Streamline
Use a Streamline plot in 2D () or 3D () to visualize a vector quantity. A streamline is a curve everywhere tangent to an instantaneous vector field. 3D streamline plot is analogous to the 2D streamline plot except that there is no height data setting and the start point selection is different. Add Deformation, Color Expression, Export Expressions, or Filter subnodes as needed. Right-click a 2D Plot Group or 3D Plot Group to add these plots..
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.
Streamline Positioning
Select one of these options from the Positioning list: On selected boundaries (the default), Start point controlled, Uniform density, or Magnitude controlled. Then follow one of the methods described:
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Method 1: Specifying the Number of Streamlines and Start Boundaries
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Method 2: Specifying Points by Entering Coordinates
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Method 3: Selecting the Specified Number of Start Points in the Geometry
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Method 4: Creating Streamlines with Uniform Density
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Method 5: Creating Streamlines with Variable Density and Magnitude Controlled
Selection
The Selection section is available for some data sets when you select On selected boundaries from the Positioning list under Streamline Positioning.
Select the boundaries from which the streamlines start. By selecting in the Graphics window and using the tools in the Selection section, select the boundaries for the starting positions for the streamlines.
Advanced
Define the following advanced streamline settings as needed.
Advanced Settings for the Streamline Plot
Under Advanced, set these general settings. See also Advanced Section Setting Effects.
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The Integration tolerance field default is 0.01 for 3D and 0.001 for 2D. Edit to specify how accurately streamlines are computed.
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The Maximum streamline length 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 Allow backward time integration check box is selected (the default), the maximum length refers to the sum of the lengths of the forward and backward parts.
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The Maximum number of integration steps field makes sure that the integration does not continue indefinitely. Edit the default (5000) to control when the computation stops.
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The Maximum integration time field sets an upper time limit for the integration. The default is infinity (inf).
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The Stationary point stop tolerance can be adjusted to make sure the integration stops near a stationary point in the field. The default is 0.01.
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The Loop tolerance 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.
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Select the Allow backward time integration 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.
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Select the Normalize vector field 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 Advanced section (for example, maximum number of integration steps and maximum integration time) are interpreted differently.
Streamline Positioning Section (Continued)
Method 1: Specifying the Number of Streamlines and Start Boundaries
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Under Streamline Positioning, from the Positioning list, select On selected boundaries.
The Selection section is made available for some data sets when On selected boundaries is selected from the Positioning list under Streamline Positioning.
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Under Selection, select the boundaries from which the streamlines start. By selecting in the Graphics window and using the tools in the Selection section, select the boundaries for the starting positions for the streamlines.
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Enter the Number of streamlines (the default is 20). This number is a suggestion for how many streamlines are generated, but there is no guarantee that you get exactly the specified number of streamlines. The reason is that the streamline start points are placed in a regular grid on the selected boundaries.
Method 2: Specifying Points by Entering Coordinates
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Under Streamline Positioning, from the Positioning list, select Start point controlled.
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Select Coordinates from the Entry method list.
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Enter x and y (2D) or x, y, and z (3D) coordinates (SI unit: m). Also use a scalar value to represent a fixed value for some of the coordinates.
Method 3: Selecting the Specified Number of Start Points in the Geometry
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Under Streamline Positioning, from the Positioning list, select Start point controlled.
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Select Number of points from the Entry method list.
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Enter the number of Points (the default is 20).
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From the Along curve or surface list, select None. The start points are then distributed semirandomly but deterministically. You can also choose a Parameterized Curve or Parameterized Surface data set, if applicable, to restrict the streamline start positions to a parametric curve or surface.
Method 4: Creating Streamlines with Uniform Density
The algorithm saturates the entire domain with evenly spaced streamlines.
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Under Streamline Positioning, from the Positioning list, select Uniform density.
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Enter the Separating distance 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 Advanced section is fulfilled).
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The Advanced parameters list defaults to Automatic. If required, select Manual to edit these parameters: Boundary element refinement, Fraction of streamline length to ignore, Starting distance factor, Terminating distance factor, or First start point.
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Edit the Boundary element refinement if streamlines do not behave as expected near boundaries on a coarse mesh — try increasing this number. It is a measurement of the density of points on the boundaries 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.
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Edit the value in the Fraction of streamlines to ignore 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.
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The Starting distance factor is a factor multiplied with the distance specified in the Separating distance 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 domain 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.
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The Terminating distance factor is a factor multiplied with the distance specified in the Separating distance 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.
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By default the First start point list defaults to Automatic, and it sets the start point for the first streamline. It is selected in the element where the highest value of the velocity of the specified vector field occurs. If required, select Manual instead to override the default and enter x and y coordinates.
Method 5: Creating Streamlines with Variable Density and Magnitude Controlled
To create streamlines with a variable density according to the magnitude of the specified vector field:
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Under Streamline Positioning, from the Positioning list, select Magnitude controlled.
The Magnitude controlled 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 domain, giving streamlines that are more dense where the magnitude of the field is high.
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This step depends if it is a 2D or 3D Component.
For 2D models, enter a Density (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 Density setting, and uses the resulting value as the flow between each pair of adjacent streamlines.
For 3D models, enter the Min (minimum) distance and Max (maximum) distance between streamlines (the default Min distance is 0.05 and the default Max distance is 0.15). These distances are specified as fractions of the mean of the lengths of the bounding box of the geometry. The minimum velocity in the model is mapped to the minimum distance and the maximum velocity to the maximum distance. Thus every point on a streamline and on the boundary has a separating distance associated with it. Given a set of streamlines, the start point for the next streamline is selected using these separating distances.
A streamline stops only if it exits the domain or gets too close to its own start point, using the Loop tolerance option in the Advanced section (or if any of the general termination criteria specified in the Advanced section is fulfilled).
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If required, from the Advanced parameters list, select Manual to set advanced parameters as described in Method 4: Creating Streamlines with Uniform Density.
Advanced Section Setting Effects
The Advanced settings have the following effects:
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When calculating streamlines, the software selects a set of starting points (controlled by the streamline start points and the number of start points).
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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.
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The algorithm integrates the points along the direction of the vector using the integration tolerance using a second-order Runge-Kutta algorithm.
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At the new positions, the algorithm finds vector values by interpolation and performs another integration.
This process stops if:
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It reaches a predetermined number of integration steps (controlled by the maximum number of integration steps entry).
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The points end up outside the geometry.
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The points reach a “stationary point” where the vector field is zero. Control the meaning of “zero” with the stationary point stop tolerance.
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It has used a predetermined amount of “time” for integrating (control this parameter with the Maximum integration time 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.