A boundary in 3D has two principal curvatures corresponding to the minimal and maximal normal curvatures. They are called curv1 and curv2, respectively. See Curvature Variables for details.
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The domain number, the boundary number, the edge number, or the vertex (point) number (all are integer values). The variable sd also exists as an alias but is considered obsolete.
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The volume scale factor variable, dvol, is the determinant of the Jacobian matrix for the mapping from local (element) coordinates to global coordinates.
For 3D domains, this is the factor that the software multiplies volumes by when moving from local coordinates to global coordinates. On surfaces in 3D and domains in 2D, it is an area scaling factor. On edges in 3D and 2D, and in 1D domains, it is a length scaling factor. In points of all dimensions, dvol is always equal to 1 by definition.
If a moving mesh is used, dvol is the mesh element scale factor for the material frame mesh. The corresponding factor for the spatial mesh is named dvol_spatial. Similarly for geometry frame and mesh frame, the factors are named dvol_geometry and dvol_mesh, respectively.
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Available on all geometric entities, the variable h represents the mesh element size in the material/reference frame (that is, the length of the longest edge of the element).
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The variable reldetjacmin is a scalar for each element defined as the minimum value of the reldetjac variable for the corresponding element.
A reldetjacmin value less than zero for an element means that the element is wrapped inside-out; that is, the element is an inverted mesh element.
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tcurvy (2D)
tcurv2z (3D)
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Tangential directions for the corresponding curvatures. See Curvature Variables for more information.
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r, z
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Local (barycentric) coordinates ξ i in each mesh element; see the section Finite Elements in the Elements and Shape Functions chapter.
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When entering the spatial coordinate, parameterization, tangent, and normal geometric variables, replace the letters highlighted below in an italic font with the actual names for the dependent variables (solution components) and independent variables (spatial coordinates) for the Component node.
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For a Cartesian geometry the default names for the spatial coordinates are x, y, and z (for the x, y, and z coordinates).
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For axisymmetric geometries the default names for the spatial coordinates are r, phi, and z (for the r, , and z coordinates).
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If a deformed mesh is used, x, y, z can be both the spatial coordinates (x, y, z) and the material/reference coordinates (X, Y, Z); see Mathematical Description of the Mesh Movement.
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If the model includes a deformed mesh, the variables xTIME, yTIME, and zTIME represent the mesh velocity. To access these variables, replace x, y, and z with the names of the spatial coordinates in the model (x, y, and z).
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If the model includes a deformed geometry, the default names for the spatial coordinates in the geometry frame and the mesh frame are Xg, Yg, and Zg (for the xg, yg, and zg coordinates).
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Most physics interfaces are based on a formulation which is either Eulerian or Lagrangian. They therefore lock their dependent variables to the spatial or the material frame, and the spatial derivatives are then defined with respect to x, y, and z (spatial frame) or X, Y, and Z (material frame), when using the default names for the spatial coordinates. See Differentiation in Space.
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The curve parameter s (or s1) in 2D. Use a line plot to visualize the range of the parameter, to see if the relationship between x and y (the spatial coordinates) and s is nonlinear, and to see if the curve parameterization is aligned with the direction of the corresponding boundary. In most cases it runs from 0 to 1 in the direction indicated by the arrows shown on the edges when in the boundary or edge selection mode and if you have selected the Show edge direction arrows check box in the Settings window for View (). You can use s on boundaries in 2D when specifying boundary conditions.
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The arc length parameter s1 available on edges in 3D. It is approximately equivalent to the arc length of the edge. Use a line plot to visualize the values of s1.
The surface parameters s1 and s2 in 3D are available on boundaries (faces). They can be difficult to use because the relationship between x, y, and z (the spatial coordinates) and s1 and s2 is nonlinear. Often it is more convenient to use expressions with x, y, and z for specifying distributed boundary conditions. To see the values of s1 and s2, plot them using a surface plot.
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In 3D, the tangent variables t1x, t1y, and t1z are defined on edges. The tangent variables t1x, t1y, t1z, t2x, t2y, and t2z are defined on surfaces according to
These most often define two orthogonal vectors on a surface, but the orthogonality can be ruined by scaling geometry objects. The vectors are normalized; ki is a normalizing parameter in the expression just given.
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The local relative element volume, spatial.relVol, is a quantity that measures the local volumetric distortion of the elements. When this measure approaches zero in some part of the mesh, frame transformations become singular causing solvers to fail.
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The minimum relative element volume, spatial.relVolMin, must be > 0; otherwise, the mesh elements are inverted. A suitable stop criterion using this variable is that the minimum relative element volume must be larger than a small positive number.
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The maximum relative element volume, spatial.relVolMax, is a positive scalar number that represents the maximum value of the relative element volume.
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The minimum mesh quality, spatial.minqual, must be > 0; an acceptable mesh quality is typically larger than 0.1 (where the quality measure is a number between 0 and 1).
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