reactive Flow Codes
The MAC method was the basis of the later particle-less
techniques for compressible and incompressible flows embodied in the SOLA
family of codes by Hirt, Nichols and others in the early 70s that were
the first T-3 codes distributed internationally. These codes included
extensions to two immiscible fluids in the SOLA-VOF code [Hirt
et al, 1975][Hirt et al, 1981], the
first broadly distributed T-3 code in its source form. One member of SOLA
family, the SOLA-DF code, included a multiphase treatment with
multiple velocity fields [Hirt et al, 1979][Rivard
et al, 1976][Travis et al, 1979].
About the same time, the first reactive flow code, RICE, was developed
by Rivard and Butler and others [Butler et al,
1976][Rivard et al, 1975], which evolved
into the most widely used of the T-3 codes, APACHE-CONCHAS-KIVA
lineage of codes [Ramshaw et al, 1979],
discussed in the next section.
LINC (Lagrangian-Incompressible)
and ALE (Arbitrary-Lagrangian-Eulerian)
In 1967 the first 2D Lagrangian method for incompressible
flows was developed in the LINC (Lagrangian-INCompressible) code.
The approach was based on restricting the movement of the vertices such
that the volume remained constant and, thus, was not based upon a global
solution to the zero divergence of the velocity field, as in previous
incompressible methods. While the LINC code was no more successful
in treating flows than other multi-dimensional Lagrangian codes, its formulation
led to the staggered mesh approach to coupling of the pressure and velocity
fields in the MAC method and was used to explore elastic-plastic
materials and surface tension effects. The most important consequence
of the LINC code was the observation that mesh rezoning was needed
for most problems. The second generation version of LINC, consequently,
included an ALE capability. This first application of the ALE
formalism paved the future for all the later ALE codes [Brackbill
et al, 1973][Hirt et al, 1974], including
SALE [Amsden, 1980] and its progeny.
This version of LINC was also the first application of the Finite
Volume method, the use of integral formulation of the conservation equations,
the close cousin to the finite element methods. The Finite Volume method
enabled straightforward treatment of nonorthogonal and three-dimensional
meshes.
Turbulence and the k-epsilon Model
Harlow and his colleagues also contributed to the early
numerical modeling of turbulence and, in particular, by the postulation
of the now ubiquitous k-e model in the 60s [Harlow
et al, 1967][Harlow et al, 1961].
The history of the early turbulence modeling in T-3 is included with the
current modeling in section 3.5 below, in order to present a unified treatment
of this complex topic.
PAF (Particle-and-Force) and Free-Lagrangian
Methods
One of the least known CFD methods outside of T-3, but
one that was the precursor to the Free-Lagrangian methods, including the
Smooth Particle and the Lattice Gas methods, is the PAF method,
first documented in 1961 [Harlow et al, 1961].
It was the first of the mesh-less (in the sense that computational points
were not associated with any mesh) and variable connectivity methods (in
the sense that the connectivity changed during the simulation). It combined
the lack of numerical diffusion of the Lagrangian methods with the robustness
of the Eulerian methods, but without the underlying mesh and the large
memory requirements of the PIC method. One way to view the method
is as a molecular dynamics approach, but applied on a macroscopic scale.
Computational points have a constant mass and carry all state information;
they do not possess any moment of inertia, i.e., they are point masses.
The particles represent parcels of fluid that interact with fluid like
forces that are chosen to duplicate the equation of state and viscous
effects [Harlow, 1963]. At any time, the
particles interact with only their neighbors. The time evolution of the
particles is just the solution of Newtons equations for a multi bodied
system.
In 1965, a summary report was published [Daly
et al, 1965] and comparison between fairly complex experimental data
and simulations were made. The PAF technique was abandoned because
of the inherent noise in the flow field as particles reconnected with
different neighbors during shear flows. The PAF method also suffered
from slowness of the calculation of the nearest neighbors, one which scales
with N2, where N is the number of particles, if no acceleration techniques
are used. Modern methods now have reduced this scaling to be linear and
the approach has become computationally attractive again.
Not until 1983 were methods developed that minimized the fluctuations
in the PAF method, such that even incompressible flows could be
modeled [Johnson, 1983]. The smooth particle
methods of recent times take a different approach and reduce this difficulty
by averaging over more particles, but at the expense of less compact support
and more computations. The Lattice Gas methods, which take the approach
of reducing the unrestricted particle motion to moving on a regular lattice,
tried to relate the fluctuations to thermal motion and averaged the solution
over a large volume to eliminate the fluctuations in the macroscopic flow
field.
Harlow has often said that 1968 was the last year that he could keep up
with all the CFD developments around the world, so much had the entire
field grown after that time. By a similar measure, the CFD methods developed
in the 70s and 80s in T-3 were more application driven with close collaboration
with the end users and less of explorations in CFD, an era had passed.
The full copy of this paper is "The
Legacy and Future of CFD at Los Alamos" (365Kb pdf file) which
is LA-UR-1426 by Norman L. Johnson.
See the viewgraphs
for this paper. (878k, pdf format)
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