Streamline Surface

Use a plot in 3D (

) to visualize a vector quantity on surfaces. A streamline is a curve everywhere tangent to an instantaneous vector field. Add Deformation, Color Expression, Export Expressions, or Filter subnodes as needed. Right-click a to add these plots from the submenu..


	Go to Common Results Node Settings for links to information about these sections: Data, Expression, Title, Coloring and Style, Quality, and Inherit Style.


	To get the length of the streamlines, use an Export node. In its Settings window, select the Only export start and end points check box to include one row with the start point, the endpoint, and the length of the streamline for each streamline.

Selection

In this section, select the surfaces on which to compute and plot the streamlines (the selected surfaces are not the boundaries where the streamlines should start). The selected surfaces must form a plane. By selecting in the window and using the tools in the section, select the boundaries (surfaces) on which you want to plot streamlines.

Streamline Positioning

Select one of these options from the list: (the default), , or . Then follow one of the methods described:

•

Method 1: Selecting the Specified Number of Start Points in the Geometry

•

Method 2: Creating Streamlines with Uniform Density

•

Method 3: Creating Streamlines with Variable Density and Magnitude Controlled

Advanced

Define the following advanced streamline settings as needed.

Advanced Settings for the Streamline Plot

Under , set these general settings. See also Advanced Section Setting Effects.

•

The field default is 0.001. Edit to specify how accurately streamlines are computed.

•

The field makes it possible to control the length of streamlines. Edit the default (Inf) to control the streamlines’ length. Enter the value as a fraction of the mean bounding box’s size. When the check box is selected (the default), the maximum length refers to the sum of the lengths of the forward and backward parts.

•

The field makes sure that the integration does not continue indefinitely. Edit the default (5000) to control when the computation stops.

•

The field sets an upper time limit for the integration. The default is infinity (inf).

•

The can be adjusted to make sure the integration stops near a stationary point in the field. The default is 0.01.

•

The field default is 0.01. This is a fraction of the mean of the lengths of the bounding box of the geometry. If a streamline gets closer to its start point than this distance, the streamline snaps to its start point and is plotted as a connected loop. See also Method 5: Creating Streamlines with Variable Density and Magnitude Controlled.

•

Select the check box to integrate points from the starting points both in the direction of the vector field and in the opposite direction. This check box is selected by default.

•

Select the check box if required. The vector field is normalized pointwise: For each point where the field was evaluated, the vector is replaced by a unit vector in the same direction. If you apply normalization, the speed along the streamline changes. This change means that the other settings in the section (for example, maximum number of integration steps and maximum integration time) are interpreted differently.

Streamline Positioning Section (Continued)

Method 1: Selecting the Specified Number of Start Points in the Geometry

Under , from the list, select .

Enter the number of (the default is 20).

Method 2: Creating Streamlines with Uniform Density

The algorithm saturates the entire surface with evenly spaced streamlines.

Under , from the list, select .

Enter the between the streamlines (the default is 0.05).

The value for the separating distance is a fraction of the mean of the lengths of the bounding box of the geometry. In this case, a streamline stops whenever it gets too close to another streamline or itself (or if any of the general termination criteria specified in the section is fulfilled).

The list defaults to . If required, select to edit these parameters: , , , or .

Edit the if streamlines do not behave as expected near edges on a coarse mesh — try increasing this number. It is a measurement of the density of points on the edges used to set up the structure and is used to measure distances between streamlines. Refining the mesh in the problematic area can also resolve the problem.

Edit the value in the field (a fraction 0–1; default value: 0.5) when a streamline is close to itself, typically for spiraling streamlines. This number controls how big part of the streamline, starting from its start point, that the streamline itself is allowed to get close to, and it might in some cases be useful in order to get a less cluttered streamline plot.

The is a factor multiplied with the distance specified in the field (as a fraction of the mean of the lengths of the bounding box of the geometry — the default value is 0.05). It sets the minimum distance between streamlines and the start point for the next streamline.

When the surface is close to be saturated with streamlines, new start points tend to be positioned where the streamline has nowhere to go before it gets too close other streamlines, resulting in short streamlines. The higher the value of this factor, the more it disqualifies the start point and thus reduces the number of short streamlines.

The is a factor multiplied with the distance specified in the field. It sets the minimum distance between any pair of streamlines. Thus, this distance is the minimal distance under which the integration of a streamline stops.

Method 3: Creating Streamlines with Variable Density and Magnitude Controlled

To create streamlines with a variable density according to the magnitude of the specified vector field:

Under , from the list, select .

The setting gives proper streamline plots only for incompressible flow fields. In this case, the algorithm places the streamlines so that the flow between each pair of adjacent streamlines is the same throughout the surface, giving streamlines that are more dense where the magnitude of the field is high.

Enter a (the default is 20). This value is roughly the number of streamlines. Prior to streamline generation, the software computes a rough estimate of the total flow of the flow field in the model, divides this value with the specified setting, and uses the resulting value as the flow between each pair of adjacent streamlines.

If required, from the list, select to specify the as described in Method 2: Creating Streamlines with Uniform Density.

Advanced Section Setting Effects

The settings have the following effects:

•

When calculating streamlines, the software selects a set of starting points (controlled by the streamline start points and the number of start points).

•

The algorithm then finds the vectors of the given vector field at these points by interpolation. It normalizes the vector field if that option is selected.

•

The algorithm integrates the points along the direction of the vector using the integration tolerance using a second-order Runge-Kutta algorithm.

•

At the new positions, the algorithm finds vector values by interpolation and performs another integration.

This process stops if:

•

It reaches a predetermined number of integration steps (controlled by the maximum number of integration steps entry).

•

The points end up outside the geometry.

•

The points reach a “stationary point” where the vector field is zero. Control the meaning of “zero” with the stationary point stop tolerance.

•

It has used a predetermined amount of “time” for integrating (control this parameter with the field).

Finally, the software connects the calculated points for each streamline consecutively with straight lines.


	When integrating, the software uses a pseudo-time that has nothing to do with the time in time-dependent problems. Use the massless particle tracing tool to integrate in time-varying fields and to control the real time in stationary fields.