Appendix: Initial Conditions

The run control file variables that are used to specify initial conditions for a simulation are discussed in the following subsections.

Uniform Initial Conditions

The most basic method of assigning initial conditions is to assign uniform conditions throughout the entire domain using the initialCondition variable in the run control file. An example of this is shown below for an incompressible, turbulent flow. Such a problem requires the specification of the initial state for the density, pressure, velocity and turbulence quantities. Here we assume that a k-omega turbulence model is in use. We note that for any given flow problem, additional variables that are specified beyond what is necessary will be ignored.

incompressible, turbulent, uniform initial condition

initialCondition:<rho=1.0 kg/m/m/m, p=10.0 atm, v=0.0 m/s, k=0.001, omega=1000.0>

The table below summarizes all variables for the main code that can be specified, as well as their definitions and default units. Additional variables for the various Stream modules are described in their respective chapters of this document.

Variable Specification for initialCondition

Variable	Description	Default Units
rho	Density	\(\frac{kg}{m^{3}}\)
p	Pressure	\(Pa\)
T	Temperature	\(K\)
mixture	Species mass fractions
v	Velocity	\(\frac{m}{s}\)
k	Turbulent kinetic energy	\(\frac{m^{2}}{s^{2}}\)
omega	Specific turbulent dissipation rate	\(s^{-1}\)
epsilon	Turbulent Dissipation rate	\(\frac{m^{2}}{s^{3}}\)

For compressible flows of a pure substance, two thermodynamic properties must be specified to establish the thermodynamic state for an initial condition. In Stream, this is done exclusively using the pressure and temperature. Given these two quantities, the initial conditions for other derived thermodynamic quantities such as density and specific internal energy are determined from the equation of state that is being employed in the simulation. Shown below is a typical uniform initial condition specification for a turbulent, compressible flow of a pure substance.

compressible, turbulent, pure substance, uniform initial condition

initialCondition: <p=10.0 atm, T=1000.0 K, v=1.0 m/s, k=0.001, omega=1000.0>

An initial condition for compressible, turbulent flow of a mixture material is similar specified, however one must now also provide an initial condition for the composition, which in Stream is given by the mixture species mass fractions, as shown below.

compressible, turbulent, mixture material, uniform initial condition

initialCondition: <p=10.0 atm, T=1000.0 K, v=1.0 m/s, k=0.001, omega=1000.0,
                   mixture=[H2=0.1, O2=0.1, H2O=0.8]>

The names of the species provided in the mixture specification must match those given in the .mdl file which specifies the mixture material. Species in the mixture material that are not explicitly assigned in the initial condition are given a default value of zero.

Left and Right State Initial Conditions

An initial condition with uniform left and right states may be needed for some problems. The run control file variables ql and qr are used to specify these states. The specification for ql and qr is identical to that shown above for initialCondition. The left and right initial condition states are separated by a plane whose location is specified at a midpoint by using either the variable xmid, ymid or zmid. If a midpoint is not specified in the vars file, the default specification is xmid with a value of zero in which case the y-z plane through the origin is the surface separating the left and right uniform initial condition states. If ymid is specified, then the cutting plane is an x-z plane located at the ymid value, while if zmid is specified, the cutting plane is an x-y plane located at the zmid value.

With the location of the cutting plane specified, the left state, ql, is used for all cells with a cell-center coordinate less than the specified midpoint coordinate value. The right state, qr, is used for cells with a cell-center coordinate greater than the specified midpoint coordinate value. The following example shows a typical specification for a laminar compressible flow of a mixture material.

compressible, mixture material, hydrogen/oxygen initial condition split at x=0.5

ql: <p=10.0 atm,T=1000.0 K,v=0.0 m/s,mixture=[H2=1.0]>
qr: <p=1.0 atm,T=300.0 K,v=0.0 m/s,mixture=[O2=1.0]>
xmid: 0.5

Initial Condition Regions

It may be desirable to assign different initial condition values to different regions of the computational domain. For example, one may have a pipe with a 90-degree bend. In this case, if one wished to assign an initial condition for velocity that is parallel to the walls of the pipe, one would need to be able to independently specify two different conditions. Stream provides a general capability based on geometric primitives (shapes) that allows the user to specify an arbitrary number of initial condition states over various regions of the entire domain. This specification is accomplished with the run control file variable initialConditionRegions. To illustrate the use of this feature, consider the example specification below for a compressible flow of a mixture material:

compressible, mixture material, hydrogen/oxygen initial condition by region

initialConditionRegions:<
  default=state(u=0.0m/s, p=1atm, T=298K, mixture=[N2=1.0]),
  hydrogen=state(u=0.0m/s, p=1atm, T=400K, mixture=[H2=1.0]),
  oxygen=state(u=0.0m/s, p=1atm, T=200K, mixture=[O2=1.0]),
  regions=[inBox(p1=[0,0,0], p2=[1,1,1], composition=hydrogen),
  inSphere(radius=0.1m, center=[0.5,0.5,0.5], composition=oxygen)] >

In this example, the default state is first used to assign values to every cell in the computational domain. The regions that are subsequently defined are processed in order of appearance, each overwriting the state of the cells contained inside the region. Thus, for this example, the default state is replaced by the hydrogen state for cells inside the defined box and then the cells contained inside the defined sphere are assigned the oxygen state.

The table below contains a complete listing of the variables for the main code that can specified inside initialConditionRegions. As with the other initial condition specifications above, consistent units other than the default units may be specified, in which case numeric values are converted internally to the default units for use in the code. If units are not specified for a quantity, the default units for that quantity are assumed.

Variables for Initial Condition Regions Input

Variable	Description	Default Units
rho	Density	\(\frac{kg}{m^{3}}\)
p	Pressure	\(Pa\)
T	Temperature	\(K\)
mixture	Species mass fractions
u	Velocity	\(\frac{m}{s}\)
M	Mach Number
k	Turbulent kinetic energy	\(\frac{m^{2}}{s^{2}}\)
omega	Specific turbulent dissipation rate	\(s^{-1}\)
epsilon	Turbulent Dissipation rate	\(\frac{m^{2}}{s^{3}}\)

The geometric primitives that are currently supported for initialConditionRegions are shown in the table below.

Geometric Primitives for Initial Condition Regions Input

Primitive	Description
inBox	Takes two arguments p1 and p2, which define two diagonally opposing corners of the box.
inSphere	Takes two arguments, radius, and center, which define respectively the size and location of the sphere.
inCylinder	Takes three arguments, radius which defines the cylinder radius, and the points p1 and p2, which define the endpoints of the axis of the cylinder.
inCone	Takes four arguments, p1 and p2 which define the endpoints of the axis of the cone, and r1 and r2 which define the radius of the cone at the locations p1 and p2, respectively.
leftPlane	Takes two arguments, point, which defines a point on the plane, and normal, which defines a vector normal to the plane. The region included in this primitive is the semi-infinite region on the side of the plane away from the direction of the specified normal.

Interpolated Initial Conditions

Often after running a simulation for a particular geometry, one decides that a refined mesh is required. In this case, one can use the solution obtained from the old simulation as an initial guess for the new simulation by using the interpolateInitialConditions variable in the run control file as follows:

puT interpolated initial condition

interpolateInitialConditions: put.1000_cavity

When running a simulation, if the user has included the variable put in the plot_output line of the run control file, Stream writes out what is known as the puT file in the output directory along with other output files according to the value of the run control file variable plot_freq. In the above example, the value 1000 indicates the time-step number at which data was written in the previous simulation, and the name cavity is the case name of the previous simulation. The puT file (the name is an acronym for pressure(p), velocity(u), and temperature(T)) contains all the basic flow variable information associated with the run, including velocity, pressure, temperature, species, and turbulence data if the simulation is employing a turbulence model.

If one is running a new case in which the type of simulation remains constant but the grid has changed, then one simply needs to select any puT file from a previous run and use it in the above manner. Note that the name of the puT file specified in the new run must include the complete path to the file. However, if the simulation type changes between runs, there are a few special cases of interest which require additional input, the details of which follow:

• Consider the case of using a puT file (compressible or incompressible) to restart to an incompressible simulation. The density is not stored in a puT file, and there is no equation of state for an incompressible flow; therefore, the variable initialCondition must be used to provide the value for density. All required values for an incompressible flow simulation (density, velocity, and pressure) must be specified in initialCondition, but only the value of density will be taken from this variable. All other values will be obtained from the file specified by interpolateInitialConditions.

• For using an incompressible puT file as an initial condition to a new compressible run, one must use the variable initialCondition to provide the value for the initial temperature. This is because the value for temperature in any incompressible puT files is zero, which is non-physical for compressible flow. A complete specification for initialCondition appropriate for compressible flow must be given, but only the temperature value will be used.