The Mesh Generator main dialog is divided up into three menus and a checkbox:
Use the File menu to import NURB (IGES) files, to control Mesh Generator project files, and write mesh files.The File menu has the following options:
All boundaries are lines which exist as one-dimensional I-ordered Tecplot zones with added geometry. Use the Boundary menu to create and edit boundaries, set and distribute the nodes along these boundaries, get information about a specific boundary, and delete boundaries. The Boundary menu has the following options:
All two-dimensional zones are called meshes, whether IJ-ordered (structured) or finite-element (unstructured). Use the Mesh menu to generate, modify and delete meshes. The Mesh dialog has the following options:
A simple method for creating a boundary line is to specify a polyline. A polyline is a set of connected line segments. A line segment is defined by entering its starting and ending point coordinates. Polylines are created by specifying the coordinates of more than two points. The points you specify are called control points.
Control points are used to define the shape of a boundary. Several options are available to let you specify control points: they may be entered manually, selected from the end point of an existing boundary line, or converted from a Tecplot polyline geometry. You may not define two identical control points, one after another.
The Line Definition area of the Polyline dialog is where control points are entered for the polyline you wish to create. On the left of this dialog is a list labeled Control Points. When you are first defining a new polyline boundary, this list will be empty. The list will expand as you add control points.
To the right of the Control Points list are two text fields labeled X and Y. These are the X- and Y-coordinate text fields where you can enter a new control point or edit an existing control point.
Next to the X and Y text fields is the Select Endpt. button, which is active only when a boundary line is selected in the current Tecplot frame. This button allows you to automatically enter the coordinates of the end point closest to a node selected with the Tecplot Selector tool. This allows an exact specification of a given end point without having to manually enter the values. It avoids mismatch errors which can create problems when attempting to combine the multiple boundaries of a mesh.
After coordinates have been entered into the X and Y text fields, you can use one of the four action buttons directly below the fields. These are:
To the right of the four action buttons is the Convert Polyline Geometry Insert After button. This is active only when a Tecplot polyline geometry is selected in the current frame with the Selector tool. Clicking on this button will convert a selected polyline geometry into a set of control points, which are then inserted after a selected point in the Control Point list. This will allow you to draw a polyline with the Tecplot drawing tool, then convert it directly into a boundary, without having to manually enter the control points.
Note: After using the Convert Polyline Geometry Insert After button, the selected geometry is deleted from the current Tecplot frame.
An option to use a subset of the control points you have specified is also available. You can do this by specifying the starting and ending indices of the desired control points as they appear in the Control Points list.
The starting and ending indices are entered into the two text fields labeled Start and End in the Line Definition area of the Polyline dialog. The default value for the starting index is 1, and the default value for the ending index is Mx. The ending index will accept any integer between 1 and Mx as well as Mx-a where a is some integer provided that Mx-a is greater than or equal to. The starting point of the newly created polyline will be the control point defined by the Start index, and the ending point will be the control point defined by the End index. Any interpolations performed on the resulting polyline will be based on all of the control points you have specified in the Control Points list, regardless of the starting and ending index values.
The number of nodes, the distribution option, and the interpolation on a boundary is set by clicking on the Node Distribution... button. The button is active only after at least two control points have been specified. When you click on the Node Distribution... button, The Node Distribution Dialog will be brought up. The default Distribution is As Is and default Number Of Nodes is the number of control points available.
Mesh Generator provides three ways to create boundaries using circular arcs.
The Line Definition area of the Circular Arc dialog allows you to create circular arcs using one of three different methods.
Two options are available by clicking on the radio buttons under Specify in the Line Definition area of the Circular Arc dialog. These are:
The default direction of circular arcs in Mesh Generator is clockwise. You may reverse the direction by clicking on the Counter Clockwise checkbox.
Note: In instances where two solutions are possible, the smaller arc will always be selected.
Depending upon which option is selected under Specify, the text fields in the Arc area of the Circular Arc dialog will be active or inactive. The X- and Y-coordinates for the appropriate points may be manually entered into the text fields labeled X and Y. You must enter a value in units of degrees in the Arc Angle text field. The value entered in the Radius text field must have units consistent with the X- and Y-coordinates.
Next to the X and Y text fields for Start and End are two Select Endpt. buttons, which are active only when another boundary line is selected in the current Tecplot frame. The Select Endpt. buttons allow you to automatically enter the coordinates of the end point closest to a node selected with the Tecplot Selector tool. This allows an exact specification of a given end point without having to manually enter the values. It avoids mismatch errors which can create problems when attempting to combine the multiple boundaries of a mesh.
To the right of the Counter Clockwise checkbox is the Convert Circle Geometry button. This is active only when a Tecplot circle geometry is selected in the current frame. By clicking on this button, the selected circle geometry is converted into a circular arc of 360 degrees. This allows you to draw a circle with the Tecplot circle drawing tool and directly convert it into a boundary in Mesh Generator.
Note: After clicking on the Convert Circle Geometry button, the selected circle geometry is deleted from the current Tecplot frame.
The number of nodes, the distribution option, and the interpolation on a circular arc is set by clicking on the Node Distribution... button. When you click on the Node Distribution... button, The Node Distribution Dialog will be brought up. This is discussed in Section 2.8, "Distributing Nodes Along Boundaries." The default Distribution is Even Spacing and default Number Of Nodes is 30.
The conic arc option allows you to create analytically defined boundaries such as ellipses, parabolas, and hyperbolas.
The Line Definition area of the Conic Arc dialog allows you to input values that control the shape and extent of your conic arc. A conic arc is defined by entering the X- and Y-coordinates of the Start and End points of the arc, and entering the Vertex, which joins the Start and End point to form a triangle enclosing the conic arc. The X- and Y-coordinates for these points are entered in the text fields labeled X and Y.
Next to the X and Y text fields for Start and End are two Select Endpt. buttons, which are active only when another boundary is selected in the current Tecplot frame. The Select Endpt. buttons allow you to automatically enter the coordinates of the end point closest to a node selected with the Tecplot Selector tool. This allows an exact specification of a given end point without having to manually enter the values. It avoids mismatch errors which can create problems when attempting to combine the multiple boundaries of a mesh.
The Length Ratio defines where the conic arc curve intersects the bisection line creating the middle point (mid point between the Start and End points) and the Vertex. This number is the ratio of length from the middle point to the intersection point, and the length from the middle point to the vertex. The value entered in the text field for the Length Ratio determines the analytic shape of the conic arc.
Acceptable values for the Length Ratio are: 0<Length Ratio<1.0.
The number of nodes, the distribution option, and the interpolation on a conic arc is set by clicking on the Node Distribution... button. When you click on the Node Distribution... button, The Node Distribution Dialog will be brought up. The default Distribution is Even Spacing and default Number Of Nodes is 30.
The NURB Curve dialog is only displayed when you edit a boundary line created by importing an IGES file, or create a new line from one of these lines. It allows you to specify a line label, and to change the node distribution for the line.
The number of nodes, the distribution option, and the interpolation on a conic arc is set by clicking on the Node Distribution... button. When you click on the Node Distribution... button, The Node Distribution Dialog will be brought up.
This option is activated by first selecting a line in your current Tecplot frame. Next, click on the Boundary menu, then select the Create From Selected Line... option.
The dialog which appears will depend on what type of boundary you selected. Options include:
This option is activated by selecting a line in your current Tecplot frame. This will then be used for extracting the new boundary. Under the Boundary menu, select the Extract From Selected Line... option. This will bring up the Extract Selected Line dialog.
In the Line Definition area of the dialog you must specify the starting and ending indices of the selected line which are to be extracted to create your new boundary. These indices are entered into the Start and End text fields. No node distribution changes are allowed when extracting. Therefore, the only editing permitted on an extracted line is modification of the starting and ending indices. Valid values for both starting and ending indices are from 1 to maximum number of nodes on the selected line.
Note: You are allowed to reverse line direction. You may do this by entering a Start index value greater than that of the End index value. This in effect reverses the line direction for your newly extracted boundary line. The extracted nodes will be the same, but the index order will proceed in the opposite direction along the line.
This option is activated by selecting a mesh (IJ-ordered zone) to be used for extracting the new boundary. On the Boundary menu, select the Extract From Selected Mesh... option. This will bring up the Extract Selected Mesh dialog.
In the Line Definition area of the dialog you must enter the starting and ending indices, and the specific boundary of the mesh from which you want to extract the new boundary. The indices are entered into the Start and End text fields.
No node distribution changes are allowed when extracting. The only editing permitted on an extracted line is the modification of the starting and ending indices and the Boundary Line option. Valid values for both starting and ending indices are from 1 to the maximum number of nodes (designated by Mx, or the actual J-index) in either the I- or J-direction of the selected mesh.
The Node Distribution dialog allows you to specify how many nodes are distributed along the boundary line you are currently creating or editing, as well as how those nodes are distributed.
The Distribution option on the Node Distribution dialog makes other areas on the dialog active or inactive, depending upon the selection. Available Distribution options are:
Selecting Multiple Tanh distribution will activate the Multiple Tanh area, located immediately below the Distribution dropdown. In it, you must specify at least one clustering control point, the spacing near this point, and the number of nodes before this point. The clustering point control is similar to the Polyline dialog, where the list is for the selection of clustering information. The text fields in the Multiple Tanh area are to enter or modify the values, and Replace, Add, and Delete are the available action buttons. Both the Initial and Final Spacing, as well as at least one clustering spacing is required. When only one clustering control point is entered, the resulting line will have two segments where the clustering will be at both ends, as well as at the clustering point.
The number of nodes to be distributed along the created boundary must be specified. This value is entered in the Number Of Nodes text field. The number of nodes includes the first and last nodes. Valid numbers are any integer number. If the Node Distribution option is set to As Is, the only valid entry for Number Of Nodes is that equal to the number of Control Points listed Line Definition.
The Reverse Line Direction checkbox enables you to switch the direction of the node index order along a boundary when it is created. It has no effect on the node distribution.
The default direction of the node index order is from starting to ending point of a line according to the order of the Control Points in the Line Definition area of the Polyline dialog. Reversing the line direction does not affect how the nodes are distributed, as it is based upon the line direction defined by your control points. Instead, reversing the line direction occurs after the nodes have been distributed along the created boundary.
For the Exponential, Tanh, Multiple Tanh, and Polynomial Distribution options, you are required to enter values for the Initial and Final Spacing. For the One-Sided options only the Initial or Final Spacing is required.
Spacing is the distance between two adjacent nodes. Initial Spacing is the spacing at the first node (index=1), and Final Spacing is the spacing next to the last node. The spacing between the nodes depends upon your distribution option. The values you enter in the Initial and Final Spacing text fields on the Node Distribution dialog must be entered in units consistent with the physical coordinates. The default values are set to 0.001.
The Multiple Tanh area of the Node Distribution dialog is active only when Distribution is set to Multiple Tanh. This area contains a list of cluster control points, text fields for entering these points, and buttons for controlling the points. The clustering control point list is used to control the clustering information. Initially, this list will be empty. In addition to the Initial and Final Spacing values, you must specify at least one additional clustering control point by entering the values in the four Multiple Tanh text fields; X, Y, Spacing, and # Nodes. The clustering points may be entered in any order, and are sorted by distance along the line starting from the first control point.
The values for X and Y are the approximate coordinates along the boundary line at which the clustering is to be focused. The actual coordinates will be calculated by determining the point on the line closest to the values you enter. Spacing at this clustering point is enforced on both sides of the point. The # Nodes is the number of the nodes to be placed on the line section between two physically adjacent clustering points, not including the clustering points. The final section is defined by the last cluster point and the last point on the line. The number of nodes placed in this section is calculated in such a way that the total number of nodes on the line will be equal to Number Of Nodes. The text fields are used to modify the values.
Replace, Add, and Delete are the available action buttons. The Add button will add your entered values to the list below the selected point. If the list is empty, it will list your values. If the list is empty and you have not selected a point, clicking on the Add button will bring up a warning message, indicating that you must select a point. The Replace button will replace a selected point with the entered values. The Delete button will remove a selected point from the list.
The Interpolation area of the Node Distribution dialog lets you select the type of interpolation which will be used to control the polyline boundary shape while distributing nodes along it. The interpolation is based on the specified control points.
There are two Interpolation options available:
No interpolation will be performed for NURB lines, circular or conic arcs, as they are treated analytically.
Selected information about a boundary you have selected in the current Tecplot frame is displayed here. The Line Info dialog lists zone number, the user or system defined label, and type of boundary, such as polyline or circular arc. It also lists the number of control points, the starting and ending node indices, the number of the currently selected node, total number of nodes, and IMin and IMax spacing. Imin spacing reports the distance between the boundary's first and second node. IMax Spacing reports the distance between the last and second to last nodes of the boundary.
Algebraic and elliptic meshes are defined by selecting the boundary lines that form the four boundaries (IMin, IMax, JMin, and JMax) of a mesh zone (block). A hyperbolic mesh is defined by selecting boundary lines which form the JMin boundary.
Algebraic and elliptic structured mesh generation requires that all four boundaries (IMin, IMax, JMin, and JMax) surrounding the mesh be specified. Each boundary consists of one or more boundary lines.
If a boundary is composed of more than one boundary line, all lines for this boundary are concatenated to form a single line. The direction of increasing node index is determined by the first line selected in the boundary. Line sections defining a boundary must be added in the order in which they form the boundary. For example, the second line selected will be connected to the first line, the fifth line selected will be connected to the first, second, third, and fourth lines. Mesh Generator requires that each sequential line used in the formation of a mesh boundary share a common node with the previous line.
The number of nodes in both the I- and J-directions is determined by the number of nodes in the corresponding boundaries. The number of nodes for the IMin boundary must equal the number in the IMax boundary; likewise for the JMin and JMax boundaries. The nodes must be coincident at the four corner points formed by the boundaries. The direction of increasing node index must be the same in IMin and IMax boundaries. Similarly, the JMin and JMax boundaries must share the same direction of increasing node index.
The lines selected to define boundaries are shown by zone numbers in the text fields labeled IMin, IMax, JMin, and JMax corresponding to the four boundaries of the mesh. Lines may be selected in one of three ways:
Once you have defined the boundaries for which a mesh, you may select any of the three algebraic methods and three elliptic to generate a structured mesh.
There are six mesh control methods in the Mesh Control section of the Algebraic/Elliptic Structured dialog. The first three represent algebraic methods, and the last three represent elliptic methods. Algebraic methods used in Mesh Generator are based on transfinite interpolation (TFI). These are very fast and usually generate meshes directly acceptable for calculations.
Elliptic methods used in Mesh Generator are based on iterative solution of Poisson's equation. They are often used to improve on the quality, the orthogonality, and to smooth minor irregularities of algebraic meshes.
When an algebraic mesh control option is selected, all other mesh control parameters are inactive. For elliptic methods, some of the below options will be active:
A name can be assigned to each mesh you create. The Mesh Label text field is located at the bottom of the Algebraic/Elliptic Structured dialog, you may enter any characters you wish.
Clicking on the Create button will generate the new structured mesh. For elliptic methods, the Working dialog will appear while the new mesh is generated. The working dialog features a Cancel button. Clicking on the Cancel button stops the mesh generation at the last iteration but does not delete the new mesh zone. When done, the new mesh will be displayed in the current Tecplot frame and added to its data set as an IJ-ordered zone.
Note: During the recording of a macro or project file, a Cancel request is not recorded.
Hyperbolic meshes are created by marching a single JMin boundary in a direction normal to itself, to add a specified number of additional mesh lines. The end points of the boundary can be unconstrained, constrained to a line of constant X or Y, or connected to each other (periodic). The JMin boundary may consist of one or more other boundary lines, which will be concatenated to form a single boundary when the mesh is created. The direction of increasing I-index on the JMin boundary is determined by the first boundary line selected. Boundary lines defining a hyperbolic boundary must be added in the order that they form the boundary. Mesh Generator requires that each sequential line section used in the formation of a boundary to share a common node with the previous line section.
The lines selected to define the JMin edge are shown by zone numbers in the text fields labeled JMin. Line segments may be selected in one of three ways:
The # Layers (JMax) text field on the Hyperbolic Structured dialog indicates the total number of mesh lines in the J-direction (the marching direction), including the JMin boundary line. The Initial Spacing text field indicates the spacing between the JMin boundary and the first generated mesh line. Total Distance is the approximate normal distance between the JMin boundary and the last added mesh line (JMax boundary). Both of these must be positive numbers, and the value for Total Distance must be greater than that in Initial Spacing.
At the IMin and IMax limits of the hyperbolic zone, you may impose one of the following boundary constraints:
Max. Smoothing Passes is a parameter related to an elliptic relaxation performed on each new mesh line. Each new line is created by a hyperbolic marching scheme, then a second "ghost" layer is added by reflecting the previous line across the new line. The node positions in the new line are then relaxed according to an elliptic equation, using the previous layer and the ghost layer as boundaries. Max. Smoothing Passes indicates the maximum number of relaxation iterations the generator will use in the relaxation. Enter 0 for a purely hyperbolic scheme, or a positive number to allow relaxation to occur. Default value for this parameter is set to be 100. Generally, the more convoluted the geometry, the larger the number of smoothing passes. The node positions in the new line are then relaxed according to an elliptic equation, using the previous layer and the ghost layer as boundaries.
The Reverse Marching Direction checkbox is used to reverse the direction normal of the marching. The default direction proceeds to the left of the JMin boundary. Selection this option will cause the marching to proceed to the right of the JMin boundary.
The Replace and Remove 1 Layer buttons are only active when the Edit Selected Mesh... option is selected. The Remove 1 Layer option allows you to remove the last layer of mesh.
A name can be assigned to each mesh you create. The Mesh Label text field is located at the bottom of the Hyperbolic Structured dialog, you may enter any characters you wish.
Clicking on the Create button will generate the new mesh. The Working dialog will appear while the new mesh is generated. The working dialog features a Cancel button. Clicking on the Cancel button stops the mesh generation at the last iteration but does not delete the new mesh zone.
Note: During the recording of a macro or project file, a Cancel request is not recorded. If a project file is saved at this point, however, only the number of layers actually generated will be saved in the file.
In Mesh Generator, an unstructured mesh is formed by filling a boundary-enclosed area with triangular mesh cells. One outer boundary must be specified to enclose the mesh, while an arbitrary number of inner boundaries may be specified to "cut out" portions of the mesh. Inner boundaries generally represent geometries, such as an airfoil in a flow field.
Each closed-loop boundary may consist of more than one boundary line. The outer boundary, along with any inner boundaries, are specified in the Closed-Loop Boundaries area on the Unstructured dialog. Each text line in the Select Mesh Boundary Zone Numbers list represents one boundary. To add a boundary to the list, click on the New Boundary button. This will generate a highlighted empty line shown as (Incomplete) in the field. You may select and use more than one line boundary to make up this boundary. Lines may be chosen in one of two ways:
All boundary lines for a boundary are concatenated to form a single line. The direction of increasing index for the boundary is determined by the first line selected. Boundary lines defining this boundary must be added in the order that they form the boundary.
Mesh Generator requires each sequential boundary line used in the formation of a boundary to share a common node with a previous line. Each boundary must form a closed-loop. Once the last node of a particular boundary coincides with the first node of the same boundary, this boundary is a complete closed-loop. Boundary lines may no longer be added.
The direction of the closed-loop boundary is important. The outer boundary must proceed counter-clockwise around the mesh, while inner boundaries must be clockwise. Mesh Generator will determine whether a boundary is external or internal once it is a closed-loop. An external boundary (counter-clockwise) will have a (Ext-Boundary) label in the list, while an internal boundary will have a (Int-Boundary) label.
Once it is determined whether a boundary is external or internal, the direction of the boundary may be reversed by clicking in the Reverse Direction checkbox. An external boundary will become internal, and vice versa. The boundary's label will be changed accordingly.
To create a mesh with more than one closed-loop boundary, you may click on the New Boundary button as many times as desired. Boundaries may be added in any order.
To remove a boundary from the list, select it, then click the Delete button. To edit a boundary you must first remove it, then create a new boundary.
The Maximum # Cells text field indicates the maximum number of triangular cells which will be used to fill an enclosed region. This number must be greater than the total number of boundary nodes (external and internal boundaries), or an error will be displayed.
It is recommended you not set this number too large, or it may result in the unnecessary usage of memory. The mesh density created by Mesh Generator depends solely on the node distribution along the boundaries. The denser the boundary, the denser the resulting mesh will be.
The Mesh Smoothing checkbox gives you the ability to use a Laplacian-type smoothing operator to smooth small irregularities.
A name can be assigned to any mesh you create. The Mesh Label text field is located at the bottom of the dialog, you may enter any characters you wish.
Clicking on the Create button will create a new unstructured zone and add it to the data set of the current frame. The initial boundary triangulation will be shown in the current frame, then refreshed after each100 points have been inserted. You may interrupt mesh creation by clicking on the Cancel button on the Working dialog.
Note: During the recording of a macro or project file, a Cancel request is not recorded.
Mesh Generator allows you to save mesh zones you create in PLOT3D format or in an augmented Tecplot format which contains boundary and inter-zone connection information. You may specify ASCII or binary. You also have the option of combining mesh zones into a single unstructured zone (triangular or quadrilateral) for use with software which requires purely unstructured meshes.
The Format dropdown on the Mesh Output dialog allows you to select between Tecplot and PLOT3D (FAST) file formats. Two radio buttons just below this menu allow you to specify ASCII or binary. ASCII is recommended for PLOT3D files, if you wish to move between different machine architectures (Windows and Unix, or different Unix platforms). ASCII is also recommended for the Tecplot file format, since software reading the mesh may not be able to read binary Tecplot files.
Mesh Generator allows you to convert all output mesh zones to a single unstructured zone, either triangular or quadrilateral. These options are available in the Mesh Conversion area of the Mesh Output dialog. With either of these options, all output mesh zones are converted to the desired type and combined into a single zone, and redundant nodes and cell edges are eliminated.
Redundant nodes and cell edges are identified using the same logic as is used for identifying inter-mesh zone connections. Each boundary line identified as an inter-mesh connection will result in only a single set of nodes and cell edges, instead of two sets (one for each mesh zone)
Note: The PLOT3D mesh file format does not support quadrilateral unstructured meshes.
Specifying conversion to a single quadrilateral mesh will result in a mesh whose cells are identical in appearance to the cells of each individual mesh being converted. In other words, cells of triangular unstructured meshes will be output as quadrilaterals with one collapsed face, and cells of structured meshes will be output as equivalent quadrilateral cells.
Using this conversion option, it is possible to generate meshes for analysis software which requires quadrilateral unstructured meshes. Quadrilateral cells may be created as an arbitrary number of structured meshes, and then output using this option.
As noted above, all internal boundaries which represent connections between the original meshes are eliminated in the converted mesh. If the mesh is output to a Tecplot mesh file, the boundary regions corresponding to the remaining boundaries are included in the mesh file to enable analysis software to identify cell edges which lie on the boundaries of the mesh.
Specifying conversion to a single triangular mesh will result in each mesh cell of the original meshes being output as one or two triangular cells. To triangulate structured meshes, the cells are divided by the shorter of the two cell diagonals.
This conversion option is useful for boundary layer flow solutions, or other singular perturbation problems where high aspect ratio cells are required. A good triangular boundary layer mesh can be generated by producing a structured mesh in the boundary layer region, and then converting the mesh to triangular upon output.
As with the quadrilateral conversion option, internal boundaries between converted meshes are eliminated, and lines lying on the boundary of the resulting triangular mesh are included as boundary regions in Tecplot mesh files.
This list displays all mesh zones in the dataset of the current Tecplot frame. It includes all meshes created with Mesh Generator, plus any 2D (I-J ordered, triangular, or quadrilateral) zones imported or created with Tecplot commands. Select the mesh zones you with to output by control-clicking in this list.