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A B
C D E F G
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M N O P Q
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adsorbate
Solute that has transferred (adsorbed)
from the fluid onto the solid.
adsorption
Adsorption (or sorption) is the transfer of
solute from the fluid onto the solid. Solute adsorbed onto the solid is called adsorbate.
SUTRA offers a choice of three equilibrium adsorption models: linear, Freundlich, and Langmuir. See Section 2.4 of the SUTRA
documentation for details.
anisotropic
Direction-dependent. The permeability tensor is
anisotropic if the effective permeability varies with the direction of
groundwater flow (see Section 2.2 of the SUTRA documentation
for details). The dispersion tensor is anisotropic if the longitudinal
dispersivity or either of the two transverse dispersivities varies with the
direction of groundwater flow (see Section 2.5 of the SUTRA
documentation for details). A property that is independent of the flow
direction is said to be isotropic.
areal simulation
A 2D simulation in which flow and transport are
modeled in the horizontal plane; the system is considered to be vertically
homogeneous. Compare cross-sectional
simulation.
basis function
A function used to describe the variation of a
variable (such as pressure or concentration) between nodes
in a finite-element discretization.
SUTRA uses bilinear basis functions in 2D and trilinear basis functions in 3D.
SUTRA basis functions vary linearly along element edges
(straight lines that connect neighboring nodes). See Sections 3.2 and 4.1 of the
SUTRA documentation for details.
boundary conditions
In SUTRA, "boundary condition" refers to a
specification of pressure, concentration/temperature, or mass/energy flux made
at a node. Boundary conditions are not restricted to
the physical boundary of the model; they can be assigned to any node. By
default, there is no flux in or out of the model domain at nodes for which a
boundary condition has not been explicitly assigned. Boundary conditions are
assigned through datasets 17, 18, 19, and 20 of the main input (".inp")
file. In SUTRA Version 2.1 and earlier, time-dependent boundary conditions must be programmed by the user in
subroutine BCTIME. In later versions, time-dependent boundary conditions can be specified using one or more input files;
no programming is required. For details, see Section 7.5 and Appendix B of the SUTRA
documentation, and "Time-dependent boundary
conditions" on the "Special
topics" page.
budget
An accounting of the input/output, production/decay, and
accumulation/depletion of mass or energy in the system. In a perfect simulation, (net
accumulation/depletion) = (net input/output) + (net production/decay). SUTRA reports separate
budgets for fluid mass and solute mass or thermal energy.
cell
The region of space associated with a node.
CG
An iterative
matrix solver. The name stands for "Conjugate Gradient".
cold start
One of two methods for initializing a SUTRA run;
compare warm start. A cold start is used
to initialize a simulation that is being run for the first time, or a
continuation run in which input parameters or boundary conditions have changed
since the previous run. See "Q: What is the difference between a "cold" and a
"warm" start, and which one should I use?" on the "Frequently
asked questions" page.
compressibility
For a fluid, the fractional change in density per
unit change in pressure. The compressibility of pure water at 20ºC is
approximately 4.47x10-10 kg/(m·s2)-1. For a
solid, minus the fractional change in volume per unit change in intergranular
stress. Compressibilities range from about 10-10 kg/(m·s2)-1
for sound bedrock to about 10-7 kg/(m·s2)-1
for clay. See also storativity.
concentration
In SUTRA, the mass fraction of solute in the fluid,
or the mass fraction of adsorbate on the solid.
conductance
In SUTRA, either of two parameters, GNUP and GNUU,
used to enforce specified pressure and specified concentration/temperature
boundary conditions. These parameters are set in dataset 5 of the main input
(".inp") file. See Sections 3.5 and 7.7 of the SUTRA
documentation, and "Q: What do the boundary conductances GNUP and GNUU do, and why are they
important?" on the "Frequently asked
questions" page.
conductivity
See hydraulic
conductivity.
constant-density flow
Groundwater flow in which the fluid density is
uniform in space and constant in time. Compare variable-density
flow.
convergence tolerance
The value to which a measure of convergence must fall
for an iterative solution to be considered acceptable. A SUTRA run can involve
two different types of iteration: non-linearity
iteration, and matrix solver iteration.
For non-linearity iteration, the convergence tolerances specify the maximum
changes in computed pressures and concentrations/temperatures allowed from one
iteration to the next; iterations continue until the changes are sufficiently
small or the maximum number of iterations allowed has been reached. For
matrix solver iteration, the convergence tolerances specify the maximum
acceptable estimated errors in the pressure and concentration/temperature
solutions; for each solution, iterations continue until the estimated error is
sufficiently small or the maximum number of iterations allowed has been reached.
cross-sectional simulation
A 2D simulation in which flow and transport in a
vertical plane are modeled; the system is considered to be homogeneous in the
direction perpendicular to the plane. Compare areal
simulation.
density
The mass of substance per unit volume. In SUTRA,
fluid density can vary linearly with solute concentration or fluid temperature.
The solid grain density is uniform and constant and is relevant only in
simulations involving energy transport or solute transport with
sorption.
density-dependent flow
See variable-density
flow.
direct matrix solver
A matrix solver that
computes the solution to a matrix problem directly (not by iteration)
using an algebraic elimination procedure. Such a solver is available in SUTRA.
Compare iterative matrix solver.
discretization
In SUTRA, discretization is the process of or result of approximating the
physical system (spatially) as an assemblage of discrete elements
and (temporally) as a series of discrete time steps. Smaller elements or steps
result in finer discretization; larger elements or steps result in coarser
discretization.
dispersion
In SUTRA, "dispersion" refers specifically
to mechanical dispersion, as distinguished from molecular diffusion.
Dispersion describes the spreading of solute mass or thermal energy relative to
the average advective motion of the fluid; it is the macroscopic (model-scale)
representation of the effect of fluid mixing at the microscopic (pore) scale. In
SUTRA, the dispersive flux depends linearly on both the
concentration/temperature gradient (it is "Fickian") and the magnitude
of the fluid velocity. To learn more about the SUTRA dispersion model, see Section 2.5 of the SUTRA documentation
and "Visualizing the SUTRA
dispersion model in 3D" on the "Special
topics" page.
dispersivity
In 3D, dispersion of solute
or energy is characterized by three dispersivities: the longitudinal
dispersivity, aL, and two transverse
dispersivities, aT1 and aT2.
The longitudinal dispersivity characterizes the tendency of solute or energy to
disperse along the direction of groundwater flow. The transverse dispersivities
characterize the tendency of solute or energy to disperse in two directions
perpendicular to the direction of groundwater flow. In 3D, SUTRA requires the
user to input six parameters (in dataset 15) that are used to compute aL,
aT1, and aT2
and their associated spreading directions as functions of the groundwater flow
magnitude and direction. In 2D, the situation is similar, except that there is
only one transverse dispersivity and one transverse spreading direction (which
is perpendicular to the direction of groundwater flow), and only four input
parameters are required. To learn more about the SUTRA dispersion model, see Section 2.5 of the SUTRA documentation
and "Visualizing the SUTRA
dispersion model in 3D" on the "Special
topics" page.
element
The basic "building block" used to model
physical systems using the finite-element
method. In SUTRA, each element is a quadrilateral
(2D) or a generalized hexahedron (3D).
elementwise
Element-by-element. Elementwise properties (such as
permeability) are assigned a value at each element in
the mesh. Compare nodewise.
energy
In SUTRA, "energy" refers specifically to thermal
energy, which is the energy associated with changes in temperature.
finite-element method
A numerical method used to approximate a physical
system as an assemblage of discrete elements. SUTRA uses a hybridization
of the Galerkin finite-element and integrated finite-difference methods. See
Section 1.5 and Chapters 3 and 4 of the SUTRA documentation
for details.
flow equation
The equation that embodies the physical laws
governing groundwater flow. The flow equation used in SUTRA results from the
combination of the fluid mass balance with Darcy's Law. It is formulated in
terms of fluid pressure. The discretized form of
the flow equation is a matrix equation that is solved for the pressure at each
node. See Section 2.2 of the SUTRA documentation for
details.
Gaussian elimination
An algebraic procedure used to solve sets of linear
equations. This is the procedure used by the direct
matrix solver available in SUTRA.
generalized hexahedron
In SUTRA, a closed 3D figure having six (not
necessarily planar) faces, with each face defined by four straight edges.
Examples include (but are not limited to) cubes and parallelepipeds. 3D SUTRA elements
are generalized hexahedra, the eight corners of which are called nodes.
global coordinates
The physical (x, y, z) coordinate system in which a
SUTRA problem is formulated by the user. Compare local
coordinates. See Sections 4.1 and 4.2 of the SUTRA
documentation for details.
GMRES
An iterative
matrix solver. The name stands for "Generalized Minimum Residual".
GNUP
A "conductance" used to enforce specified
pressure boundary conditions. This parameter is set in dataset 5 of the main input
(".inp") file. See Section 3.5 and Appendix B of the SUTRA
documentation, and "Q: What do the boundary conductances GNUP and GNUU do, and why are they
important?" on the "Frequently asked
questions" page.
GNUU
A "conductance" used to enforce specified
concentration/temperature boundary conditions. This parameter is set in dataset 5 of the main input
(".inp") file. GNUU works analogously to GNUP; see
Section 3.5 and Appendix B of the
SUTRA
documentation, and "Q: What do the boundary conductances GNUP and GNUU do, and why are they
important?" on the "Frequently asked
questions" page.
head
Hydraulic head is defined as the sum of the pressure
head and the elevation. Pressure head is, in turn, defined as p/(rg),
where p is the fluid pressure, r is the fluid
density, and g is the acceleration of gravity.
hexahedron
A closed 3D figure having 6 planar faces. 3D SUTRA elements
are generalized hexahedra.
hydraulic conductivity
Hydraulic conductivity is a measure of the ease with
which fluid flows through a porous medium under the influence of a hydraulic head
gradient. Conductivity depends on the properties of both the fluid and the
solid. It is most useful in the context of isothermal,
constant-density flow. See Section 2.2 of
the SUTRA documentation for details. Compare permeability.
incidence list
A list of the nodes that are
associated with each element in a SUTRA model. The
incidence list is entered in dataset 22 of the main input (".inp")
file.
isothermal
Having uniform, constant temperature.
isotropic
Independent of direction. The permeability tensor is
isotropic if the effective permeability does not vary with the direction of
groundwater flow. The dispersion tensor is anisotropic if the longitudinal and
transverse dispersivities do not vary with the direction of groundwater flow. A
property that depends on the flow direction is said to be anisotropic.
iteration
The process of arriving at a solution through a
series of steps that, ideally, computes solutions that are progressively closer
to the correct answer. Also, a single step in such a process. A SUTRA run can
involve two different types of iteration: non-linearity
iteration, and matrix solver iteration.
iterative matrix solver
A matrix solver that
computes the solution to a matrix problem by iteration.
Three such solvers, CG, GMRES, and ORTHOMIN, are available in SUTRA. Compare direct
matrix solver.
Jacobian matrix
The matrix that defines the linear transformation
between global and local
coordinates.
local coordinates
A coordinate system used to simplify and carry out
calculations within an element. The local coordinate
system is unique to each element. The user formulates the SUTRA problem in terms
of the global coordinates (x, y, z), and SUTRA
automatically performs transformations between local and global coordinates as
needed. See Sections 4.1 and 4.2 of the SUTRA documentation
for details.
logically rectangular
Having the same logical organization as a regular
array of squares (2D) or cubes (3D). In SUTRA 2.0 (2D3D.1), 3D SUTRA meshes had to be logically
rectangular, although their geometry could be deformed. This restriction was removed beginning with SUTRA 2.1.
See Section 3.1 of the SUTRA documentation for details.
longitudinal
Along the direction of groundwater flow.
longitudinal dispersivity
See dispersivity.
matrix solver
A numerical algorithm designed to solve matrix
problems. In SUTRA, matrix solvers are used to solve the flow
equation for pressure and the transport
equation for concentration or temperature.
matrix solver iteration
The scheme employed by an iterative
matrix solver to converge to the correct solution to a matrix problem to
within a specified convergence tolerance.
Also, a single step in such a scheme. Not to be confused with non-linearity
iteration.
max direction
The direction of groundwater flow for which the
effective permeability is at its maximum value; a.k.a. the maximum
permeability direction. The max direction is perpendicular to the min
direction and (in 3D) the mid direction. See
Section 2.2 of the SUTRA documentation for details.
mesh
The assemblage of nodes and elements
used to model a physical system using the finite-element
method.
mesh spacing
The distance between opposite sides of an element
in a SUTRA mesh. The mesh spacing can vary from place
to place within a model, and can depend on the direction in which it is
measured. The mesh spacing can be important in determining the accuracy and
numerical stability of SUTRA simulations; see Section 7.2 of the SUTRA
documentation for details.
mid direction
In 3D, the direction that is perpendicular to both
the max direction and the min
direction, and for which the effective permeability assumes a value between
the maximum and minimum values; a.k.a. the middle permeability direction.
See Section 2.2 of the SUTRA documentation for details.
min direction
The direction of groundwater flow for which the
effective permeability is at its minimum value; a.k.a. the minimum
permeability direction. The min direction is perpendicular to the max
direction and (in 3D) the mid direction. See
Section 2.2 of the SUTRA documentation for details.
node
A corner of an element.
nodewise
Node-by-node. Nodewise properties (such as porosity)
are assigned a value at each node in the mesh. Compare elementwise.
non-linearity iteration
Variable-density
and/or unsaturated problems yield a non-linear
set of equations that must be solved for pressure
(p) and concentration or temperature
(U). However, the SUTRA flow equation is linear
with respect to p alone, and the SUTRA transport
equation is linear with respect to U alone. Thus, the non-linear set of
equations can be solved by iterating between the flow and transport equations,
solving two linear matrix equations in succession on each iteration.
First, the latest U solution is used in setting up the flow equation, which is
then solved for p using a matrix solver.
Then, the new p solution is used in setting up the transport equation, which is
then solved for U. This so-called non-linearity (or "Picard")
iteration cycle continues until a user-specified convergence
tolerance has been satisfied or the maximum allowable number of iterations
has been reached. Non-linearity iteration is not to be confused with matrix
solver iteration.
numbering directions
The three indexing directions, I, J, and K, in a logically
rectangular, 3D SUTRA mesh, ordered to indicate the order in which the nodes
are numbered.
ORTHOMIN
An iterative
matrix solver.
permeability
Permeability is a measure of the ease with which
fluid flows through a porous medium under the influence of a pressure gradient
and/or gravity. Permeability is, in most situations, essentially independent of
pressure, temperature, and concentration and depends only on the nature of the
porous medium. SUTRA simulations are formulated in terms of permeability (rather
than hydraulic conductivity). The effective
permeability at any point in the system can depend on the direction of groundwater flow. See
Section 2.2 of the SUTRA documentation for details.
Picard iteration
An
iterative scheme used to solve a set of non-linear equations simultaneously. See non-linearity
iteration.
pinch node
A type of node used to effect
large changes in mesh spacing over relatively short
distances. The pinch node option was discontinued in SUTRA Version
2.0 (2D3D.1).
porosity
The fractional volume of pore space in a porous
medium. In SUTRA, the porosity is assumed to remain constant with time.
quadrilateral
A closed plane (2D) figure having four straight
sides. Examples include (but are not limited to) squares, rectangles,
parallelograms, and trapezoids. 2D SUTRA elements are
quadrilaterals, the four corners of which are called nodes.
saturated flow
Groundwater flow in which all available pore space
is filled with water. Compare unsaturated flow.
saturation
The fraction of the total available pore space that
is filled with water. When the saturation equals unity (Sw = 1), the
groundwater flow is said to be saturated.
sorption
See adsorption.
storativity
The specific pressure storativity is the volume of
water released from saturated pore storage, per volume of porous medium, due to
a unit drop in fluid pressure. SUTRA computes the specific pressure storativity
from the fluid and solid compressibilites under
the assumption that individual solid grains are incompressible and that the total stress
(the sum of the fluid pore pressure and the intergranular stress) remains
constant.
See Section 2.1 of the SUTRA documentation for details.
time step size
The size of a time increment in a transient
simulation. Time step size can be important in determining the accuracy and
numerical stability of the solution. See Section 7.2 of the SUTRA
documentation for details.
transport equation
The equation that embodies the physical laws
governing the transport of solute mass or thermal energy. The transport equation
used in SUTRA results from the combination of the solute mass or energy balance
with the dispersion and adsorption
models. It is formulated in terms of the solute concentration or temperature.
The discretized form of the transport equation is
a matrix equation that is solved for the solute concentration or temperature at
each node. The SUTRA transport equation is formulated such that it can represent
either solute mass transport or thermal energy transport, depending on how its
coefficients are defined. See Sections 2.3, 2.4, and 2.6 of the SUTRA
documentation for details.
transverse
Perpendicular to the direction of groundwater flow.
transverse dispersivity
See dispersivity.
unsaturated flow
Groundwater flow in which the available pore space
is only partially filled with water. SUTRA is capable of simulating both saturated
and unsaturated flow. See Sections 2.1, 2.2, and 7.5 of the SUTRA
documentation, and "Unsaturated flow
functions" on the "Special topics"
page.
variable-density flow
Groundwater flow in which the fluid density is
variable in space and/or in time as a result of its dependence on solute
concentration or fluid temperature. Compare constant-density
flow.
velocity
In SUTRA, velocity refers to the average fluid
velocity relative to the stationary solid matrix. It is an average
velocity in the sense that it represents fluid movement as viewed at the model
scale, rather than at the microscopic (pore) scale. The average fluid velocity
defined here is not to be confused with the Darcy velocity, which is a measure
of the volumetric flux of fluid and is equal to eSwv,
where e is porosity, Sw
is saturation, and v is average fluid velocity. See Section 2.2 of the SUTRA documentation
for details.
viscosity
A measure of a fluid's resistance to shearing, which
in part determines its resistance to flowing through a porous medium. In SUTRA,
viscosity is a function of temperature in energy transport simulations and is
uniform and constant in solute transport simulations. See Section 2.1 of the SUTRA
documentation for details.
warm start
One of two methods for initializing a SUTRA run;
compare cold start. A warm start is used to
continue an earlier simulation as though it had never been interrupted. See
"Q: What is the difference between a "cold" and a
"warm" start, and which one should I use?" on the "Frequently
asked questions" page.
water table
In saturated-unsaturated
flow, the surface along which the fluid pressure is equal to
atmospheric pressure. SUTRA does not explicitly track the position of the water
table. Rather, the transition from saturated to unsaturated flow is modeled
using unsaturated flow functions provided by the user. See Sections 2.1, 2.2,
and 7.5 of the SUTRA documentation, and "Unsaturated
flow functions" on the "Special
topics" page.
x-coordinate
The x-component of the physical (x, y, z) coordinate
system in which the user has formulated the SUTRA problem. See also global
coordinates.
y-coordinate
The y-component of the physical (x, y, z) coordinate
system in which the user has formulated the SUTRA problem. See also global
coordinates.
z-coordinate
The z-component of the physical (x, y, z) coordinate
system in which the user has formulated the SUTRA problem. See also global
coordinates.
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