Typical Applications
Some of the more common coupled pore fluid diffusion/stress (and,
optionally, thermal) analysis problems that can be analyzed with
Abaqus/Standard
are:
- Saturated flow
-
Soil mechanics problems generally involve fully saturated flow, since the
solid is fully saturated with ground water. Typical examples of saturated flow
include consolidation of soils under foundations and excavation of tunnels in
saturated soil.
- Partially saturated
flow
-
Partially saturated flow occurs when the wetting liquid is absorbed into or
exsorbed from the medium by capillary action. Irrigation and hydrology problems
generally include partially saturated flow.
- Combined
flow
-
Combined fully saturated and partially saturated flow occurs in problems
such as seepage of water through an earth dam, where the position of the
phreatic surface (the boundary between fully saturated and partially saturated
soil) is of interest.
- Moisture
migration
-
Although not normally associated with soil mechanics, moisture migration
problems can also be solved using the coupled pore fluid diffusion/stress
procedure. These problems may involve partially saturated flow in polymeric
materials such as paper towels and sponge-like materials; in the biomedical
industry they may also involve saturated flow in hydrated soft tissues.
- Combined heat
transfer and pore fluid flow
-
In some applications, such as a source of heat buried in soil, it is
important to model the coupling between the mechanical deformation, pore fluid
flow, and heat transfer. In such problems the difference in the thermal
expansion coefficients between the soil and the pore fluid often plays an
important role in determining the rate of diffusion of the pore fluid and heat
from the source.
Flow through Porous Media
A porous medium is modeled in
Abaqus/Standard
by a conventional approach that considers the medium as a multiphase material
and adopts an effective stress principle to describe its behavior. The porous
medium modeling provided considers the presence of two fluids in the medium.
One is the “wetting liquid,” which is assumed to be relatively (but not
entirely) incompressible. Often the other is a gas, which is relatively
compressible. An example of such a system is soil containing ground water. When
the medium is partially saturated, both fluids exist at a point; when it is
fully saturated, the voids are completely filled with the wetting liquid. The
elementary volume, ,
is made up of a volume of grains of solid material, ;
a volume of voids, ;
and a volume of wetting liquid, ,
that is free to move through the medium if driven. In some systems (for
example, systems containing particles that absorb the wetting liquid and swell
in the process) there may also be a significant volume of trapped wetting
liquid, .
The porous medium is modeled by attaching the finite element mesh to the
solid phase; fluid can flow through this mesh. The mechanical part of the model
is based on the effective stress principle defined in
Effective stress principle for porous media.
The model also uses a continuity equation for the mass of wetting fluid in a
unit volume of the medium. This equation is described in
Continuity statement for the wetting liquid phase in a porous medium.
It is written with pore pressure (the average pressure in the wetting fluid at
a point in the porous medium) as the basic variable (degree of freedom 8 at the
nodes). The conjugate flux variable is the volumetric flow rate at the node,
. The porous medium is
partially saturated when the pore liquid pressure, ,
is negative.
Coupled Flow and Heat Transfer through Porous Media
Optionally, heat transfer due to conduction in the soil skeleton and pore
fluid, as well as convection in the pore fluid, can also be modeled. This
capability represents an enhancement to the basic pore fluid flow capabilities
discussed in the earlier paragraphs and requires the use of coupled
temperature–pore pressure elements that have temperature as an additional
degree of freedom (degree of freedom 11 at the nodes) in addition to the pore
pressure and the displacement components. When you use the coupled
temperature–pore pressure elements,
Abaqus
solves the heat transfer equation in addition to and in a fully coupled manner
with the continuity equation and the mechanical equilibrium equations. Only
linear brick, first-order axisymmetric, and second-order modified tetrahedrons
are available for modeling coupled heat transfer with pore fluid flow and
mechanical deformation.
Total and Excess Pore Fluid Pressure
The coupled pore fluid diffusion/stress analysis capability can provide
solutions either in terms of total or “excess” pore fluid pressure. The excess
pore fluid pressure at a point is the pore fluid pressure in excess of the
hydrostatic pressure required to support the weight of pore fluid above the
elevation of the material point. The difference between total and excess pore
pressure is relevant only for cases in which gravitational loading is
important; for example, when the loading provided by the hydrostatic pressure
in the pore fluid is large or when effects like “wicking” (transient capillary
suction of liquid into a dry column) are being studied. Total pore pressure
solutions are provided when the gravity distributed load is used to define the
gravity load on the model. Excess pore pressure solutions are provided in all
other cases; for example, when gravity loading is defined with body force
distributed loads.
Steady-State Analysis
Steady-state coupled pore pressure/effective stress analysis assumes that
there are no transient effects in the wetting liquid continuity equation; that
is, the steady-state solution corresponds to constant wetting liquid velocities
and constant volume of wetting liquid per unit volume in the continuum. Thus,
for example, thermal expansion of the liquid phase has no effect on the
steady-state solution: it is a transient effect. Therefore, the time scale
chosen during steady-state analysis is relevant only to rate effects in the
constitutive model used for the porous medium (excluding creep and
viscoelasticity, which are disabled in steady-state analysis).
Mechanical loads and boundary conditions can be changed gradually over the
step by referring to an amplitude curve to accommodate possible geometric
nonlinearities in the response.
The steady-state coupled equations are strongly unsymmetric; therefore, the
unsymmetric matrix solution and storage scheme is used automatically for
steady-state analysis steps (see
Defining an Analysis).
If heat transfer is modeled using the coupled temperature–pore pressure
elements, the steady-state solution neglects all transient effects in the heat
transfer equation and provides only the steady-state temperature distribution.
Incrementation
You can specify a fixed time increment size in a coupled pore fluid
diffusion/stress analysis, or
Abaqus/Standard
can select the time increment size automatically. Automatic incrementation is
recommended because the time increments in a typical diffusion analysis can
increase by several orders of magnitude during the simulation. If you do not
activate automatic incrementation, fixed time increments will be used.
Transient Analysis
In a transient coupled pore pressure/effective stress analysis the backward
difference operator is used to integrate the continuity equation and the heat
transfer equation (if heat transfer is modeled): this operator provides
unconditional stability so that the only concern with respect to time
integration is accuracy. You can provide the time increments, or they can be
selected automatically.
The coupled partially saturated flow equations are strongly unsymmetric, so
the unsymmetric solver is used automatically if you request partially saturated
analysis (by including absorption/exsorption behavior in the material
definition). The unsymmetric solver is also activated automatically when
gravity distributed loading is used during a soils consolidation analysis.
For fully saturated flow analyses in which finite-sliding coupled pore
pressure-displacement contact is modeled using contact pairs, certain
contributions to the model's stiffness matrix are unsymmetric. Using the
unsymmetric solver can sometimes improve convergence in such cases since
Abaqus
does not automatically do so.
For fully saturated flow analyses in which heat transfer is also modeled,
the contributions to the model's stiffness matrix arising from convective heat
transfer due to pore fluid flow are unsymmetric. Using the unsymmetric solver
can sometimes improve convergence in such cases since
Abaqus
does not automatically do so.
Spurious Oscillations due to Small Time Increments
The integration procedure used in
Abaqus/Standard
for consolidation analysis introduces a relationship between the minimum usable
time increment and the element size, as shown below for fully saturated and
partially saturated flows. If time increments smaller than these values are
used, spurious oscillations may appear in the solution (except for partially
saturated cases when linear elements or modified triangular elements are used;
in these cases
Abaqus/Standard
uses a special integration scheme for the wetting liquid storage term to avoid
the problem). These nonphysical oscillations may cause problems if
pressure-sensitive plasticity is used to model the porous medium and may lead
to convergence difficulties in partially saturated analyses. If the problem
requires analysis with smaller time increments than the relationships given
below allow, a finer mesh is required. Generally there is no upper limit on the
time step except accuracy, since the integration procedure is unconditionally
stable unless nonlinearities cause convergence problems.
Fully Saturated Flow
A simple guideline that can be used for the minimum usable time increment
in the case of fully saturated flow is
where
-
is the time increment,
-
is the specific weight of the wetting liquid,
- E
-
is the Young's modulus of the soil,
-
is the permeability of the soil (see
Permeability),
-
is the magnitude of the velocity of the pore fluid,
-
is the velocity coefficient in Forchheimer's flow law
(
in the case of Darcy flow),
-
is the bulk modulus of the solid grains (see
Porous Bulk Moduli),
and
-
is a typical element dimension.
Partially Saturated Flow
In partially saturated flow cases the corresponding guideline for the
minimum time increment is
where
- s
-
is the saturation;
-
is the permeability-saturation relationship;
-
is the rate of change of saturation with respect to pore pressure (see
Sorption);
-
is the initial porosity of the material; and the other parameters are as
defined for the case of fully saturated flow.
Including a Stabilization Term to Eliminate Spurious Oscillations
For materials with very low permeability, a highly refined mesh with very small element
lengths is required to satisfy the minimum time increment in the above equations.
However, such time increment and mesh size requirements may not be feasible for
practical problems. Competing time increment requirements in a fracture analysis are
another complication.
The spurious oscillations are due to equal-order approximations for the pore pressure
and displacement equations in the finite element analysis. Pressure projections into the
strain space can be considered to eliminate the approximation inconsistency. A local
stabilized method involving polynomial projections over individual elements is
implemented. In this stabilization approach that follows Dohrmann and Bochev, a stabilization term that
penalizes pressure deviations from the consistent polynomial order supplements the local
pressure projections.
When you apply stabilization, you should ensure that the stabilized viscous fluid
volume fluxes are relatively small compared with the applied fluxes and the reaction
fluid volume fluxes due to prescribed pressure in the model.
Fixed Incrementation
If you choose fixed time incrementation, fixed time increments equal to the
size of the user-specified initial time increment, ,
will be used. Fixed incrementation is not generally recommended because the
time increments in a typical diffusion analysis can increase over several
orders of magnitude during the simulation; automatic incrementation is usually
a better choice.
Automatic Incrementation
If you choose automatic time incrementation, you must specify two (three if
heat transfer is also modeled) tolerance parameters.
The accuracy of the time integration of the flow continuity equations is
governed by the maximum wetting liquid pore pressure change,
,
allowed in an increment.
Abaqus/Standard
restricts the time increments to ensure that this value is not exceeded at any
node (except nodes with boundary conditions) during any increment in the
analysis.
If heat transfer is modeled, the accuracy of time integration is also
governed by the maximum temperature change, ,
allowed in an increment.
Abaqus/Standard
restricts the time increments to ensure that this value is not exceeded at any
node (except nodes with boundary conditions) during any increment of the
analysis.
The accuracy of the integration of the time-dependent (creep) material
behavior is governed by the maximum strain rate change allowed at any point
during an increment, ,
as described in
Rate-Dependent Plasticity: Creep and Swelling.
Ending a Transient Analysis
Transient soils analysis can be terminated by completing a specified time
period, or it can be continued until steady-state conditions are reached. By
default, the analysis will end when the given time period has been completed.
Alternatively, you can specify that the analysis will end when steady state is
reached or the time period ends, whichever comes first. When heat transfer is
not modeled, steady state is defined by a maximum permitted rate of change of
pore pressure with time: when all pore pressures are changing at less than the
user-defined rate, the analysis terminates. However, with heat transfer
included, the analysis terminates only when both the pore pressure and
temperature are changing at less than the user-defined rates.
Neglecting Creep during a Transient Analysis
You can specify that creep or viscoelastic response should be neglected
during a consolidation analysis, even if creep or viscoelastic material
properties have been defined.
Unstable Problems
Some types of analyses may develop local instabilities, such as surface
wrinkling, material instability, or local buckling. In such cases it may not be
possible to obtain a quasi-static solution, even with the aid of automatic
incrementation.
Abaqus/Standard
offers the option to stabilize this class of problems by applying damping
throughout the model in such a way that the viscous forces introduced are
sufficiently large to prevent instantaneous buckling or collapse but small
enough not to affect the behavior significantly while the problem is stable.
The available automatic stabilization schemes are described in detail in
Automatic Stabilization of Unstable Problems.
Optional Modeling of Coupled Heat Transfer
When coupled temperature–pore pressure elements are used, heat transfer is
modeled in these elements by default. However, you may optionally choose to
switch off heat transfer within these elements during some steps in the
analysis. This feature may be helpful in reducing computation time during
certain phases in the analysis when heat transfer is not an important part of
the overall physics of the problem.
Units
In coupled problems where two or more different fields are being solved, you
must be careful when choosing the units of the problem. If the choice of units
is such that the numbers generated by the equations for the different fields
differ by many orders of magnitude, the precision on some computers may be
insufficient to resolve the numerical ill-conditioning of the coupled
equations. Therefore, choose units that avoid badly conditioned matrices. For
example, consider using units of Mpascal instead of pascal for the stress
equilibrium equations to reduce the disparity between the magnitudes of the
stress equilibrium equations and the pore flow continuity equations.
Initial Conditions
Initial conditions can be applied as defined in
Initial Conditions.
Defining Initial Pore Fluid Pressures
Initial values of pore fluid pressures, ,
can be defined at the nodes.
Defining Initial Void Ratios
Initial values of the void ratio, e, can be given at
the nodes. The void ratio is defined as the ratio of the volume of voids to the
volume of solid material (see
Effective stress principle for porous media).
The evolution of void ratio is governed by the deformation of the different
phases of the material, as discussed in detail in
Constitutive behavior in a porous medium.
Defining Initial Saturation
Initial saturation values, s, can be given at the
nodes. Saturation is defined as the ratio of wetting fluid volume to void
volume (see
Effective stress principle for porous media).
Defining Initial Stresses
An initial (effective) stress field can be specified (see
Initial Conditions).
Most geotechnical problems begin from a geostatic state, which is a
steady-state equilibrium configuration of the undisturbed soil or rock body
under geostatic loading and usually includes both horizontal and vertical
components. It is important to establish these initial conditions correctly so
that the problem begins from an equilibrium state. The geostatic procedure can
be used to verify that the user-defined initial stresses are indeed in
equilibrium with the given geostatic loads and boundary conditions (see
Geostatic Stress State).
Defining Initial Temperature
Initial temperature values can be defined at the nodes.
Boundary Conditions
Boundary conditions can be applied to displacement degrees of freedom 1–6
and to pore pressure degree of freedom 8 (Boundary Conditions).
In addition, boundary conditions can also be applied to temperature degree of
freedom 11 if heat transfer is modeled using coupled temperature–pore pressure
elements. During the analysis prescribed boundary conditions can be varied by
referring to an amplitude curve (Amplitude Curves).
If no amplitude reference is given, the default variation of a boundary
condition in a coupled pore fluid diffusion/stress analysis step is as defined
in
Defining an Analysis.
If the pore pressure is prescribed with a boundary condition, fluid is
assumed to enter and leave through the node as needed to maintain the
prescribed pressure. Likewise, if the temperature is prescribed with a boundary
condition, heat is assumed to enter and leave through the node as needed to
maintain the prescribed temperature.
Loads
The following loading types can be prescribed in a coupled pore fluid
diffusion/stress analysis:
-
Concentrated nodal forces can be applied to the displacement degrees of
freedom (1–6); see
Concentrated Loads.
-
Distributed pressure forces or body forces can be applied; see
Distributed Loads.
The distributed load types available with particular elements are described in
Abaqus Elements Guide.
The magnitude and direction of gravitational loading are usually defined by
using the gravity distributed load type.
-
Pore fluid flow is controlled as described in
Pore Fluid Flow.
If heat transfer is modeled, the following types of thermal loading can also
be prescribed (Thermal Loads).
-
Concentrated heat fluxes.
-
Body fluxes and distributed surface fluxes.
-
Convective film conditions and radiation conditions; film properties can
be made a function of temperature.
Predefined Fields
The following predefined fields can be prescribed, as described in
Predefined Fields:
-
For a coupled pore fluid diffusion/stress analysis that does not model
heat transfer and uses regular pore pressure elements, temperature is not a
degree of freedom and nodal temperatures can be specified. Any difference
between the applied and initial temperatures will cause thermal strain if a
thermal expansion coefficient is given for the material (Thermal Expansion).
The specified temperature also affects temperature-dependent material
properties, if any.
-
Predefined temperature fields are not allowed in coupled pore fluid
diffusion/stress analysis that also models heat transfer. Boundary conditions
should be used instead to specify temperatures, as described earlier.
-
The values of user-defined field variables can be specified; these
values affect only field-variable-dependent material properties, if any.
Material Options
Any of the mechanical constitutive models available in
Abaqus/Standard
can be used to model the porous material.
In problems formulated in terms of total pore pressure, you must include the
density of the dry material in the material definition (see
Density).
You can use a permeability material property to define the specific weight
of the wetting liquid, ;
the permeability, , and its dependence
on the void ratio, e, and saturation,
;
and the flow velocity,
(see
Permeability).
You can define the compressibility of the solid grains and of the permeating
fluid in both fully and partially saturated flow problems (see
Elastic Behavior of Porous Materials).
If you do not specify the porous bulk moduli, the materials are assumed to be
fully incompressible.
For partially saturated flow you must define the porous medium's
absorption/exsorption behavior (see
Sorption).
Gel swelling (Swelling Gel)
and volumetric moisture swelling of the solid skeleton (Moisture Swelling)
can be included in partially saturated cases. These effects are usually
associated with modeling of moisture migration in polymeric systems rather than
with geotechnical systems.
Thermal Properties If Heat Transfer Is Modeled
In problems that model heat transfer, the thermal conductivity for either
the solid material or the permeating fluid, or more commonly for both phases,
must be defined. Only isotropic conductivity can be specified for the pore
fluid. The specific heat and density of the phases must also be defined for
transient heat transfer problems. Latent heat for the phases can be defined if
changes in internal energy due to phase changes are important. See
About Thermal Properties
for details on defining thermal properties in
Abaqus.
Examples of problems that model fully coupled heat transfer along with pore
fluid diffusion and mechanical deformation can be found in
Consolidation around a cylindrical heat source
and
Permafrost thawing–pipeline interaction.
The thermal properties can be defined separately for the solid material and
the permeating fluid.
Thermal Expansion
Thermal expansion can be defined separately for the solid material and for
the permeating fluid. In such a case you should repeat the expansion material
property, with the necessary parameters, to define the different thermal
expansion effects (see
Thermal Expansion).
Thermal expansion will be active only in a consolidation (transient) analysis.
Elements
The analysis of flow through porous media in
Abaqus/Standard
is available for plane strain, axisymmetric, and three-dimensional problems.
The modeling of coupled heat transfer effects is available only for plane
strain, axisymmetric, and three-dimensional problems. Continuum pore pressure
elements are provided for modeling fluid flow through a deforming porous medium
in a coupled pore fluid diffusion/stress analysis. These elements have pore
pressure degree of freedom 8 in addition to displacement degrees of freedom
1–3. Heat transfer through the porous medium can also be modeled using
continuum coupled temperature–pore pressure elements. These elements have
temperature degree of freedom 11 in addition to pore pressure degree of freedom
8 and displacement degrees of freedom 1–3. Stress/displacement elements can be
used in parts of the model without pore fluid flow. See
Choosing the Appropriate Element for an Analysis Type
for more information.
Output
The element output available for a coupled pore fluid diffusion/stress
analysis includes the usual mechanical quantities such as (effective) stress;
strain; energies; and the values of state, field, and user-defined variables.
In addition, the following quantities associated with pore fluid flow are
available:
- VOIDR
-
Void ratio, e.
- POR
-
Pore pressure, .
- SAT
-
Saturation, s.
- GELVR
-
Gel volume ratio, .
- FLUVR
-
Total fluid volume ratio, .
- FLVEL
-
Magnitude and components of the pore fluid effective velocity vector,
.
- FLVELM
-
Magnitude, , of the pore fluid
effective velocity vector.
- FLVELn
-
Component n of the pore fluid effective velocity
vector (n=1, 2, 3).
If heat transfer is modeled, the following element output variables
associated with heat transfer are also available:
- HFL
-
Magnitude and components of the heat flux vector.
- HFLn
-
Component n of the heat flux vector
(n=1, 2, 3).
- HFLM
-
Magnitude of the heat flux vector.
- TEMP
-
Integration point temperatures.
-
TEMPR
-
Integration point temperature rate.
- GRADT
-
Temperature gradient vector.
- GRADTn
-
Component n of the temperature gradient
(n=1,2,3).
The nodal output available includes the usual mechanical quantities such as
displacements, reaction forces, and coordinates. In addition, the following
quantities associated with pore fluid flow are available:
- CFF
-
Concentrated fluid flow at a node.
- POR
-
Pore pressure at a node.
- RVF
-
Reaction fluid volume flux due to prescribed pressure. This flux is the rate
at which fluid volume is entering or leaving the model through the node to
maintain the prescribed pressure boundary condition. A positive value of RVF indicates that fluid is entering the model.
- RVT
-
Reaction total fluid volume (computed only in a transient analysis). This
value is the time integrated value of RVF.
-
If heat transfer is modeled, the following nodal output variables associated
with heat transfer are also available:
- NT
-
Nodal point temperatures.
- RFL
-
Reaction flux values due to prescribed temperature.
- RFLn
-
Reaction flux value n at a node
(n=11, 12, …).
- CFL
-
Concentrated flux values.
- CFLn
-
Concentrated flux value n at a node
(n=11, 12, …).
All of the output variable identifiers are outlined in
Abaqus/Standard Output Variable Identifiers.
Input File Template
HEADING
…
***********************************
**
** Material definition
**
***********************************
MATERIAL, NAME=soil
Data lines to define mechanical properties of the solid material
…
EXPANSION
Data lines to define the thermal expansion coefficient of the solid grains
EXPANSION, TYPE=ISO, PORE FLUID
Data lines to define the thermal expansion coefficient of the permeating fluid
PERMEABILITY, SPECIFIC=
Data lines to define permeability, , as a function of the void ratio, e
PERMEABILITY, TYPE=SATURATION
Data lines to define the dependence of permeability on saturation,
PERMEABILITY, TYPE=VELOCITY
Data lines to define the velocity coefficient,
POROUS BULK MODULI
Data line to define the bulk moduli of the solid grains and the permeating fluid
SORPTION, TYPE=ABSORPTION
Data lines to define absorption behavior
SORPTION, TYPE=EXSORPTION
Data lines to define exsorption behavior
SORPTION, TYPE=SCANNING
Data lines to define scanning behavior (between absorption and exsorption)
GEL
Data line to define gel behavior in partially saturated flow
MOISTURE SWELLING
Data lines to define moisture swelling strain as a function of saturation
in partially saturated flow
CONDUCTIVITY
Data lines to define thermal conductivity of the solid grains if heat transfer is modeled
CONDUCTIVITY,TYPE=ISO, PORE FLUID
Data lines to define thermal conductivity of the permeating fluid if heat transfer is modeled
SPECIFIC HEAT
Data lines to define specific heat of the solid grains if transient heat transfer is modeled
SPECIFIC HEAT,PORE FLUID
Data lines to define specific heat of the permeating fluid if transient heat transfer is modeled
DENSITY
Data lines to define density of the solid grains if transient heat transfer is modeled
DENSITY,PORE FLUID
Data lines to define density of the permeating fluid if transient heat transfer is modeled
LATENT HEAT
Data lines to define latent heat of the solid grains if phase change due to temperature change
is modeled
LATENT HEAT,PORE FLUID
Data lines to define latent heat of the permeating fluid if phase change due to temperature change
is modeled
…
***********************************
**
** Boundary conditions and initial conditions
**
***********************************
BOUNDARY
Data lines to specify zero-valued boundary conditions
INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC
Data lines to specify initial stresses
INITIAL CONDITIONS, TYPE=PORE PRESSURE
Data lines to define initial values of pore fluid pressures
INITIAL CONDITIONS, TYPE=RATIO
Data lines to define initial values of the void ratio
INITIAL CONDITIONS, TYPE=SATURATION
Data lines to define initial saturation
INITIAL CONDITIONS, TYPE=TEMPERATURE
Data lines to define initial saturation
AMPLITUDE, NAME=name
Data lines to define amplitude variations
***********************************
**
** Step 1: Optional step to ensure an equilibrium
** geostatic stress field
**
***********************************
STEP
GEOSTATIC
CLOAD and/or DLOAD and/or TEMPERATURE and/or FIELD
Data lines to specify mechanical loading
FLOW and/or SFLOW and/or DFLOW and/or DSFLOW
Data lines to specify pore fluid flow
CFLUX and/or DFLUX
Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled
BOUNDARY
Data lines to specify displacements or pore pressures
END STEP
***********************************
**
** Step 2: Coupled pore diffusion/stress analysis step
**
***********************************
STEP (,NLGEOM)
** Use NLGEOM to include geometric nonlinearities
SOILS
Data line to define incrementation
CLOAD and/or DLOAD and/or DSLOAD
Data lines to specify mechanical loading
FLOW and/or SFLOW and/or DFLOW and/or DSFLOW
Data lines to specify pore fluid flow
CFLUX and/or DFLUX
Data lines to define concentrated and/or distributed heat fluxes if heat transfer is modeled
FILM
Data lines referring to film property table if heat transfer is modeled
BOUNDARY
Data lines to specify displacements, pore pressures, or temperatures
END STEP
References
- Dohrmann, C., and P. Bochev, “A Stabilized Finite Element Method for the Stokes Problem Based on Polynomial Pressure Projections,” International Journal for Numerical Methods in Fluids, vol. 46, pp. 183–201, 2004.
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