# SpatialTools

source: `proteus.SpatialTools`

and
`proteus.mprans.SpatialTools`

## Usage

Using spatial tools

Create a domain from

`proteus.Domain`

.Create geometries that will be part of this domain from

`proteus.SpatialTools`

or`proteus.mprans.SpatialTools`

.Assemble domain with

`proteus.SpatialTools.assembleDomain()`

or`proteus.mprans.SpatialTools.assembleDomain()`

.

### Import

The base SpatialTools module can be imported as follows:

```
from proteus import SpatialTools as st
```

The mprans version of SpatialTools, adding functionality specific to multi-phase flows, can be imported as follows:

```
from proteus.mprans import SpatialTools as st
```

### Choosing the domain

The domain class instance is what will hold all geometrical information once it is assembled, and must be passed as an argument to all shapes created from SpatialTools. Usually, the following class types are used from proteus.Domain:

2D:

`PlanarStraightLineGraphDomain`

3D:

`PiecewiseLinearComplexDomain`

Those classes should be instantiated with no argument, e.g.:

```
from proteus import Domain
domain = Domain.PlanarStraightLineGraphDomain().
```

### Assembling the domain

A very important final step not to forget is to assemble the domain once
all the desired geometries have been defined, so that the `Domain`

instance
from proteus.Domain holds all the relevant geometrical information necessary
for running the simulation.

```
st.assembleDomain(domain)
```

### BoundaryConditions with SpatialTools

#### Usage

The mprans version of SpatialTools also associate geometry boundaries with
BoundaryCondition instances from mprans.BoundaryConditions. These
BoundaryCondition instances are easily accessible through a dictionary with
predefined names, e.g. for a Rectangle shape instance named my_rectangle,
`my_rectangle.BC['x-']`

is for accessing the boundary conditions of the left
segment, `'x+'`

for the right, `'y+'`

for the top, and `'y-'`

for the
bottom.

Note

The boundary conditions associated with the geometry do not have to be modified/set before assembling the domain, but removing/adding boundary conditions to a geometry on top of the predefined ones must be done before.

#### Linking it to _p.py files

Warning

This does not apply to the TwoPhaseFlow module, which takes care of setting this automatically.

Linking the boundary conditions to the physical options _p.py files is done the following way (here for RANS2P boundary condition dictionnaries):

```
dirichletConditions = {0: lambda x, flag: domain.bc[flag].p_dirichlet.uOfXT,
1: lambda x, flag: domain.bc[flag].u_dirichlet.uOfXT,
2: lambda x, flag: domain.bc[flag].v_dirichlet.uOfXT,
3: lambda x, flag: domain.bc[flag].w_dirichlet.uOfXT}
advectiveFluxBoundaryConditions = {0: lambda x, flag: domain.bc[flag].p_advective.uOfXT,
1: lambda x, flag: domain.bc[flag].u_advective.uOfXT,
2: lambda x, flag: domain.bc[flag].v_advective.uOfXT,
2: lambda x, flag: domain.bc[flag].w_advective.uOfXT}
diffusiveFluxBoundaryConditions = {0:{},
1:{1: lambda x, flag: domain.bc[flag].u_diffusive.uOfXT},
2:{2: lambda x, flag: domain.bc[flag].v_diffusive.uOfXT},
3:{3: lambda x, flag: domain.bc[flag].w_diffusive.uOfXT}}
```

This is always the same in the _p files, as long as it is pointing to the right boundary conditions (e.g. p_dirichlet for pressure dirichlet). The boundary conditions themselves can and should be manipulated externally (not from the _p.py file), such as in the file where the geometries are first defined.

## Complete Examples

### 2D

```
from proteus import Domain
from proteus.mprans import SpatialTools as st
domain = Domain.PlanarStraightLineGraphDomain()
my_tank = st.Tank2D(domain=domain,
dim=[10.,5.])
my_rectangle = st.Rectangle(domain=domain,
dim=[1.,1.]
coords=[5.,2.5],
barycenter=[5.,2.5])
my_rectangle.rotate(rot=3.14/4)
my_rectangle.translate(trans=[0.1,0.1])
st.assembleDomain(domain)
my_tank.BC['x-'].setNoSlip()
my_tank.BC['x-'].u_dirichlet.uOfXT = lambda x, t: 0.1*x
my_tank.BC['x-'].p_dirichlet.uOfXT = lambda x, t: -0.1*x
my_tank.BC['x+'].setFreeSlip()
my_tank.BC['y-'].setFreeSlip()
my_tank.BC['y+'].setAtmosphere()
my_rectangle.BC['x-'].setNoSlip()
my_rectangle.BC['x+'].setNoSlip()
my_rectangle.BC['y-'].setNoSlip()
my_rectangle.BC['y+'].setNoSlip()
```

### 3D

```
from proteus import Domain
from proteus.mprans import SpatialTools as st
domain = Domain.PiecewiseLinearComplexDomain()
my_tank = st.Tank3D(domain=domain,
dim=[10.,10.,5.])
my_cylinder = st.Cylinder(domain=domain,
radius=1.,
height=3.,
nPoints=20,
coords=[5.,5.,2.5],
barycenter=[5.,5.,2.5])
my_cylinder.rotate(rot=3.14/4,
axis=[1.,0.,0.],
pivot=my_cylinder.barycenter)
my_cylinder.translate(trans=[0.1,0.1,0.1])
st.assembleDomain(domain)
my_tank.BC['x-'].setNoSlip()
my_tank.BC['x-'].u_dirichlet.uOfXT = lambda x, t: 0.1*x
my_tank.BC['x-'].p_dirichlet.uOfXT = lambda x, t: -0.1*x
my_tank.BC['x+'].setFreeSlip()
my_tank.BC['y-'].setFreeSlip()
my_tank.BC['y+'].setFreeSlip()
my_tank.BC['z-'].setFreeSlip()
my_tank.BC['z+'].setFreeSlip()
my_cylinder.BC['x-'].setNoSlip()
my_cylinder.BC['x+'].setNoSlip()
my_cylinder.BC['y-'].setNoSlip()
my_cylinder.BC['y+'].setNoSlip()
```

### 3D with STL

```
#See complete case in https://github.com/erdc/air-water-vv/tree/master/3d/STLShape
from proteus import Domain
from proteus.mprans import SpatialTools as st
from proteus.Profiling import logEvent as log
domain = Domain.PiecewiseLinearComplexDomain()
SG=st.ShapeSTL(domain,'Blocks.stl')
log("Boundary Tags are:" + str(SG.boundaryTags))
# All boundaries are free-slip for simplicity.
#See https://github.com/erdc/air-water-vv/tree/master/3d/STLShape for more advanced BC's
SG.BC['Top0'].setFreeSlip()
SG.BC['Wall0'].setFreeSlip()
SG.BC['Bed0'].setFreeSlip()
SG.BC['Concrete0'].setFreeSlip()
SG.BC['Inlet0'].setFreeSlip()
SG.BC['Outlet0'].setFreeSlip()
```

### 3D with STL and Relaxation Zones

```
#See complete case in https://github.com/erdc/air-water-vv/tree/master/3d/STLShape_Zones
from proteus import Domain
from proteus.mprans import SpatialTools as st
from proteus.Profiling import logEvent as log
domain = Domain.PiecewiseLinearComplexDomain()
SG=st.ShapeSTL(domain,'NWT.stl')
log("Boundary Tags are:" + str(SG.boundaryTags))
SG.regions=np.array([[-13., 2.5, 0.], [-3., 2.5, 0.], [9., 2.5, 0.]]
SG.regionFlags=np.array([1, 2, 3])
# All external boundaries are free-slip for simplicity.
SG.BC['Top0'].setFreeSlip()
SG.BC['Wall0'].setFreeSlip()
SG.BC['Bed0'].setFreeSlip()
SG.BC['Concrete0'].setFreeSlip()
SG.BC['Top_Gen'].setFreeSlip()
SG.BC['Bed_Gen'].setFreeSlip()
SG.BC['Wall_Gen'].setFreeSlip()
SG.BC['Top_Abs'].setFreeSlip()
SG.BC['Bed_Abs'].setFreeSlip()
SG.BC['Wall_Abs'].setFreeSlip()
SG.BC['Inlet0'].setNonMaterial()
SG.BC['Outlet0'].setNonMaterial()
SG.setGenerationZones(flags=1,
epsFact_solid=2.,
center=np.array([-13., 2.5, 0.]),
orientation=np.array([1., 0., 0.]),
waves=wave,
dragAlpha=dragAlpha,
vert_axis=1,
smoothing=smoothing,
)
SG.setAbsorptionZones(flags=3,
epsFact_solid=4.,
center=np.array([9., 2.5, 0.]),
orientation=np.array([-1., 0., 0.]),
dragAlpha=dragAlpha,
vert_axis=1
)
SG.BC['Inlet_Gen'].setUnsteadyTwoPhaseVelocityInlet(wave=wave,
vert_axis=1,
smoothing=3.*opts.he,
orientation=np.array([-1.,0.,0.]),
vof_air=1.,
vof_water=0.)
SG.BC['Outlet_Abs'].setHydrostaticPressureOutletWithDepth(seaLevel= opts.mwl,
rhoUp=opts.rho_1,
rhoDown=opts.rho_0,
g=opts.g,
refLevel=xTop,
smoothing=smoothing,
orientation=np.array([1.,0.,0.]),
vert_axis=1)
```

## Classes

### Base classes

The following classes are accessible with an import from proteus.SpatialTools and/or proteus.mprans.SpatialTools. Importing them from the mprans module adds functionality such as the possibility to set multi-phase flow boundary conditions and relaxation zones.

This is the same procedure as creating a Domain from scratch, with the added benefit of being able to add more shapes to the domain as separate instances and easy access to boundary conditions.

#### CustomShape

The most flexible type of shape, where everything is defined by the user. Any
geometry can be created with this. The minimum arguments necessary for setting
a custom geometry in 2D are: `domain`

, `boundaryTags`

, `vertices`

,
`vertexFlags`

, `segments`

, and `segmentFlags`

. In 3D, the necessary
arguments are: `domain`

, `boundaryTags`

, `vertices`

, `vertexFlags`

,
`facets`

, and `facetFlags`

. For additional arguments, please refer to the
source code in proteus.SpatialTools.

```
boundaryTags = {'my_tag1': 1,
'my_tag2': 2,
'my_tag3': 3}
vertices = [[0.,0.],
[1.,0.],
[1.,1.],
[0.,1.]]
vertexFlags = [boundaryTags['my_tag1'],
boundaryTags['my_tag1'],
boundaryTags['my_tag2'],
boundaryTags['my_tag2']]
segments = [[0, 1],
[1, 2],
[2, 3],
[3, 0]]
# flags can also be set from numbers included in the boundaryTags dictionary
segmentFlags = [1, 2, 3, 2]
my_customshape = st.CustomShape(domain=domain,
vertices=vertices,
vertexFlags=vertexFlags,
segments=segments,
segmentFlags=segmentFlags,
boundaryTags=boundaryTags)
my_customshape.BC['my_tag1'].setNoSlip()
```

#### Rectangle

A simple rectangular shape.

```
my_rectangle = st.Rectangle(domain=domain,
dim=[10.,2.],
coords=[5.,1.],
barycenter=[5.,1.])
```

#### Circle

A simple circular shape.

```
my_circle = st.Circle(domain=domain,
radius=5.,
coords=[5.,5.],
barycenter=[5.,5.],
nPoints=20)
```

#### Cuboid

A simple cuboidal shape.

```
my_cuboid = st.Cuboid(domain=domain,
dim=[10.,10.,2.],
coords=[5.,5.],
barycenter=[5.,5.])
```

#### Cylinder

A simple cylindrical shape.

```
my_cylinder = st.Circle(domain=domain,
radius=5.,
height=10.
nPoints=20,
coords=[5.,5.,7.5],
barycenter=[5.,5.,7.5])
```

#### Sphere

A simple spherical shape.

```
my_sphere = st.Sphere(domain=domain,
radius=5.,
coords=[2.,2.],
barycenter=[2.,2.],
nSectors=10)
```

#### ShapeSTL

For importing STL geometries. It needs a .stl ASCII file, and does not currently work with binary files. The STL geometry is converted in a Proteus readable format, automatically creating vertices and facets, and a single boundary tag/flag for the whole STL geometry.

```
my_stl = st.ShapeSTL(domain=domain,
filename='path/to/my/file.stl')
```

The function has the capability of reading multi-block stl ASCII files. Multiblock files can be created by concatenating multiple STL files containing a single geometry block into one file. You can do this quickly in a bash shell as follows:

```
cat file_1.stl file_2.stl file_3.stl > block.stl
```

```
solid block0
...
facet normal ni nj nk
outer loop
vertex v1x v1y v1z
vertex v2x v2y v2z
vertex v3x v3y v3z
endloop
endfacet
...
endsolid
solid block1
...
endsolid
...
solid blockFinal
...
endsolid
```

When reading the block stl file, the `ShapeSTL`

class will read also the stl blocks and, in addition to vertices and facets, tags for boundaryTags, vertices and facets will be assigned. The names of boundaries are given according to the naming of the blocks. E.g. block0 will form boundary block0 etc.

The user should be able to mesh a whole domain, as long as the STL files create a watertight domain. A simple example of setting up a 3D domain is given in the beginning of this section and the air-water-vv repository https://github.com/erdc/air-water-vv/blob/master/3d/STLShape/

ShapeSTL also provides the capability to incorporate relaxation zones for wave genearation and absorption. The STL file must be generated with this in mind as additional definition of STL blocks is required. Internal blocks to designate the boundary of absorbtion zone and main tank are required. As these create a line intersection of at least three blocks, the user must take care to ensure the vertices are coincident in all three blocks. Each region is tagged, which allows the relaxation zone to be defined. A simple example of setting up a 3D domain with relaxation zones is given in the beginning of this section and the air-water-vv repository https://github.com/erdc/air-water-vv/blob/master/3d/STLShape_Zones/

### mprans specific

The following classes are for use with multi-phase flow and can only be imported from proteus.mprans.SpatialTools.

#### Tank2D

The Tank2D class can be used to create a rectangular tank. This class allows for “sponge layers”, or “relaxation zones” that are usually used for wave absorption or wave generation to get rid of reflected waves in the domain. The lower left corner of the tank is at the origin [0.,0.] when created (but it can still be translated later on), and sponge layers extend outwards of the numerical tank. A Tank2D of dimensions [10.,2.] and sponge layers of length 3. on both sides will have a total domain size of [16,2], spanning from x=-3 to x=13.

```
my_tank = st.Tank2D(domain=domain,
dim=[10.,2.])
# make sponge layers
my_tank.setSponge(x_n=3., x_p=3.)
# set absorption zone (x_p -> x+)
my_tank.setAbsorptionZones(dragAlpha=1.e6,
x_p=True)
# set generation zone
from proteus import WaveTools as wt (x_n -> x-)
my_wave = wt.MonochromaticWave()
he = 0.01
my_tank.setGenerationZones(dragAlpha=1.e6,
smoothing=3*he,
wave=wave,
x_n=True)
# set boundary conditions
my_tank.BC['y+'].setAtmosphere()
my_tank.BC['y-'].setFreeSlip()
my_tank.BC['x+'].setFreeSlip()
my_tank.BC['x-'].setUnsteadyTwoPhaseVelocityInlet(wave=my_wave
smoothing=3*he)
my_tank.BC['sponge'].setNonMaterial()
```

Important

Tank2D instances should not be rotated as this can lead to problems with relaxation zones and boundary conditions.

#### Tank3D

Very similar to the Tank3D, it is a cuboid for 3D domains with the possibility of adding sponge layers.

```
my_tank = st.Tank2D(domain=domain,
dim=[10.,10., 2.])
# make sponge layers
my_tank.setSponge(x_n=3., x_p=3., y_p=3., y_n=3.)
# set absorption zones
my_tank.setAbsorptionZones(dragAlpha=1.e6,
x_p=True,
y_p=True,
y_n=True)
# set generation zone
from proteus import WaveTools as wt (x_n -> x-)
my_wave = wt.MonochromaticWave()
he = 0.01
my_tank.setGenerationZones(dragAlpha=1.e6,
smoothing=3*he,
wave=wave,
x_n=True)
# set boundary conditions
my_tank.BC['z+'].setAtmosphere()
my_tank.BC['z-'].setFreeSlip()
my_tank.BC['y-'].setFreeSlip()
my_tank.BC['x+'].setFreeSlip()
my_tank.BC['x-'].setUnsteadyTwoPhaseVelocityInlet(wave=my_wave
smoothing=3*he)
my_tank.BC['sponge'].setNonMaterial()
```

Important

Tank3D instances should not be rotated as this can lead to problems with relaxation zones and boundary conditions.