Streamline

Use a 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 starting point selection is different. In 3D, you can also use a Streamline Surface plot to plot streamlines on 3D surfaces. Add Color Expression, Deformation, Export Expressions, Filter, Material Appearance, Selection (Plot Attribute), Translation, Transparency (3D only), and Visual Effects (3D only) subnodes as needed. Right-click a or to add these plots.


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


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

Streamline Positioning

Select one of these options from the list: (the default), , , or . 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 Starting 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 datasets 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 window and using the tools in the section, select the boundaries for the starting positions for the streamlines.

Coloring and Style

In this section you can control the style and color of the streamlines and add points or arrows to them, if desired.

Line Style

Under , choose , (the default), , or from the list to determine the type of streamlines.

If you chose , no streamlines appear, but you can plot arrows that are tangential to the streamlines.

If you chose , then enter an expression for the ribbon width in the field (SI unit: m). If desired, you can also adjust the width by selecting the check box and enter a scale factor in the corresponding text field.

If you chose , then enter an expression for the tube radius in the field (SI unit: m). If desired, you can also adjust the radius by selecting the check box and enter a scale factor in the corresponding text field. The check box is selected by default. Clear it to remove the rounded end caps from the tubes.

Point Style

Under , you can add points or arrows and control their appearance.

From the list, choose (the default) for no points or arrows, for static arrows that are tangential to the streamlines, for arrows that are tangential to the streamlines and that can move along the streamlines with the local integration time, or for points that can move along the streamlines with the local integration time.

If you chose , these additional settings are available:

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From the list, choose (the default) to distribute the arrows uniformly over the streamlines’ arc length, to distribute the arrows using the weight function dt/darc, or to distribute the arrows using the weight function darc/dt.

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Select the check box to enter a number for the total number of arrows, on all streamlines, that are plotted. By default, the COMSOL Multiphysics software provides a reasonable number of arrows.

If you chose , these additional settings are available:

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Specify a value in the field (default: 0) for the local integration time along the streamlines for which the arrows are plotted. It is possible for integration times to be negative: For a starting point in the interior of a domain, streamlines are integrated both forward and backward in time unless you clear the check box in the section.

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You can move the arrows along the local time by moving the slider. You can also create this effect using a player animation in an node under , using a sequence type.

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In the field, enter any additional times for releasing arrows, or click the button (

) to define the extra release times. By default, there are no extra times.

The following settings are available for both the and the types:

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From the list, choose (the default), , or .

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From the list, choose (the default), , or to make the arrows’ sizes depend on the magnitude of the plotted quantity, if desired. If you choose , the length of the arrows is proportional to the natural logarithm of the magnitude of the quantity they represent. This makes arrows representing small values relatively larger. The value in the field (default: 100) determines the ratio between the smallest and largest values in the range of values for the logarithmic arrow length.

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Use the slider, or select the check box and enter a scale factor in the associated text field if you want to use another scaling than the one used by default.

If you chose , these following settings are available:

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Specify a value in the field (default: 0) for the local integration time along the streamlines for which the points are plotted. It is possible for integration times to be negative: For a starting point in the interior of a domain, streamlines are integrated both forward and backward in time unless you clear the check box in the section.

•

You can move the points along the local time by moving the slider. You can also create this effect using a player animation in an node under , using a sequence type.

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In the field, enter any additional times for releasing points, or click the button (

) to define the extra release times. By default, there are no extra times.

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Select or enter an expression for the points’ radii in the field (SI unit: m). By default, the radius is scaled automatically. To enter a scale factor for the radius, select the check box and enter a scale factor in the corresponding text field.

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Select the check box if you want to display the points with a fixed onscreen size.

From the list, choose a color for the streamlines and arrows. Choose to add a custom color using a color palette. Choose to use a background color that changes with the selected color theme. This list is not available if you use a subnode to define the colors for the streamlines.

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.

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The 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 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.

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

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The 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 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 starting point than this distance, the streamline snaps to its starting 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 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 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: Specifying the Number of Streamlines and Start Boundaries

Under , from the list, select .


	The Selection section is made available for some datasets when On selected boundaries is selected from the Positioning list under Streamline Positioning.

Under , select the boundaries from which the streamlines start. By selecting in the window and using the tools in the section, select the boundaries for the starting positions for the streamlines.

From the list, choose (the default) or , to place the starting points in the barycenters of boundary elements.

Enter the of streamlines (the default is 20), if is . 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 starting points are placed in a regular grid on the selected boundaries. If is , you can instead specify a refinement as a positive integer (default: 1) in the field.

Method 2: Specifying Points by Entering Coordinates

Under , from the list, select .

Select from the list.

Enter and (2D) or , , and (3D) coordinates (SI unit: m). You can use a scalar value to represent a fixed value for some of the coordinates.

Method 3: Selecting the Specified Number of Starting Points in the Geometry

Under , from the list, select .

Select from the list.

Enter the number of (the default is 20).

From the (3D) or (2D) list, select . The starting points are then distributed semirandomly but deterministically. You can also choose a , , , or dataset, if applicable, to restrict the streamline start positions to a cut line, cut plane, parameterized curve, or parameterized surface, respectively.

Method 4: Creating Streamlines with Uniform Density

The algorithm saturates the entire domain with evenly spaced streamlines.

Under , from the list, select .

Enter the between the streamlines (the default is 0.05 in 2D and 0.15 in 3D).

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 .

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). It sets the minimum distance between streamlines and the starting point for the next streamline.

When the domain is close to be saturated with streamlines, new starting 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 starting 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. It is possible to make the streamlines extend closer to the boundary by decreasing this factor.

By default the list defaults to , and it sets the starting 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 instead to override the default and enter and (2D) or , , and (3D) 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:

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 domain, giving streamlines that are more dense where the magnitude of the field is high.

Enter the and between streamlines (the default is 0.025 in 2D and 0.05 in 3D, and the default is 0.05 in 2D and 0.15 in 3D). These distances are specified as fractions of the mean of the lengths of the bounding box of the geometry and control what minimum and maximum distances correspond to the minimum and maximum values of the flow magnitude. 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 starting point for the next streamline is selected using these separating distances.

If required, from the list, select to set advanced parameters as described in Method 4: Creating Streamlines with Uniform Density.

Advanced Section Setting Effects

The settings have the following effects:

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