Specifying a geometry

The following inputs are defined using the mfix prefix.

Description

Type

Default

geometry

Specify the simulation geometry.

box - predefined box geometry
cylinder - predefined cylinder geometry
generic - user-defined geometry
csg - use Constructive Solid Geometry file
stl - use Standard Triangle Language file

If left undefined, then the system should be fully periodic, or planar regions should be used to enclose the domain.

String

‘’

levelset__refinement

Refinement factor of levelset resolution relative to level 0 resolution

Int

1

Most simulations require a user to specify some kind of geometry. For example, the geometry could be a basic cylinder used to model flow inside a pipe, or it may be an irregularly shaped solid to study external flow around a bluff body, or the geometry may be the proposed design of a complex, multi-stage chemical reactor undergoing performance assessment. In the following sections, several options for specifying a geometry are described.

Caution

Any domain extent that is not periodic or defined as a Dirichlet or Neumann boundary condition must be fully covered. To state this another way, if a domain extent is not periodic or an inflow or outflow boundary condition, then it should be excluded from (outside of) the domain by the embedded boundary geometry.

Predefined geometries

The mfix.geometry input is used to choose one of the basic predefined geometries, or to select the option to use a user-defined geometry constructed from native AMReX implicit functions.

`box` geometry

The following inputs are defined using the box prefix.

	Description	Type	Default
Lo	Low corner of the embedded boundary box	Reals	`prob_lo`
Hi	High corner of the embedded boundary box	Reals	`prob_hi`
internal_flow	Flag to indicate that flow is inside the box.	Bool	true
offset	Shift low side box walls by `+offset` and high side walls by `-offset`. An example use of this input would be to define a a box with `Lo` and `Hi` equal to `prob_lo` and `prob_hi`. The offset slightly shrinks the `box` so the walls do not coincide with the domain extents.	Real	1.0e-15

`box` limitations

The predefined EB box geometry has several limitations:

The sides of the box should not coincide with the domain extents.
A box is aligned with the coordinate axes and cannot be rotated in any direction.
There can only be one box. Multiple boxes cannot be defined and combined.

`box` example

The domain is a \(2 \times 2 \times 8\) cuboid where X and Y span \([-1,1]\), and Z spans \([0,8]\). A \(10\) meter long embedded boundary box with a \(1 \times 1\) cross-section runs lengthwise through the domain, centered about the Z axis. The EB is shifted down the Z axis so that there is a \(-1\) meter overhang on the low and high Z domain faces.

Listing 1 Snippet of intpus for predefined EB box geometry example. This is not a complete input file.

# Define periodicity and domain extents
# -------------------------------------------------------------
geometry.coord_sys   =  0            # Cartesian coordinates
geometry.is_periodic =  0    0   1   # periodicity for each direction
geometry.prob_lo     = -1.  -1.  0   # lo corner of physical domain.
geometry.prob_hi     =  1.   1.  8.  # hi corner of physical domain

# Select box geometry and specify settings
# -------------------------------------------------------------
mfix.geometry = box

box.Lo = -0.5  -0.5  -1.0
box.Hi =  0.5   0.5   9.0

box.offset = 0.

box.internal_flow = true

Fig. 1 illustrates the (grey) domain and (blue) embedded boundary box geometry. The left image is a 3D rendering of the setup, and the center and right images are 2D slices along the XZ and XY planes, respectively.

domain used with box embedded boundary — Fig. 1 Example of predefined embedded boundary `box` geometry with the EB colored blue and the domain colored grey. Left: the domain and EB are rendered in 3D. Center: a 2D slice showing the XZ plane. Right: a 2D slice showing the XY plane.

This is an internal flow setup, therefore the sections of the domain that do not intersect the EB box are covered and thereby excluded from run-time calculations.

No boundary conditions are needed for the low and high domain faces in X and Y because they are fully covered.
The low and high Z domain faces remain uncovered, however no boundary conditions are needed because the domain is periodic in Z (see the inputs snippet for this example ).

`cylinder` geometry

The following inputs are defined using the cylinder prefix.

	Description	Type	Default
radius	Cylinder radius	Real	0.0002
height	Height (length) of cylinder. If the height is not defined (-1), then the cylinder is made infinitely long to overhang the domain extents.	Real	-1
direction	Axis the cylinder runs along. (`0`: X, `1`: Y, `2`: Z)	int	0
center	Center of cylinder. For a cylinder with an undefined `height`, the center value in the height `direction` can be any value.	Reals
rotation	Rotation angle in degrees of cylinder. Only cylinders with an undefined `height` (i.e., infinitely long) can be rotated. Rotation is applied about the `center` of the cylinder.	Real
rotation_axe	Axis to rotate the cylinder about. (`0`: X, `1`: Y, `2`: Z)	int	0
internal_flow	Flag to indicate that flow is inside the box.	Bool	true

The inputs for the predefined cylinder embedded boundary geometry are illustrated in Fig. 2.

`cylinder` limitations

The predefined EB cylinder geometry has several limitations:

The ends of the cylinder should not coincide with the domain extents. The cylinder should be shorter than the domain, or sufficiently long that it overhangs the ends of the domain.
Rotations are about a single axis.
There can only be one cylinder. Multiple cylinders cannot be defined and combined.

`cylinder` example

The domain is a \(4 \times 1 \times 1\) cuboid where Y and Z span \([0,1]\), and X spans \([0,4]\). An embedded boundary cylinder with \(0.45\) radius runs lengthwise through the domain, offset by \([0.5]\) in the Y and Z, respectively. The cylinder is not assigned a length, therefore it runs past the low and high X domain faces.

Listing 2 Snippet of intpus for predefined EB cylinder geometry example. This is not a complete input file.

# Define periodicity and domain extents
# -------------------------------------------------------------
geometry.coord_sys   =  0           # Cartesian coordinates
geometry.is_periodic =  0   0   0   # periodicity for each direction
geometry.prob_lo     =  0.  0.  0   # lo corner of physical domain.
geometry.prob_hi     =  4.  1.  1.  # hi corner of physical domain

# Select cylinder geometry and specify settings
# -------------------------------------------------------------
mfix.geometry = cylinder

cylinder.internal_flow = true

cylinder.radius = 0.45

cylinder.direction = 0
cylinder.center    =  0.0  0.5   0.5

Fig. 3 illustrates the (grey) domain and (blue) embedded boundary cylinder geometry. The left image is a 3D rendering of the setup, and the center and right images are 2D slices along the XZ and YZ planes, respectively.

This is an internal flow setup, therefore the sections of the domain that do not intersect the EB cylinder are covered and thereby excluded from calculations.

No boundary conditions are needed for the low and high domain faces in Y and Z because they are fully covered.
The low and high X domain faces remain uncovered, therefore boundary conditions are needed to fully specify the problem. Example boundary conditions include a mass inflow on the low X face and a pressure outflow on the X high face.

`generic` geometry

The generic geometry option is used to select the user-programed embedded boundary geometry.

A custom embedded boundary geometry is programmed by the user in src/eb/mfixeb_generic.cpp using AMReX native implicit functions and operations.
An executable containing the geometry modifications is compiled.
The geometry is accessed using the generic input.

Note

A full description of this feature is beyond the scope of this section. A future update to the documentation may include a tutorial to better demonstrate this capability.

Regions and boundary conditions

Simple geometries can be created by combining planar regions and no-slip wall boundary conditions. The mfix.geometry and mfix.geometry_file inputs should remain undefined when using this method.

In the following example, the domain is periodic in the x- and z- directions; therefore, walls only need to cover the low and high xz faces. First, wall1 and wall2 are defined in the regions section, then they are used to specify two no-slip wall boundary conditions.

Listing 3 Example geometry created using regions and boundary conditions.

# Define periodicity and domain extents
# -------------------------------------------------------------
geometry.coord_sys   = 0
geometry.is_periodic = 1      0      1
geometry.prob_lo     = 0.     0.     0.
geometry.prob_hi     = 0.01   0.01   0.005

# Define two planar regions
# -------------------------------------------------------------
mfix.regions = wall1  wall2

regions.wall1.lo       = 0.000  1.25e-6  0.000
regions.wall1.hi       = 0.010  1.25e-6  0.005

regions.wall2.lo       = 0.000  9.99875e-3  0.000
regions.wall2.hi       = 0.010  9.99875e-3  0.005

# Use the regions to define no-slip wall boundaries
# -------------------------------------------------------------
bc.regions = wall1  wall2

bc.wall1 = nsw
bc.wall1.normal = 0.0  1.0  0.0

bc.wall2 = nsw
bc.wall2.normal = 0.0 -1.0  0.0

Caution

It is highly recommended that planar regions not be defined coincident to domain boundaries. It is better to specify planes slightly offset from the domain as demonstrated in the above example.

Constructive solid geometry (CSG)

A constructive solid geometry can be created using OpenSCAD.
This option requires that the executable be built with CSG support. See the build documentation for for details.

The following inputs are defined using the csg prefix.

	Description	Type	Default
geometry_filename	The CSG file that defines the EB geometry	String	‘’
internal_flow	Flag to indicate that flow is inside the box.	Bool	true
scaling_factor	scale the geometry	Reals
translation	translate the geometry	Reals

Note

A full description of this feature is beyond the scope of this section. A future update to the documentation may include a tutorial to better demonstrate this feature.

Standard triangle language (STL)

A standard triangle language (STL) geometry can be created using numerous CAD programs.

The following inputs are defined using the stl prefix.

	Description	Type	Default
geometry_filename	The STL file that defines the EB geometry	String	‘’
scaling_factor	scale the geometry	Real
translation	translate the geometry	Reals

Note

A full description of this feature is beyond the scope of this section. A future update to the documentation may include a tutorial to better demonstrate this feature.

Specifying a geometry

Predefined geometries

box geometry

box limitations

box example

cylinder geometry

cylinder limitations

cylinder example

generic geometry

Regions and boundary conditions

Constructive solid geometry (CSG)

Standard triangle language (STL)

`box` geometry

`box` limitations

`box` example

`cylinder` geometry

`cylinder` limitations

`cylinder` example

`generic` geometry