Plugin options

Plugin object types

The Advective Diffusion FEM Physics only publishes one object type (named "Pressure") and so references to the plugin name while creating a physics object don't need to include a type name.

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State variables

The Advective Diffusion FEM physics requires the model to contain a single pressure state variable named P. It must be a scalar variable. The physics don't have a unit by default.

Example:

StateVar{id = 'Pressure', description = 'Pressure Distribution' , format = '1.6e', affectedNodes = 'both'}

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Material types

The Advective Diffusion FEM physics doesn't uses the concept of a metrial type since it doesn't feature multiple constitutive laws. The material behavior is fully described by the material properties below.

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Material properties

The following material properties are supported (required) by the Advective Diffusion Fem physics:

Property	Description	Type	Required
\(\phi\)	Porosity.	Scalar	Yes
K	Permeability Tensor.	Scalar/Vector/Matrix	Yes
F	Source/Sink term.	Scalar	Yes
P_IC	Initial Condition ( \(p_0\)).	Scalar	Yes
Q_IC	Initial Condition ( \(\mathbf{u}_0\)).	Vector	Yes
PT	Analytic Solution ( \(p_t\)).	Scalar	No
QT	Analytic Solution ( \(\mathbf{u}_t\)).	Vector	No
DQT	Analytic Solution ( \(\text{grad}(p_t)\)).	Vector	No
GPT	Analytic Solution ( \(\text{div}(\mathbf{u}_t)\)).	Scalar	No

1) The Permeability Tensor K have a 'nxn' matrix representation, where 'n' is either 2 or 3 depending on the model dimension. It can be replaced by a scalar instead in one dimension problems or vector in two dimensional problems.

2) The Analytic Solution Set (PT, QT, DQT and GPT) is only required in error/convergence tests.

Example

PropertySet{
        id          = 'MatProp',
        typeName    = 'GemaPropertySet',
        description = 'Material parameters',
--
        properties  ={
        {id = 'Phi' ,description = 'Porosity',          functions = true},      
        {id = 'K'   ,description = 'Permeability Tensor',  functions = true, dim = '2x2'},
        {id = 'F'   ,description = 'Source Term',          functions = true},
        {id = 'P_IC',description = 'Initial Pressure Distribution',functions = true},
        {id = 'Q_IC',description = 'Initial Flux Distribution',    functions = true , dim = 2},
        {id = 'PT'  ,description = 'Pressure Distribution',functions = true},
        {id = 'QT'  ,description = 'Flux Distribution',    functions = true , dim = 2},
        {id = 'DQT' ,description = 'Divergence Flux ',     functions = true},
        {id = 'GPT' ,description = 'Gradient of Pressure ',functions = true , dim = 2},
        
        },
--      
        values = {
        {
         Phi = 'Porosity', 
         K   = 'Permeability',
         F   = 'Source',
         P_IC= 'PressureIC',
         Q_IC= 'FluxIC',
         PT  = 'Pressure',
         QT  = 'Flux',
         DQT = 'DivFlux',
         GPT = 'GradPressure',
        }
  }
}

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Mesh attributes

In AdvDiffusionFEMPhysics is necessary a topology mesh and a pair ( \(p\geq 1\), \(q\geq 1\)) local degree approximations for hierarquical elements.

Attribute	Description	Type	Required
id	The mesh name .	String	Yes
	Example: id = 'mesh',
typeName	Mesh used in GeMA Framework .	String	Yes
	Example: typeName = 'GemaMesh.elem'
description	Description of Mesh .	String	Yes
	Example: description = 'Regular 2D Mesh'
coordinateDim	Dimesional Space.	Integer	Yes
	Example: coordinateDim = 2
coordinateUnit	Unit of Lenght used in the Mesh.	Unit	No
	Example: coordinateUnit = 'm'
stateVars	State Variavel associated to Physics.	State Variavel	Yes
	Example: stateVars = {'Pressure'}
nodeData	Node List of geometrical mesh .	List	Yes
	Example: nodeData = mesh_nodes
cellProperties	Cell properties associad to mesh .	PropertySet	Yes
	Example: cellProperties = {'MatProp'}
cellData	Element List of geometrical mesh .	List	Yes
	Example: cellData = mesh_elements
hOrder	Local degree approximation for hierarchical elements for pressure and velocity subspaces.	List	Yes
	Example: hOrder = {p = POrder,q = Qrder }
boundaryEdgeData	Boundarie list of geometrical mesh.	List	Yes
	Example: boundaryEdgeData= mesh_bnd
userghostNodes	AdvDiffusionFEMPhysics physics use ghost nodes .	Bool	Yes
	Example: useGhostNodes = true
elementRules	Lobbato Integration rule with \( 2\text{max}(p,q)+1 \) points for each dimension.	Integration Rule	Yes
	Example: elementRules = {{hquadp = 2* max(p,q) + 1}}

Example

Mesh{
        id              = 'mesh',
        typeName        = 'GemaMesh.elem',
        description     = 'Regular 2D Mesh',
        coordinateDim   =  2,
        coordinateUnit  = 'm',
        stateVars       = {'Pressure'},
        nodeData        = mesh_node ,
        cellProperties  = {'MatProp'},
        cellData        = mesh_elements,
        hOrder          = {P = POrder,Q = QOrder},
        boundaryEdgeData= mesh_bnd,
        useGhostNodes   = true,
        elementRules    = {{hquadp = 2.*math.max(POrder,QOrder) + 1}},
}

Physics attributes

When defining a AdvDiffusionFEMPhysics object, the following fields are available for usage during the definition:

Attribute	Description	Type	Required	Def. Unit
id	The physics name.	String	Yes	-
	Example: id = 'DG_FEM'
typeName	Physics plugin name. Should be equal to 'DGFemPhysics.Galerkin'.	String	Yes	-
	Required value: typeName = 'DGFemPhysics.Galerkin'
type	Type of physics object. Should be equal to 'fem'.	String	Yes	-
	Required value: type= 'fem'
description	An optional description for this physics role in the simulation.	String	No	Empty
	Example: description = 'Discontinuous Galerkin Method'
mesh	The mesh name.	String	Yes	-
	Example: mesh = 'myMeshName'
NodsX	Number of nodes arranged in the regular mesh in the x direction.	Integer	Yes	-
	Example: NodsX = NodsX
NodsY	Number of nodes arranged in the regular mesh in the y direction.	Integer	Yes	-
	Example: NodsY = NodsY
NodsY	Is or not a Transient Analysis?.	Bool	Yes	false
	Example: Transient = true
NodsY	Is or not a Error Analysis Test?	Bool	No	false
	Example: ErrorAnalysis = true
boundaryConditions	Table filled with the names of the boundary conditions associated with this physics.	String table	Yes	-
	Example: boundaryConditions = {'Border_Concentration','Free_Concentration'}
unitSystem	Unit of length.	Unit	Yes	-
	Example: unitSystem = { coord = 'm'}

Like other Fem physics, stateVar, property and attribute renaming fields are supported. Likewise, restricting the physics application domain to a set of cell groups, setting the desired integration rule and unit system remapping are also available. Those common optional fields are detailed at the Common Fem physics plugin options page.

Example:

PhysicalMethod{
        id           = 'Darcy_Problem',
        description  = 'Single Phase Flux in a Porous Media',
        typeName     = 'AdvDiffusionFemPhysics',
        type         = 'fem',
        mesh         = 'mesh',
        NodsX        = nx,
        NodsY        = ny,
        Transient    = true,
        ErrorAnalysis= true,
        boundaryConditions = {'Pressure_Border'},
        unitSystem = { coord = 'm'},
}

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Boundary conditions

The AdvDiffusionFEM physics supports Dirichlet boundary conditions for both pressure and velocity variavels. Available boundary condition types are:

1) Pressure BC : Boundary condition type for fixed pressure. Always applied on element node/edge/face. Supported attributes are:

Attribute	Description	Type	Required	Def. Unit
P	Prescribe Edge/Face Pressure.	Scalar	Yes	-

Example:

BoundaryCondition{
        id         = 'Pressure_Border',
        type       = 'Dirichlet Boundary Condition',
        description= 'Face/Edge Pressure Boundary Condition',
        mesh       = 'mesh',
        properties = {{id = 'P',functions = true}},
        edgeValues = {{'LeftBnd' , 'Pressure_Boundary_Function'},{'RigthBnd', 'Pressure_Boundary_Function'}}
}

2) Velocity BC : Boundary condition type for natural boundary condition for velocity. Always applied on element edge/face. Supported attributes are:

Attribute	Description	Type	Required	Default
Q	Surface Velocity	Vector	Yes	-

Example:

BoundaryCondition{
        id         = 'Flux_Border',
        type       = 'Neumann Boundary Condition',
        description= 'Face/Edge Flux Boundary Condition',
        mesh       = 'mesh',
        properties = {{id = 'Q', functions = true, dim = 2}},
        edgeValues = {{'BottomBnd','Flux_Boundary_Function'} , {'TopBnd','Flux_Boundary_Function'}}
}

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Temporal Integration Scheme

The AdvDiffusionFEMPhysics use a implicit Backward Euler Method scheme by default for temporal integration .

Attribute	Description	Type	Required	Default
linearTransientMethod	Implicit Temporal Integration Scheme. Euler.	String	Yes	nil

Example

local solverOptions = {
    type                 = 'transient linear',
    timeMax              = Tf + 1.e-15,            -- Total time of analysis
    timeInitIncrement    = dt,                     -- Initial time increment
    assemblerDofMode     = 'add fixed dofs',
}

Constants

The AdvDiffusionFEM physics doesn't includes any constants in the constants.AdvDiffusionFemPhysics table.

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External loads

The AdvDiffusionFEMPhysics doesn't supports the concept of integration with other physics through external loads.

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Derived results

The AdvDiffusionFEMPhysics doesn't supports derived results.

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Supported elements

The AdvDiffusionFEMPhysics supports 1D, 2D and 3D elements. Supported elements are: hlinep, hquadp and hhexp.