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 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), Transformation, Transparency (3D only), and Visual Effects (3D only) 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, 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 checkbox 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 Positioning list: On selected entities (the default in 3D), On selected boundaries (the default in 2D), Starting-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 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 in for some datasets when you select On selected entities (3D) or On selected boundaries from the Positioning list under Streamline Positioning.
In 3D, from the Geometric entity level list, select Boundary or Edge to select the boundaries or edges, respectively, from which the streamlines start. By selecting in the Graphics window and using the tools in the Selection section, select the boundaries or edges (3D only) 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 Line style, choose None, Line (the default), Ribbon, or Tube from the Type list to determine the type of streamlines.
If you chose None, no streamlines appear, but you can plot arrows that are tangential to the streamlines.
If you chose Ribbon, then enter an expression for the ribbon width in the Width expression field (SI unit: m). If desired, you can also adjust the width by selecting the Width scale factor checkbox and enter a scale factor in the corresponding text field.
If you chose Tube, then enter an expression for the tube radius in the Tube radius expression field (SI unit: m). If desired, you can also adjust the radius by selecting the Radius scale factor checkbox and enter a scale factor in the corresponding text field. The Rounded end caps checkbox is selected by default. Clear it to remove the rounded end caps from the tubes.
Point Style
Under Point style, you can add points or arrows and control their appearance.
From the Type list, choose None (the default) for no points or arrows, Arrow for static arrows that are tangential to the streamlines, Interactive arrow for arrows that are tangential to the streamlines and that can move along the streamlines with the local integration time, or Interactive point for points that can move along the streamlines with the local integration time.
If you chose Arrow, these additional settings are available:
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From the Arrow distribution list, choose Equal arc length (the default) to distribute the arrows uniformly over the streamlines’ arc length, Equal time to distribute the arrows using the weight function dt/darc, or Equal inverse time to distribute the arrows using the weight function darc/dt.
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Select the Number of arrows checkbox 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 Interactive arrow, these additional settings are available:
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Specify a value in the Local time 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 Allow backward time integration checkbox in the Advanced 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 Animation node under Export, using a Streamline sequence type.
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In the Extra release times field, enter any additional times for releasing arrows, or click the Range button () to define the extra release times. By default, there are no extra times.
The following settings are available for both the Arrow and the Interactive arrow types:
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From the Arrow type list, choose Arrowhead (the default), Arrow, or Cone.
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From the Arrow length list, choose Normalized (the default), Logarithmic, or Proportional to make the arrows’ sizes depend on the magnitude of the plotted quantity, if desired. If you choose Logarithmic, 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 Range quotient 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 Scale factor checkbox 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 Interactive point, these following settings are available:
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Specify a value in the Local time 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 Allow backward time integration checkbox in the Advanced section.
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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 Animation node under Export, using a Streamline sequence type.
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In the Extra release times field, enter any additional times for releasing points, or click the Range 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 Point radius expression field (SI unit: m). By default, the radius is scaled automatically. To enter a scale factor for the radius, select the Radius scale factor checkbox and enter a scale factor in the corresponding text field.
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Select the Fixed size checkbox if you want to display the points with a fixed onscreen size.
From the Color list, choose a color for the streamlines and arrows. Choose Custom to add a custom color using a color palette. Choose From theme to use a background color that changes with the selected color theme. This list is not available if you use a Color Expression subnode to define the colors 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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Enter the Step length as a factor of the length of the bounding box’s edge. The default is 0.1. Edit to specify how accurately streamlines are computed. If using higher-order integration and/or adaptive integration, a longer step length can be used.
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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 checkbox 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 (1,000,000 in 2D and 200,000 in 3D) 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 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 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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From the Integrator list, choose one of the following Runge-Kutta integration methods: Runge-Kutta 2 (the default) or Runge-Kutta 4.
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When Starting-point controlled is selected from the Positioning list, in the Streamline Positioning section, the Adaptive integration step length checkbox is available. It is selected by default so that the integrator automatically chooses a smaller step length in areas of high curvature. Clear the checkbox to not use adaptive step length.
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Select the Allow backward time integration checkbox to integrate points from the starting points both in the direction of the vector field and in the opposite direction. This checkbox is selected by default.
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 datasets 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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From the Point distribution list, choose Uniform (the default), Magnitude controlled, or Mesh based.
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Specify the number of streamlines that originates from the selected boundary:
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If Point distribution is Uniform, 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 starting points are placed in a regular grid on the selected boundaries.
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If Point distribution is Magnitude controlled, the density of the streamline starting points follow the evaluated values on the selected boundary. In the Minimum relative distance (default: 0.02) and Maximum relative distance (default: 0.1) fields, enter the desired distance between starting points for the locations where the magnitude reaches its minimum and maximum values, respectively. By default, the density of the starting points is determined by the magnitude of the vector field. Choose Custom expression from the Magnitude expression field to use an expression to control the density.
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If Point distribution is Mesh based, the starting points are placed in the barycenters of boundary elements. You can specify a refinement as a positive integer (default: 1) in the Element refinement field.
Method 2: Specifying Points by Entering Coordinates
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Under Streamline Positioning, from the Positioning list, select Starting-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). 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
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Under Streamline Positioning, from the Positioning list, select Starting-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 (3D) or Along curve (2D) list, select None. The starting points are then distributed semirandomly but deterministically. You can also choose a Cut Line, Cut Plane, Parametric Curve, or Parametric Surface dataset, if applicable, to restrict the streamline start positions to a cut line, cut plane, parametric curve, or parametric surface, respectively.
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 Density level of the streamlines (the default is 5).
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The Advanced parameters list defaults to Automatic. If required, select Manual to edit these parameters: Starting distance factor, Terminating distance factor, or First starting point.
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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). 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 to 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.
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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. It is possible to make the streamlines extend closer to the boundary by decreasing this factor.
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By default the First starting point list defaults to Automatic, 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 Manual instead to override the default and enter x and y (2D) or x, y, and z (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:
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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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Enter the density level for the region where the magnitude of the vector field is at its minimum value in the Minimum density level field, and for the region where the magnitude of the vector field is at its maximum value in the Maximum density level field (the default Minimum density level is 5, and the default Maximum density level is 12.3 in 2D and 9 in 3D).
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 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.
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The algorithm integrates the points along the direction of the vector using the integration tolerance using a second- or fourth-order Runge–Kutta algorithm. Adaptive integration is used if that option is selected.
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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.
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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.