Plugin object types

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

State variables

The Discontinuous Galerkin FEM physics requires the model to contain a single concentration state variable named C. It must be a scalar variable. The physics don't have a unit by default.

Example:

StateVar{id = 'C', description = 'Concentration' , format = '1.6e', affectedNodes = 'ghost'}

Material types

The Discontinuous Galerkin 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.

Material properties

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

Property	Description	Type	Required
\(\phi\)	Porosity.	Scalar	Yes
v	Velocity.	vector	Yes
R	Reaction.	Scalar	Yes
f	Source/Sink term.	Scalar	Yes
IC	Initial Condition ( \(c_0\)).	Scalar	Yes
A	Analytic Solution ( \(c\)).	Scalar	No

1) The velocity vector is a 'n' vector, where 'n' is either 2 or 3 depending on the model dimension. It can be replaced by a scalar instead in one dimension problems.

2) The Analytic Solution is only required in convergence tests.

Example

PropertySet{
        id          = 'MatProp',
        typeName    = 'GemaPropertySet',
        description = 'Material parameters',
--
        properties  ={
        {id = 'Phi',description = 'Scalar Value',       functions = true},
        {id = 'V'  ,description = 'Advective Velocity', functions = true, dim = 1},
        {id = 'R'  ,description = 'Reactive Term',      functions = true},
        {id = 'F'  ,description = 'Source Term',        functions = true},
        {id = 'IC' ,description = 'Initial Condition',  functions = true},
        {id = 'A'  ,description = 'Analytic Solution',  functions = true},
        },
--      
        values = {
        {Phi = 'Porosity',
         V   = 'Velocity',
         R   = 'Reactive',      
         F   = 'Source',
         IC  = 'InitialCondition',
         A   = 'Analytic',
        }
  }
}

Mesh attributes

In DGFEMPhysics is necessary a topology mesh and a \(p\geq 1\) local degree approximation for hierarquical elements.

Attribute	Description	Type	Required
id	The mesh name .	String	Yes
id	Example: id = 'mesh',
typeName	Mesh used in GeMA Framework .	String	Yes
typeName	Example: typeName = 'GemaMesh.elem'
description	Description of Mesh .	String	Yes
description	Example: description = 'Regular 2D Mesh'
coordinateDim	Dimesional Space.	Integer	Yes
coordinateDim	Example: coordinateDim = 2
coordinateUnit	Unit of Lenght used in the Mesh.	Unit	No
coordinateUnit	Example: coordinateUnit = 'm'
stateVars	State Variavel associated to Physics.	State Variavel	Yes
stateVars	Example: stateVars = {'C'}
nodeData	Node List of geometrical mesh .	List	Yes
nodeData	Example: nodeData = mesh_nodes
cellProperties	Cell properties associad to mesh .	PropertySet	Yes
cellProperties	Example: cellProperties = {'MatProp'}
cellData	Element List of geometrical mesh .	List	Yes
cellData	Example: cellData = mesh_elements
hOrder	Local degree approximation \(p\) for hierarchical elements. For DGFEM physics is not necessary the flux degree, default is 1.	List	Yes
hOrder	Example: hOrder = {P = POrder,Q = 1}
boundaryEdgeData	Boundarie list of geometrical mesh.	List	Yes
boundaryEdgeData	Example: boundaryEdgeData= mesh_bnd
userghostNodes	DGFEM physics use ghost nodes .	Bool	Yes
userghostNodes	Example: useGhostNodes = true
elementRules	Lobbato Integration rule with \( 2p+1 \) points for each dimension.	Integration Rule	Yes
elementRules	Example: elementRules = {{dgquad = 2*POrder + 1}}

Example

Mesh{
        id              = 'mesh',
        typeName        = 'GemaMesh.elem',
        description     = 'Regular 2D Mesh',
        coordinateDim   =  2,
        coordinateUnit  = 'm',
        stateVars       = {'C'},
        nodeData        = mesh_nodes,
        cellProperties  = {'MatProp'},
        cellData        = mesh_elements,
        hOrder          = {P = POrder,Q = 1},
        boundaryEdgeData= mesh_bnd,
        useGhostNodes   = true,
        elementRules    = {{dgquad = 2*POrder + 1}},
}

Physics attributes

When defining a Chemical Fem Physics object, the following fields are available for usage during the definition:

Attribute	Description	Type	Required	Def. Unit
id	The physics name.	String	Yes	-
id	Example: id = 'DG_FEM'
typeName	Physics plugin name. Should be equal to 'DGFemPhysics.Galerkin'.	String	Yes	-
typeName	Required value: typeName = 'DGFemPhysics.Galerkin'
type	Type of physics object. Should be equal to 'fem'.	String	Yes	-
type	Required value: type= 'fem'
description	An optional description for this physics role in the simulation.	String	No	Empty
description	Example: description = 'Discontinuous Galerkin Method'
mesh	The mesh name.	String	Yes	-
mesh	Example: mesh = 'myMeshName'
NodsX	Number of nodes arranged in the regular mesh in the x direction.	Integer	Yes	-
NodsX	Example: NodsX = NodsX
NodsY	Number of nodes arranged in the regular mesh in the y direction.	Integer	Yes	-
NodsY	Example: NodsY = NodsY
Upwind	Numerical flow defined in the variational form. Can be choose Upwind or Lax-Friederich.	Boolean	Yes	Upwind = true
Upwind	Example: Upwind = false,
Implicit	Use of an implicit or explicit temporal integration scheme. If the RK2 / RK4 scheme is used, the boolean must be set to false.	Boolean	Yes	False
Implicit	Example: Implicit = false,
Limiter	Use of a linear degree limiter that prevents spurious oscillations in non-regular solutions.	Boolean	Yes	-
Limiter	Example: Limiter = true,
RegularMesh	As an improvement in the performance of the physics, a regular mesh can be used.	Boolean	Yes	-
RegularMesh	Example: RegularMesh = true,
boundaryConditions	Table filled with the names of the boundary conditions associated with this physics.	String table	Yes	-
boundaryConditions	Example: boundaryConditions = {'Border_Concentration','Free_Concentration'}
unitSystem	Unit of length.	Unit	Yes	-
unitSystem	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          = 'DG_FEM',
        typeName    = 'DGFemPhysics.Galerkin',
        type        = 'fem',
        description = 'Discontinuous Galerkin Method',
        mesh        = 'mesh',   
        NodsX       = NodsX,
        NodsY       = NodsY,
        Upwind      = false,
        Implicit    = false,
        Limiter     = true,
        RegularMesh = true,
        boundaryConditions = {'Border_Concentration','Free_Concentration'},
    unitSystem = { coord = 'm'},
}
}

Boundary conditions

The DGFEM physics supports Inflow, Outflow and Periodic conditions. The prescribe node concentration and prescribe concentration flow are available for 2D and 3D elements. Available boundary condition types are:

1) Inflow BC : Boundary condition type for inflow concentration. Always applied on element node/edge/face. Supported attributes are:

Attribute	Description	Type	Required	Def. Unit
C	Prescribe Edge/Face concentration.	Scalar	Yes	-

Example:

BoundaryCondition{
        id         = 'Border_Concentration',
        type       = 'Inflow Boundary Condition',
        description= 'Face/Edge Inflow Concentration',
        mesh       = 'mesh',
        properties = {{id = 'C',functions = true}},
        edgeValues = {{'LeftBnd' , 'Inflow_Boundary_Function'}}
}

2) Outflow BC : Boundary condition type for natural boundary condition in advective problems. Always applied on element edge/face. Supported attributes are:

Attribute	Description	Type	Required	Default
C	Surface Outflow Concentration	Scalar	Yes	nil

Example:

BoundaryCondition{
        id         = 'Free_Concentration',
        type       = 'Free Boundary Condition',
        description= 'Face/Edge Free Boundary Condition',
        mesh       = 'mesh',
        properties = {{id = 'C' , functions = false}},
        edgeValues = {{'RigthBnd',nil},{'BottomBnd',nil},{'TopBnd',nil}}
}

3) Periodic BC : Boundary condition type used in periodic boundary for advective problems defined on large periodic domains. Always applied on element edge/face. Supported attributes are:

Attribute	Description	Type	Required	Default
C	Periodic Boundary Condition .	Scalar	Yes	nil

Example:

BoundaryCondition{
        id         = 'Periodic_BND',
        type       = 'Periodic Boundary Condition',
        description= 'Face/Edge Periodic Boundary Condition',
        mesh       = 'mesh',
        properties = {{id = 'C' , functions = false}},
        edgeValues = {{'LeftBnd',nil},{'RigthBnd',nil},{'BottomBnd',nil},{'TopBnd',nil}}
}

Temporal Integration Scheme

The DGFEM physics use a explicit Runge-Kutta2/Runge-Kutta4 Method scheme for temporal integration.

Attribute	Description	Type	Required	Default
linearTransientMethod	Explicit Temporal Integration Scheme. RK2/RK4.	String	Yes	nil
linearTransientMethod	Example: linearTransientMethod = 'Runge-Kutta-4'

Example

local solverOptions = {
        type                  = 'transient linear',
        timeMax               = 500 * 0.002 + 1.e-8 ,           -- Total time of analysis
        timeInitIncrement     = 0.002,                           -- Initial time increment
        assemblerDofMode      = 'automatic',
        linearTransientMethod = 'Runge-Kutta-4',        
}

Constants

The DGFEM physics doesn't includes any constants in the constants.DGFEMPhysics table.

External loads

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

Derived results

The DGFEM physics doesn't supports derived results.

Supported elements

The DGFEM physics supports 1D, 2D and 3D elements. Supported elements are: dgline, dgquad and dghex.