Geometry and Meshing¶
Origin & coordinate system¶
planingFSI uses a two-dimensional Cartesian coordinate system, with the primary coordinates being x and y, positive to the right and up, respectively.
The fluid is assumed to flow in the -x direction (equivalently, the body moves in the +x direction at steady speed).
There is a point with ID 0 located at the origin, (0.0, 0.0).
Units¶
planingFSI does not consider units.
Thus, for all coordinates and input values, one must be careful to maintain a consistent set of units.
To do so, it is recommended to use SI units (kg, m, s) or English units (slug, ft, s) for (mass, length, time).
Creating a mesh¶
Specification of the computational mesh begins with the instantiation of a Mesh object:
from planingfsi import Mesh
mesh = Mesh()
The geometry may then be specified, first by adding control points.
These control points are connected with Curves or Lines.
There are four methods for adding Point objects to the Mesh.
Direct coordinate specification¶
Points can be placed in the mesh with direct coordinate specification.
The form of this is as follows, where 1 is the new point’s ID:
from planingfsi import Mesh
mesh = Mesh()
mesh.add_point(1, "dir", [1.0, 1.0])
Relative coordinate specification¶
Similarly, points can be placed relative to another existing point.
In this case, the position argument is an iterable of (base point id, angle, radius)
For example, the following places a point at an angle 45 degrees counter-clockwise from the origin at a distance of 10:
from planingfsi import Mesh
mesh = Mesh()
mesh.add_point(1, "rel", [0, 45.0, 10.0])
Constraining points to a specific x- or y-coordinate¶
Sometimes, it is useful to place points relative to another at an unknown distance, where the distance is calculated such that a specific x- or y-coordinate is achieved.
For example, the code below will place a point at an angle of 45 degrees counter-clockwise from the origin, but the x-coordinate will be 10.0, rather than the distance (~14.14).
In this method, the position argument is an iterable of (base point id, constrained coordinate (x or y), value) and an optional angle keyword argument may be provided.
The angle defaults to 0.0 if x is selected, and 90.0 if y is selected as the direction.
from planingfsi import Mesh
mesh = Mesh()
mesh.add_point(1, "con", [0, "x", 10.0], angle=45.0)
Placing points along a line between two other points¶
Points can be placed along the line between two existing points.
In this case, the position argument is an iterable of (first point id, second point id, fractional distance).
For example, the following will place a point 3/4 of the way between two points (at (7.5, 7.5)):
from planingfsi import Mesh
mesh = Mesh()
mesh.add_point(1, "dir", [10.0, 10.0]) # Second point
mesh.add_point(2, "pct", [0, 1, 0.75]) # First point is the origin