# Specifying a geometry

The following inputs are defined using the `mfix` prefix.

| Description | Type | Default
--- | --- | --- | ---
geometry | Select a basic `box` or `cylinder` predefined EB geometry, or the user-programed `generic` geometry. Details about these geometry options and associated additional inputs are provided in the following sections. | String | ‘’
geometry_filename | The CSG file that defines the EB geometry | 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.

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.

Fig. 2 Illustration of predefined embedded boundary `cylinder` geometry inputs where the cylinder geometry is blue and the domain is grey.

#### `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.

Fig. 3 Example of predefined embedded boundary `cylinder` 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 YZ plane.

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

Use the `mfix.geometry_filename` input to select a constructive solid geometry (CSG) that defines the system geometry.

- 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.

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.