Navier-Stokes equations
<ParameterList name="Closure Model">
<ParameterList name="model_id">
...
...
...
</ParameterList> <!--model_id-->
</ParameterList> <!--Closure Model-->
- Closure Factory Type
- Type:
string
- Value:
Navier-Stokes
- Usage:
Optional
- Default:
Navier-Stokes
- Description:
Closure factory type to set source terms and material properties to solve the Navier-Stokes equation.
<SUPG_FLUX>
- Type
- Type:
string
- Value:
IncompressibleSUPGFlux
- Usage:
Required
- Description:
Closure model name to add SUPG fluxes to the incompressible Navier-Stokes equations.
1 <ParameterList name="SUPG_FLUX">
2 <Parameter name="Type" type="string" value="IncompressibleSUPGFlux"/>
3 </ParameterList> <!-- SUPG_FLUX -->
<SUPG_TAU>
- Type
- Type:
string
- Value:
IncompressibleTauSUPG
- Usage:
Required
- Description:
Closure model name to compute SUPG coefficient \(\tau\) used in the SUPG flux.
- Tau model for Navier-Stokes equations
- Type:
string
- Value:
Transient, Steady, NoSUPG
- Usage:
Optional
- Default:
Transient
- Description:
Definition of \(\tau\) used in the SUPG flux.
- SUPG coefficient for continuity equation
- Type:
double
- Value:
\([0,1]\)
- Usage:
Optional
- Default:
0.5
- Description:
Coefficient \(\beta\) in the expression of \(\tau\) in the continuity equation.
- SUPG coefficient for momentum equations
- Type:
double
- Value:
\([0,1]\)
- Usage:
Optional
- Default:
0.5
- Description:
Coefficient \(\beta\) in the expression of \(\tau\) in the momentum equations.
- Tau model for temperature equation
- Type:
string
- Value:
TempMultiDSUPGTransient, TempMultiDSUPGSteady, TempNoSUPG
- Usage:
Optional
- Default:
Transient
- Description:
Definition of \(\tau\) used in the SUPG flux.
- SUPG coefficient for temperature equation
- Type:
double
- Value:
\([0,1]\)
- Usage:
Optional
- Default:
0.5
- Description:
Coefficient \(\beta\) in the expression of \(\tau\) in the temperature equation.
1 <ParameterList name="TAU_SUPG">
2 <Parameter name="Type" type="string" value="IncompressibleTauSUPG"/>
3 <Parameter name="Tau model for Navier-Stokes equations" type="string" value="NoSUPG"/>
4 <Parameter name="SUPG coefficient for continuity equation" type="double" value="0.5"/>
5 <Parameter name="SUPG coefficient for momentum equations" type="double" value="0.5"/>
6 <Parameter name="Tau model for temperature equation" type="string" value="TempNoSUPG"/>
7 <Parameter name="SUPG coefficient for temperature equation" type="double" value="0.5"/>
8 </ParameterList> <!-- TAU_SUPG -->
Note
The definition of the SUPG coefficient is \(\tau = \beta \left( \left( \frac{2.0}{\Delta t}\right)^2 + 4.0 \frac{|\vec{u}|^2}{h^2} + 36.0 \frac{\nu^2}{h^2} \right)^\frac{-1}{2}\) for Transient where \(\beta\) is an user-input coefficient. The Steady version is obtained by removing the time step contribution \(\frac{2.0}{\Delta t}\) where \(\Delta t\) is the solver time step. When used with the temperature equation, the same definition applies but with the thermal diffusivity \(\alpha\) instead of the kinematic viscosity \(\nu\). The local mesh size is denoted by \(h\). The fluid velocity is \(\vec{u}\).
Fluid Properties
- Fluid Property Type
- Type:
string
- Value:
constant, power_law
- Usage:
Optional
- Default:
constant
- Description:
Viscosity model to use with the incompressible Navier-Stokes equations. constant option corresponds to Newtonian viscosity model with a constant viscosity. Non-Newtonian viscosity model is selected with power_law.
- Build Viscous Flux
- Type:
bool
- Value:
True or False
- Usage:
Optional
- Default:
True
- Description:
Add viscous flux to momentum equation.
- Build Temperature Equation
- Type:
bool
- Value:
True or False
- Usage:
Optional
- Default:
False
- Description:
Build the temperature equation.
- Build Buoyancy Source
- Type:
bool
- Value:
True or False
- Usage:
Optional
- Default:
False
- Description:
Add Buoyancy force to momentum equation
- Build Viscous Heat
- Type:
bool
- Value:
True or False
- Usage:
Optional
- Default:
False
- Description:
Add viscous heating to temperature equation
- Continuity Model
- Type:
string
- Value:
AC, EDAC, NCTempEDAC
- Usage:
Optional
- Default:
AC
- Description:
Continuity model to chose between artificial compressibility (AC), entropically damped AC (EDAC), and non-conservative temperature with EDAC (NCTempEDAC).
- Density
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Optional
- Default:
1.0
- Description:
Fluid density (\(\rho\)).
- Kinematic viscosity
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required
- Description:
Fluid kinematic viscosity (\(\nu\)).
- Flow consistency index
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required when setting Fluid Property Type to power_law.
- Description:
Fluid consistency index (\(K\)) for the Power-law model \(\mu = K \dot{\gamma}^{n-1} = K(2 D : D)^\frac{n-1}{2}\) where D is the strain-rate tensor and \(n\) is the flow behavior index. Shear-thinning (\(n < 1\)) and shear-thickening (\(n > 1\)).
- Flow behavior index
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required when setting Fluid Property Type to power_law.
- Description:
Fluid behavior index (\(n\)) for the Power-law model \(\mu = K \dot{\gamma}^{n-1} = K(2 D : D)^\frac{n-1}{2}\) where D is the strain-rate tensor and \(n\) is the flow behavior index. Shear-thinning (\(n < 1\)) and shear-thickening (\(n > 1\)).
- Artificial compressibility
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required.
- Description:
Artificial compressibility coefficient (\(\beta\)) in the continuity equation.
- Thermal conductivity
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required if temperature equation is enabled.
- Description:
Fluid thermal conductivity (\(\kappa\)).
- Specific heat capacity
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required if temperature equation is enabled.
- Description:
Fluid specific heat capacity (\(c_p\)).
- Expansion coefficient
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required if temperature equation and Buoyancy effects are enabled.
- Description:
Fluid thermal expansion coefficient (\(\alpha\)) to use with Buoyancy force \(\rho \alpha (T -T_{ref})\).
- Reference temperature
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required if temperature equation and Buoyancy effects are enabled.
- Description:
Fluid reference temperature (\(T_{ref}\)) to use with Buoyancy force \(\rho \alpha (T -T_{ref})\).
1 <ParameterList name="Fluid Properties">
2 <Parameter name="Continuity Model" type="string" value="AC"/>
3 <Parameter name="Build Temperature Equation" type="bool" value="true"/>
4 <Parameter name="Build Buoyancy Source" type="bool" value="true"/>
5 <Parameter name="Kinematic viscosity" type="double" value="2.081e-5"/>
6 <Parameter name="Density" type="double" value="1.225"/>
7 <Parameter name="Thermal conductivity" type="double" value="0.0262"/>
8 <Parameter name="Specific heat capacity" type="double" value="1000.0"/>
9 <Parameter name="Artificial compressibility" type="double" value="1000.0"/>
10 <Parameter name="Heat capacity ratio" type="double" value="1.0"/>
11 <Parameter name="Expansion coefficient" type="double" value="3.4722e-3"/>
12 <Parameter name="Reference temperature" type="double" value="288.0"/>
13 </ParameterList> <!-- Fluid Properties -->
Turbulence Parameters
- Turbulence Model Name
- Type:
string
- Value:
No Turbulence Model, Spalart-Allmaras, Chien K-Epsilon, Standard K-Epsilon, Realizable K-Epsilon, K-Omega, SST K-Omega, K-Tau, WALE
- Usage:
Required
- Description:
Name of the turbulence model to use.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="K-Tau"/>
Spalart-Allamras turbulence model
The Spalart–Allmaras turbulence model has no user-exposed parameters in the input file.
Standard K-Epsilon turbulence model
The Standard K-Epsilon turbulence model has no user-exposed parameters in the input file.
Realizabe K-Epsilon turbulence model
The Realizable K-Epsilon turbulence model has no user-exposed parameters in the input file.
K-Omega turbulence model
- sigma_k
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.6
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + \sigma_k \nu_t\).
- sigma_w
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent dissipation equation: \(\nu + \sigma_w \nu_t\).
- beta_star
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.09
- Usage:
Optional
- Description:
Controls the turbulent kinetic energy destruction term.
- gamma
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.52
- Usage:
Optional
- Description:
Multiplies the production term in the specific dissipation rate equation.
- beta_0
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.0708
- Usage:
Optional
- Description:
Controls the destruction term in the specific dissipation rate equation.
- sigma_d
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.125
- Usage:
Optional
- Description:
Multiplies the cross-diffusion term in the dissipation rate equation.
- Limit Production Term
- Type:
bool
- Value:
true, false
- Default:
true
- Usage:
Optional
- Description:
Limits the production term in the turbulent kinetic energy. The production term is limited to 20 times the destruction term.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="K-Omega"/>
3 <Parameter name="Limit Production Term" type="bool" value="false"/>
4 </ParameterList> <!-- Turbulence Parameters -->
K-Tau turbulence model
- sigma_k
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.6
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + \sigma_k \nu_t\) (inverse of the turbulent Prandtl number).
- sigma_w
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent dissipation equation: \(\nu + \sigma_w \nu_t\) (inverse of the turbulent Prandtl number).
- beta_star
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.09
- Usage:
Optional
- Description:
Controls the turbulent kinetic energy destruction term.
- gamma
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.52
- Usage:
Optional
- Description:
Multiplies the production term in the specific dissipation rate equation.
- beta_0
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.0708
- Usage:
Optional
- Description:
Controls the destruction term in the specific dissipation rate equation.
- sigma_d
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.125
- Usage:
Optional
- Description:
Multiplies the cross-diffusion term in the dissipation rate equation.
- sigma_t
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Multiplies the destruction term in \(\tau\) equation.
- Limit Production Term
- Type:
bool
- Value:
true, false
- Default:
true
- Usage:
Optional
- Description:
Limits the production term in the turbulent kinetic energy. The production term is limited to 10 times the destruction term.
- Limit Destruction Term
- Type:
bool
- Value:
true, false
- Default:
true
- Usage:
Optional
- Description:
Limits the destruction term in the \(\tau\) equation.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="K-Tau"/>
3 <Parameter name="Limit Production Term" type="bool" value="false"/>
4 <ParameterList name="SUPG Parameters">
5 <Parameter name="Tau model" type="string" value="Transient"/>
6 <Parameter name="SUPG coefficient" type="double" value="0.1"/>
7 </ParameterList> <!-- SUPG Parameters -->
8 </ParameterList> <!-- Turbulence Parameters -->
Chien K-Epsilon turbulence model
- Boundary Surface Area
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required
- Description:
Surface area of the boundary that has the “Friction Velocity” Scalar response.
Note
The friction velocity is computed on a wall surface area using a scalar response. The scalar response is defined in the input file by the user. The wall surface area is to be set as the Boundary Surface Area.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="Chien K-Epsilon"/>
3 <Parameter name="Boundary Surface Area" type="double" value="1.0"/>
4 </ParameterList> <!-- Turbulence Parameters -->
- Build MHD Source Term
- Type:
bool
- Value:
true, false
- Default:
false
- Usage:
Optional
- Description:
Includes MHD source term to Chien K-Epsilon model.
MHD parameters
- Inlet Surface Area
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required for MHD turbulent source term
- Description:
Surface area of the boundary that has the “Velocity” Scalar response.
Note
The velocity is computed on the inlet surface area using a scalar response. The scalar response is defined in the input file by the user. The name of the response function to compute the inlet surface area is to be set as the Inlet Surface Area.
- Characteristic Length
- Type:
double
- Value:
\((0;\infty]\)
- Usage:
Required for MHD turbulent source term
- Description:
Characteristic length of the channel to compute the Reynolds number and the Hartmann number (radius for a pipe).
- C3 Coefficient
- Type:
double
- Value:
\((0;\infty]\)
- Default:
1.9
- Usage:
Required when setting Build MHD Source Term to true.
- Description:
C3 coefficient in the MHD turbulent source term. The parameter is used to compute the MHD turbulent source term as follows: \(C_k = C_3 exp(-1 \frac{Ha^2}{Re})\) where \(Ha\) is the Hartmann number, \(Re\) is the Reynolds number.
- C4 Coefficient
- Type:
double
- Value:
\((0;\infty]\)
- Default:
1.9
- Usage:
Required when setting Build MHD Source Term to true.
- Description:
C4 coefficient in the MHD turbulent source term. The parameter is used to compute the MHD turbulent source term as follows: \(C_{\epsilon} = C_4 exp(-2 \frac{Ha^2}{Re})\) where \(Ha\) is the Hartmann number, \(Re\) is the Reynolds number.
- Streamwise Magnetic Field
- Type:
bool
- Value:
true, false
- Default:
false
- Usage:
Required for MHD turbulent source term
- Description:
The boolean that controls the source term contribution depending on the orientation of the magnetic field. If the magnetic field is streamwise, \(C_k\) is set to the parallel value. If the magnetic field is not streamwise, \(C_k\) is set to the non-parallel value. The source term is computed as follows: \(k_{mhd_{destruction}} = C_{k} \frac{\sigma}{\rho} B^2 k\) and \(\epsilon_{mhd_{destruction}} = C_{\epsilon} \frac{\sigma}{\rho} B^2 \epsilon\).
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="Chien K-Epsilon"/>
3 <Parameter name="Boundary Surface Area" type="double" value="0.3"/>
4 <Parameter name="Build MHD Source" type="bool" value="true"/>
5 <ParameterList name="MHD Parameters">
6 <Parameter name="Inlet Surface Area" type="double" value="2.0"/>
7 <Parameter name="Characteristic Length" type="double" value="1.0"/>
8 <Parameter name="C3 Coefficient" type="double" value="2.626647480520049"/>
9 <Parameter name="C4 Coefficient" type="double" value="5.071654948768135"/>
10 <Parameter name="Streamwise Magnetic Field" type="bool" value="false"/>
11 </ParameterList> <!-- MHD Parameters -->
12 </ParameterList> <!-- Turbulence Parameters -->
SST turbulence model
- sigma_k1
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.85
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + (\sigma_{k1} f + \sigma_{w1} (1. -f ) \nu_t\).
- sigma_w1
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + (\sigma_{k1} f + \sigma_{w1} (1. -f )) \nu_t\).
- sigma_k2
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.85
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + (\sigma_{k2} f + \sigma_{w2} (1. -f )) \nu_t\).
- sigma_w2
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Coefficient that multiplies the turbulent eddy viscosity \(\nu_t\) to compute the diffusivity coefficient of the turbulent kinetic energy equation: \(\nu + (\sigma_{k2} f + \sigma_{w2} (1. -f )) \nu_t\).
- beta_star
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.09
- Usage:
Optional
- Description:
Control the turbulence length scale denoted by \(A\) in the log region. \(A\) decreases as beta_star increases.
- a_1
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.31
- Usage:
Optional
- Description:
Tuning parameter used in the turbulent eddy viscosity \(\nu_t\).
- beta_1
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.075
- Usage:
Optional
- Description:
Coefficient used to compute gamma_1 that controls the blending of the production term in the dissipation rate equation.
- beta_2
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.828
- Usage:
Optional
- Description:
Coefficient used to compute gamma_2 that controls the blending of the production term in the dissipation rate equation.
- sigma_w1
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.5
- Usage:
Optional
- Description:
Coefficient used to compute gamma_1 that controls the blending of the production term in the dissipation rate equation.
- sigma_w2
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.856
- Usage:
Optional
- Description:
Tuning parmater used in the positive part of the cross diffusion term. This parameter is also used to compute gamma_2 that controls the blending of the production term in the dissipation rate equation.
- kappa
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.075
- Usage:
Optional
- Description:
Coefficient used to compute gamma_1 and gamma_2 that control the blending of the production term in the dissipation rate equation.
- Limit Production Term
- Type:
bool
- Value:
true, false
- Default:
true
- Usage:
Optional
- Description:
Limits the production term in the turbulent kinetic energy. The production term is limited to 20 times the destruction term.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="SST K-Omega"/>
3 <Parameter name="Limit Production Term" type="bool" value="true"/>
4 </ParameterList> <!-- Turbulence Parameters -->
WALE turbulence model
- C_w
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.275
- Usage:
Optional
- Description:
Value of the wall coefficient used in the WALE turbulence model to adjust dissipation in the turbulent boundary layers.
- LES Element Length
- Type:
string
- Value:
ElementLength, MeasureElementLength, MetricTensorElementLength, SingularValueElementLength
- Default:
ElementLength
- Usage:
Optional
- Description:
Method to compute the local mesh size \(\Delta\) when using WALE turbulence model.
- Element Length Method
- Type:
string
- Value:
singular_value_min, singular_value_max
- Usage:
Required when setting LES Element Length to SingularValueElementLength.
- Description:
SingularValueElementLength computes the eigenvalues of the local cell Jacobian matrix. singular_value_min returns the minimum local eigenvalue while singular_value_max returns the maximum local eigenvalue.
- C_k
- Type:
double
- Value:
\((0;\infty]\)
- Default:
0.094
- Usage:
Optional
- Description:
Value of the sub-grid kinetic energy coefficient used in the WALE turbulence model to adjust dissipation in the turbulent boundary layers \(\left(\frac{\nu_t}{C_k\Delta}\right)^2\) where \(\Delta\) is a measure of the local mesh size..
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="WALE"/>
3 <Parameter name="C_w" type="double" value="0.275"/>
4 <Parameter name="LES Element Length" type="string" value="ElementLength"/>
5 </ParameterList> <!-- Turbulence Parameters -->
SUPG Parameters
- Tau model
- Type:
string
- Value:
Steady, Transient, NoSUPG
- Usage:
Required
- Description:
Model for stabilization parameter used in SUPG numerical method.
- Tau coefficient
- Type:
double
- Value:
\([0;1]\)
- Default:
0.5
- Conflict:
None
- Usage:
Optional
- Description:
Coefficient that multiplies the stabilization parameter \(\tau\) defined with Tau model.
1 <ParameterList name="Turbulence Parameters">
2 <Parameter name="Turbulence Model Name" type="string" value="K-Tau"/>
3 <Parameter name="Limit Production Term" type="bool" value="false"/>
4 <ParameterList name="SUPG Parameters">
5 <Parameter name="Tau model" type="string" value="Transient"/>
6 <Parameter name="SUPG coefficient" type="double" value="0.1"/>
7 </ParameterList> <!-- SUPG Parameters -->
8 </ParameterList> <!-- Turbulence Parameters -->
Stability Parameters
- GradDiv Stabilization Coefficient
- Type:
double
- Value:
\([0;\infty]\)
- Usage:
Required
- Description:
Stabilization coefficient denoted by \(\gamma\) used in the Grad-Div stabilization method: \(\nabla ( \gamma \nabla \vec{u} )\).