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  • Goma User Manual

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  • Goma User Manual

Section Navigation

  • Introduction
  • Background Information
  • Code Structure and I/O
  • Problem Description (Input File)
    • File Specification
      • FEM File
      • Output EXODUS II File
      • Guess File
      • SOLN File
      • Write Intermediate Results
      • Write Initial Solution
      • External Decomposition
      • Decomposition Type
    • General Specifications
      • Output Level
      • Debug
      • Number of Jacobian File Dumps
      • Initial Guess
      • Initialize
      • External Field
      • Export Field
      • External Pixel Field
      • Pressure Datum
      • Anneal Mesh on Output
    • Time Integration Specifications
      • Time Integration
      • delta_t
      • Maximum Number of Time Steps
      • Maximum Time
      • Minimum Time Step
      • Maximum Time Step
      • Minimum Resolved Time Step
      • Courant Number Limit
      • Time Step Parameter
      • Time Step Error
      • Printing Frequency
      • Fix Frequency
      • Second Frequency Time
      • Initial Time
    • Level Set Specifications
      • Fill Subcycle
      • Fill Weight Function
      • Level Set Interface Tracking
      • Level Set Semi_Lagrange
      • Level Set Subgrid Integration Depth
      • Level Set Subelement Integration
      • Level Set Adaptive Integration
      • Level Set Adaptive Order
      • Overlap Quadrature Points
      • Level Set PSPP Filtering
      • Level Set Length Scale
      • Level Set Initialize
      • Level Set Adaptive Mesh
      • Level Set Adapt Width
      • Level Set Adapt Inner Size
      • Level Set Adapt Outer Size
      • Level Set Adapt Frequency
      • Level Set Initialization Method
      • Level Set Periodic Planes
      • Level Set Control Width
      • Level Set Timestep Control
      • Level Set Renormalization Tolerance
      • Level Set Renormalization Method
      • Level Set Renormalization Frequency
      • Restart Time Integration After Renormalization
      • Level Set Reconstruction Method
      • Level Set Contact Extension
      • Level Set Slave Surface
      • Ignore Level Set Dependencies
      • Force Initial Level Set Renormalization
    • Phase Field Specifications
      • Number of Phase Functions
      • Phase Function Slave Surface
      • Phase Function Initialization Method
      • Phase Function Renormalization Tolerance
      • Phase Function Renormalization Method
    • Continuation Specifications
    • Hunting Specifications
    • Augmenting Conditions Specifications
    • Solver Specifications
      • Total Number of Matrices
      • Solution Algorithm
      • Matrix Storage Format
      • Stratimikos File
      • Preconditioner
      • Matrix Subdomain Solver
      • Matrix Scaling
      • Matrix Residual Norm Type
      • Matrix Output Type
      • Matrix Factorization Reuse
      • Matrix Graph Fillin
      • Matrix Factorization Overlap
      • Matrix Overlap Type
      • Matrix Auxiliary Vector
      • Matrix Drop Tolerance
      • Matrix Polynomial Order
      • Matrix Reorder
      • Matrix Factorization Save
      • Matrix ILUT Fill Factor
      • Matrix RILU Relax Factor
      • Matrix BILU Threshold
      • Matrix Relative Threshold
      • Matrix Absolute Threshold
      • Size of Krylov Subspace
      • Orthogonalization
      • Maximum Linear Solve Iterations
      • Number of Newton Iterations
      • Modified Newton Tolerance
      • Jacobian Reform Time Stride
      • Newton Correction Factor
      • Normalized Residual Tolerance
      • Normalized Correction Tolerance
      • Residual Ratio Tolerance
      • Pressure Stabilization
      • Pressure Stabilization Scaling
      • Linear Stability
      • Filter Concentration
      • Disable Viscosity Sensitivities
    • Eigensolver Specifications
    • Electromagnetic Problem Properties
      • EM Frequency
      • EM Free Space Permittivity
      • EM Free Space Permeability
    • Boundary Condition Specifications
      • Number of BC
      • Category 1: Any Equation
      • Category 2: Mesh Equations
      • Category 3: Real Solid Equations
      • Category 4: Fluid Momentum Equations
      • Category 5: Energy Equations
      • Category 6: Mass Equations
      • Category 7: Continuity Equation
      • Category 8: Porous Equations
      • Category 9: Stress Equations
      • Category 10: Gradient Equations
      • Category 11: Shear Rate Equation
      • Category 12: Fill Equation
      • Category 13: Potential Equation
      • Category 14: Fluid-Solid Interaction
      • Category 15: Level Set Interfaces
      • Category 16: Shell Equations
      • Category 17: Acoustic Equations
      • END OF BC
    • Rotation Specifications
      • Rotation Specifications
      • ROT SURFACE
      • ROT EDGE
      • ROT VERTEX
      • END OF ROT
    • Problem Description
      • Number of Materials
      • MAT
      • Coordinate System
      • Element Mapping
      • Mesh Motion
      • Number of Bulk Species
      • Material is Nondilute
      • Number of Bulk Species Equations
      • Default Material Species Type
      • Number of Viscoelastic Modes
      • Number of Matrices
      • MATRIX
      • Disable time step control
      • Normalized Residual Tolerance
      • Number of EQ
      • energy
      • momentum
      • pmomentum
      • stress
      • species_bulk
      • mesh
      • mom_solid
      • continuity
      • fill
      • lagr_mult_1, lagr_mult_2, lagr_mult_3
      • level set
      • voltage
      • efield
      • enorm
      • shear_rate
      • vort_dir
      • vort_lambda
      • porous_sat
      • porous_unsat
      • porous_liq
      • porous_gas
      • porous_deform
      • porous_energy
      • surf_charge
      • shell_tension
      • shell_curvature
      • shell_angle
      • shell_diff_flux
      • shell_diff_curv
      • shell_normal
      • shell_surf_curv
      • shell_surf_div_v
      • grad_v_dot_n1, grad_v_dot_n2, grad_v_dot_n3
      • n_dot_curl_v
      • acous_preal
      • acous_pimag
      • acous_reyn_stress
      • potential1
      • potential2
      • lubp
      • lubp_2
      • shell_energy
      • shell_filmp
      • shell_filmh
      • shell_partc
      • shell_sat_closed
      • shell_sat_gasn
      • shell_sat_open
      • shell_sat_open_2
      • shell_deltah
      • moment
      • END OF EQ
      • END OF MAT
    • Post Processing Specifications
      • Stream Function
      • Streamwise Normal Stress
      • Cross-Stream Shear Rate
      • Mean Shear Rate
      • Pressure Contours
      • Fill Contours
      • Concentration Contours
      • Stress Contours
      • First Invariant of Strain
      • Second Invariant of Strain
      • Third Invariant of Strain
      • Velocity Divergence
      • Particle Velocity Divergence
      • Total Velocity Divergence
      • Electric Field
      • Electric Field Magnitude
      • Enormsq Field
      • Enormsq Field Norm
      • Viscosity
      • Density
      • Lame MU
      • Lame LAMBDA
      • Von Mises Strain
      • Von Mises Stress
      • Navier Stokes Residuals
      • Moving Mesh Residuals
      • Mass Diffusion Vectors
      • Diffusive Mass Flux Vectors
      • Mass Fluxlines
      • Energy Conduction Vectors
      • Energy Fluxlines
      • Time Derivatives
      • Mesh Stress Tensor
      • Real Solid Stress Tensor
      • Mesh Strain Tensor
      • Viscoplastic Def_Grad Tensor
      • Lagrangian Convection
      • Normal and Tangent Vectors
      • Error ZZ Velocity
      • Error ZZ Heat Flux
      • Error ZZ Pressure
      • User-Defined Post Processing
      • Porous Saturation
      • Total Density of Solvents in Porous Media
      • Density of Solvents in Gas Phase in Porous Media
      • Density of Liquid Phase in Porous Media
      • Gas Phase Darcy Velocity in Porous Media
      • Liquid Phase Darcy Velocity in Porous Media
      • Capillary Pressure in Porous Media
      • Grid Peclet Number in Porous Media
      • SUPG Velocity in Porous Media
      • Vorticity Vector
      • Map Conf Stress
    • Post Processing Fluxes and Data
      • Post Processing Fluxes
      • FLUX
      • END OF FLUX
      • Post Processing Data
      • DATA
      • END OF DATA
      • Post Processing Flux Sensitivities
      • FLUX_SENS
      • END OF FLUX_SENS
      • Post Processing Data Sensitivities
      • DATA_SENS
      • END OF DATA_SENS
    • Post Processing Particle Traces
      • Post Processing Particle Traces
      • PARTICLE
      • END OF PARTICLES
    • Volumetric Integration
      • Post Processing Volumetric Integration
      • VOLUME_INT
      • END OF VOLUME_INT
    • Average post processing
      • Post Processing Averages
      • AVERAGE
      • END OF AVERAGES
  • Material Files
    • Physical Properties
      • Default Database
      • Density
    • Mechanical Properties and Constitutive Equations
      • Solid Constitutive Equation
      • Plasticity Equation
      • Convective Lagrangian Velocity
      • Lame MU
      • Lame LAMBDA
      • Stress Free Solvent Vol Frac
      • Solid Thermal Expansion
      • Solid Reference Temperature
      • Plastic Viscosity
      • EVP Yield Stress
      • Polymer Viscosity
      • Pseudo-Solid Lame MU
      • Pseudo-Solid Lame LAMBDA
      • Liquid Constitutive Equation
      • Viscosity
      • Low Rate Viscosity
      • Power Law Exponent
      • High Rate Viscosity
      • Time Constant
      • Aexp
      • Thermal Exponent
      • Thermal WLF Constant2
      • Yield Stress
      • Yield Exponent
      • Suspension Maximum Packing
      • Suspension Species Number
      • Cure Gel Point
      • Cure A Exponent
      • Cure B Exponent
      • Cure Species Number
      • Unreacted Gel Temperature
      • Polymer Constitutive Equation
      • PTT Form
      • Polymer Stress Formulation
      • Polymer Weight Function
      • Polymer Shift Function
      • Polymer Weighting
      • Polymer Shock Capturing
      • Discontinuous Jacobian Formulation
      • Adaptive Viscosity Scaling
      • Polymer Viscosity
      • Polymer Time Constant
      • Polymer Yield Stress
      • Mobility Parameter
      • PTT Xi parameter
      • PTT Epsilon parameter
      • Surface Tension
      • Second Level Set Conductivity
      • Second Level Set Density
      • Second Level Set Heat Capacity
      • Second Level Set Momentum Source
      • Second Level Set Viscosity
      • Shell Bending Stiffness
    • Thermal Properties
      • Heat Flux Model
      • Conductivity
      • Heat Capacity
      • Volume Expansion
      • Reference Temperature
      • Liquidus Temperature
      • Solidus Temperature
      • Energy Weight Function
    • Electrical Properties
      • Electrical Conductivity
      • Electrical Permittivity
      • Magnetic Permeability
      • Electromagnetic Incident Wave
      • Extinction Index
      • Refractive Index
    • Microstructure Properties
      • Media Type
      • Porosity
      • Permeability
      • Liquid phase compressibility
      • Liquid phase reference pressure
      • Flowing Liquid Viscosity
      • Inertia Coefficient
      • Capillary Network Stress
      • Rel Gas Permeability
      • Rel Liq Permeability
      • Saturation
      • Porous Weight Function
      • Porous Mass Lumping
      • Porous Diffusion Constitutive Equation
      • Porous Gas Diffusivity
      • Porous Latent Heat Vaporization
      • Porous Latent Heat Fusion
      • Porous Vapor Pressure
      • Porous Liquid Volume Expansion
      • Porous Gas Constants
    • Species Properties
      • Number of Species
      • Diffusion Constitutive Equation
      • Species Weight Function
      • Number of Chemical Reactions
      • Reaction Rate
      • Thermodynamic Potential
      • Interfacial Area
      • Butler_Volmer_j
      • Butler_Volmer_ij
      • Solution Temperature
      • Porosity
      • Diffusivity
      • Shear Rate Diffusivity
      • Viscosity Diffusivity
      • Curvature Diffusivity
      • Fickian Diffusivity
      • Gravity-based Diffusivity
      • Q Tensor Diffusivity
      • Species Time Integration
      • Advective Scaling
      • Latent Heat Vaporization
      • Latent Heat Fusion
      • Vapor Pressure
      • Species Volume Expansion
      • Standard State Chemical Potential
      • Pure Species Chemical Potential
      • Chemical Potential
      • Reference Concentration
      • Molecular Weight
      • Specific Volume
      • Molar Volume
      • Charge Number
      • Non-condensable Molecular Weight
      • Non-volatile Molar Volume
      • Non-volatile Specific Volume
      • Flory-Huggins parameters
    • Source Terms
      • Navier-Stokes Source
      • Solid Body Source
      • Mass Source
      • Heat Source
      • Species Source
      • Current Source
      • Moment Source
      • Initialize
    • Shell Equation Properties and Models
      • Upper Height Function Constants
      • Lower Height Function Constants
      • Upper Velocity Function Constants
      • Lower Velocity Function Constants
      • Upper Contact Angle
      • Lower Contact Angle
      • Lubrication Fluid Source
      • Lubrication Momentum Source
      • Turbulent Lubrication Mode
      • Shell Energy Source QCONV
      • Shell Energy Source Sliding Contact
      • Shell Energy Source Viscous Dissipation
      • Shell Energy Source External
      • FSI Deformation Model
      • Film Evaporation Model
      • Disjoining Pressure Model
      • Diffusion Coefficient Model
      • Porous Shell Radius
      • Porous Shell Height
      • Porous Shell Closed Porosity
      • Porous Shell Closed Gas Pressure
      • Porous Shell Atmospheric Pressure
      • Porous Shell Reference Pressure
      • Porous Shell Cross Permeability
      • Porous Shell Gas Diffusivity
      • Porous Shell Gas Temperature Constant
      • Porous Shell Henrys Law Constant
    • Moment Properties
  • References
  • Appendix 1: Goma Documentation Lists

Navier-Stokes Source#

Navier-Stokes Source = {model_name} {float_list} [varies]

Description / Usage#

This required card is used to specify the model for the fluid momentum source term vector in the Navier-Stokes equations. Gravitational and buoyancy effects often enter through this card.

Definitions of the input parameters are as follows:

{model_name}

Name of the fluid momentum source term model for the Navier-Stokes equations. The model name will be one of the following strings:

  • CONSTANT

  • USER

  • BOUSS

  • BOUSS_JXB

  • BOUSSINESQ

  • FILL

  • PHASE_FUNCTION

  • SUSPEND

  • SUSPENSION

  • VARIABLE_DENSITY

  • EHD_POLARIZATION

  • ACOUSTIC

{float_list}

One or more floating point numbers (<float1> through <floatn>); the specific number is determined by the selection for {model _name}.

Choices for {model_name} and the accompanying parameter list are given below; additional user guidance can be found in the Technical Discussion section following the Examples.

CONSTANT <float1> <float2> <float3>

For a constant source model where the body force [M/L2t2] for this material does not vary. The {float_list} contains three values to specify the three components of the body force vector, where:

  • <float1> - a0, x-component of body force

  • <float2> - a1, y-component of body force

  • <float3> - a2, z-component of body force

Note this source term has units of force/volume or, equivalently, density times acceleration. This is not true of all source term models.

USER <float1>… <floatn>

For a user-defined model; the set of {float_list} parameters are those required by specifications in the function usr_momentum_source.

BOUSS <float1> <float2> <float3>

This option specifies a generalized Boussinesq source where the density is linearly dependent upon temperature and concentration (species). The individual components of the constant acceleration vector a0 are read from the three entries in the {float_list}:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

Unlike the CONSTANT model the units for these vector components are (L/t2), that is, they are true acceleration values. See the technical discussion below for the other parameters needed for this model.

BOUSSINESQ <float1> <float2> <float3>

This model prescribes a body force source term that is very similar to the BOUSS option except that the hydrostatic component is eliminated. The individual components of the constant acceleration vector a0 are read from the three entries in the {float_list}:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

BOUSS_JXB <float1> <float2> <float3> <float4>

This source model option specifies a generalized Boussinesq source term, as above, but also including Lorentz (electromagnetic) forces. The constant acceleration vector a0 is again specified using the first three constants that appear in the {float_list}. The fourth constant of the list is a Lorentz scaling factor (lsf). It may be used to scale the Lorentz term; see the Technical Discussion for more information.

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

  • <float4> - lsf, Lorentz scaling factor.

EHD_POLARIZATION <float1>

This source model option can be used to add on a dielectrophoretic force to the Navier-Stokes equations of the form ρE • ∇E ., where E is the electric field vector and ρ is a user-supplied constant with dimensions [q2T2/ L3]. This term requires the vector efield equation and the voltage equation to be solved simultaneously with the fluid-phase momentum equation. cf. EQ card definitions.

  • <float1> is the constant ρ as described above

FILL <float1> <float2> <float3>

This model prescribes the body force momentum source term for problems making use of volume-of-fluid interface tracking. The card prescribes a constant acceleration vector, usually the gravitational acceleration [L/T2]. It can only be employed when using the FILL density model.

The individual components of the constant acceleration vector a0 are read from the three entries after the FILL string in the {float_list}, where:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

LEVEL_SET <float1> <float2> <float3>

This model prescribes the body force momentum source term for problems making use of level set interface tracking. The card prescribes a constant acceleration vector, usually the gravitational acceleration [L/T2]. It can only be used when also using the LEVEL_SET density model.

The individual components of the constant acceleration vector a0 are read from the three entries after the LEVEL_SET string in the {float_list}, where:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

PHASE_FUNCTION <float1> <float2> <float3>

This model prescribes the body force momentum source term for problems making use of phase function interface tracking (a generalization of the level set method for more than two phases). The card prescribes a constant acceleration vector, usually the gravitational acceleration [L/T2]. It can only be used when also using the CONST_PHASE_FUNCTION density model.

The individual components of the constant acceleration vector a0 are read from the three entries after the PHASE_FUNCTION string in the {float_list}, where:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

VARIABLE_DENSITY <float1> <float2> <float3>

This model sets the momentum body force source term for problems that employed the SOLVENT_POLYMER density model. The three parameters on the card are the individual components of a constant acceleration vector (usually due to gravity):

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

The actual body force applied is the local density computed from the SOLVENT_POLYMER model multiplied by this vector.

SUSPEND <float1> <float2> <float3> <float4>

This model prescribes a body force source term for suspensions where the carrier fluid and the particle phase have different densities. Four parameters must be set for this card using the {float_list}. The first three parameters (<float1>. <float2>, and <float3>) are the three components of the gravity vector. The fourth parameter (<float4>) is a reference concentration, Cref.

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

  • <float4> - Cref, reference concentration

This source model requires a SUSPENSION density model be specified for the Density model. The density parameters on this card are used in this source model. If this momentum source term is used in conjunction with the HYDRODYNAMIC mass flux option, only one species can use the HYDRO diffusivity model.

SUSPENSION <float1> <float2> <float3> <float4>

This model is identical to the SUSPEND momentum source model (above), with the addition of mass source terms in the continuity equation due to transport of species with different densities.

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

  • <float4> - Cref, reference concentration

This source model requires a SUSPENSION density model be specified for the Density model. The density parameters in this card are used in this source model. If this momentum source term is used in conjunction with the HYDRODYNAMIC mass flux option, only one species can use the HYDRO diffusivity model.

ACOUSTIC <float1> <float2> <float3> <float4>

This model includes the gradient of the acoustic Reynolds stress as a momentum source in addition to the usual gravitational source terms. The {float_list} contains four values to specify the three components of the body force vector plus a Reynolds stress gradient multiplier, where:

  • <float1> - a0, x-component of acceleration

  • <float2> - a1, y-component of acceleration

  • <float3> - a2, z-component of acceleration

  • <float4> - acoustic term multiplier

WARNING: Make sure the equation term multipliers for the source terms are set to unity.

Examples#

Following are some sample input cards:

Navier-Stokes Source = BOUSS 0. -980. 0.
Navier-Stokes Source = LEVEL_SET 0. -980. 0.

Technical Discussion#

This section contains user guidance, and theoretical background when appropriate, for each of the options for Navier-Stokes Source models.

CONSTANT

A constant source model has a body force [M/L2t2] for the material which does not vary. A common usage of this model is for an incompressible fluid in a uniform gravitational field. Note that the source term has units of force/volume or, equivalently, density times acceleration. Thus, the values in the {float_list} would need to be specified as the product of the fluid density and the acceleration of gravity.

USER

This model option provides a means for the user to create a custom Navier-Stokes Source model for his/her special problem. The parameters of the model will be used by the source term model defined in the usr_momentum_source function. The {float_list} parameters are passed to this function as a one dimensional array named param in the order in which they appear on the card. The model must return a body force (force/volume) vector. An example use of this specification might be to construct a Coriolis acceleration term for a fluid in a rotating reference frame.

BOUSS

A generalized Boussinesq source term has the form where the linear dependence of the density upon temperature and concentration is used for this source term only. Density is assumed constant wherever else it happens to appear in the governing conservation equations. The density has been expanded in a Taylor series to first order about a reference state that is chosen so that, at the reference temperature T0 and concentration C0 the density is ρ0. The reference density is taken from the CONSTANT density model specified earlier in the material file on the Density card. The coefficient of thermal expansion of the fluid, β, is taken from the Volume Expansion card specified under Thermal Properties for this material. βc, is taken from the Species Volume Expansion card specified under species Properties for this material. The individual components of the constant acceleration vector a0 are the three entries of the {float_list} after the BOUSS string.

Note that this BOUSS form includes the body force of the reference state so that a motionless fluid at a uniform temperature of T0 must be sustained by a linearly varying pressure field. Below, an alternative means for solving Boussinesq problems is presented that eliminates the constant hydrostatic feature of the BOUSS formulation. T0 is set on the Reference Temperature card.

../../_images/463_goma_physics.png

BOUSSINESQ

This model prescribes a body force source term that is very similar to the BOUSS option except that the hydrostatic component is eliminated. Thus the form so that a no-flow solution with uniform temperature and concentration may be maintained by a constant pressure field. This form for the Boussinesq equations can sometimes provide a more well-conditioned equation system for weakly buoyant flows. Note again the implied convention that the coefficient of thermal expansion is positive when the density decreases with increasing temperature. That is, The same convention holds for the coefficient of solutal expansion. A source of confusion with buoyancy problems is that many sign conventions are applied. In addition to the convention for β, another possible source of confusion arises from a negative sign on the gravitational acceleration vector in many coordinate systems. That is, is a frequent choice for the constant acceleration for a twodimensional problem posed in Cartesian coordinates.T0 is set on the Reference Temperature card.

../../_images/464_goma_physics.png
../../_images/465_goma_physics.png
../../_images/466_goma_physics.png

BOUSS_JXB

This model is a generalized Boussinesq source term, as above, but also includes Lorentz forces. That is, the source term has the form where, in addition to the term defined for the BOUSS option, there is an added term due to electromagnetic forces acting upon a conducting fluid. The constant acceleration vector a0 is again specified using the first three constants that appear in the {float_list}. The fourth constant, lsf, may be used to scale the Lorentz term as desired (for example, lsf = 1 using a Gaussian system of units, or lsf = 1/c using a rationalized MKSA system of units).

The two vector fields J, the current flux, and B, the magnetic induction, must be supplied to Goma in order to activate this option. At present, these fields must be supplied with the External Field cards, which provide the specific names of nodal variable fields in the EXODUS II files from which the fields are read. The three components of the J field must be called JX_REAL, JY_REAL, and JZ_REAL. Likewise the B field components must be called BX_REAL, BY_REAL, and BZ_REAL. These names are the default names coming from the electromagnetics code TORO II (Gartling, 1996). Because of the different coordinate convention when using cylindrical components, the fields have been made compatible with those arising from TORO II. It is the interface with TORO that also makes the Lorentz scaling (lsf) necessary so that the fixed set of units in TORO (MKS) can be adjusted to the userselected units in Goma. T0 is set on the Reference Temperature card.

../../_images/467_goma_physics.png

FILL

The body force applied when using this momentum source model is as follows: where ρ1 and ρ0 are the phase densities obtained from the FILL density card, F is the value of the fill color function and the constant acceleration vector a0 is read from the three entries in the {float_list} of the FILL momentum source card.

../../_images/468_goma_physics.png

LEVEL_SET

The body force applied when this model is used is given by the following function of the level set function value, φ: where is a smooth Heaviside function, φ is the value of the level set function, ρ+ and ρ- are the positive and negative phase densities, and α is the density transition length scale. The latter three parameters are obtained from the LEVEL_SET density card. The individual components of the constant acceleration vector a0 are three float parameters appearing in the {float_list} following the LEVEL_SET model name.

../../_images/469_goma_physics.png

PHASE_FUNCTION

The body force applied when this model is specified is identical in concept to that applied with the above LEVEL_SET model. The parameters on this card are simply the components of a constant acceleration vector (gravity in most applications). This card must be used in conjunction with the CONST_PHASE_FUNCTION density model because the actual body force vector is obtained by multiplying the acceleration vector specified with this card by the density computed by that latter model. Again this is identical in concept to the LEVEL_SET body force source model.

SUSPEND

This model prescribes a body force source term that is for simulating suspensions when the suspending fluid and particle phase have different densities. The difference in density can lead to buoyancy driven flow. The form of the source term is given below: where Ci is the solid particle volume fraction tracked using a species equation with a HYDRO diffusion model. Four parameters must be set for this card using the {float_list}. The first three parameters are the three components of the gravity vector. The fourth parameter is a reference concentration, Cref. The density values are those entered by a SUSPENSION density model on the Density card.

NOTE: If this momentum source term is used in conjunction with the HYDRODYNAMIC mass flux option, only one species can use the HYDRO diffusivity model.

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SUSPENSION

This model is identical to the SUSPEND momentum source model in terms of the assembly of the momentum equation. However, this model creates a source term that gets applied during the assembly of the continuity equation due to transport of species with different densities. The suspension density models meet the definition of a locally variable density model, so the Lagrangian derivative of their densities can be represented as a divergence of mass flux. This term is integrated by parts and this particle phase flux is included separately as a source term for the continuity equation.

ACOUSTIC

This model contains the usual gravitational source terms in the CONSTANT model plus the gradient of the acoustic Reynolds stress as an additional momentum source. The acous_reyn_stress equation must be present to use this source model.

The user should take special note of the distinction between the different use of the {float_list} for CONSTANT body force problems and for the various buoyant options. For the CONSTANT model, the three components are the force per unit volume, and the user must remember to include density specifically if it is desired. For the buoyancy options, the three components are acceleration, and the density value specified on a previous card is automatically used by Goma to construct the overall body force source term. This is also true for the FILL, LEVEL_SET, SUSPENSION and SUSPEND momentum source models.

The user must also take special care that the source term multipliers for the momentum equation are set to unity.

References#

Gartling, D. K., TORO II - A Finite Element Computer Program for Nonlinear Quasi- Static Problems in Electromagnetics, Part I - Theoretical Background, SAND95-2472, Sandia National Laboratories, Albuquerque, NM, May 1996.

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