Curved Structured Mesh
- 1 Parameter File
- 2 Curved Structured Mesh
- 3 Stretching Functions for Curved Structured Meshes
- 4 Sketches
- 5 Output Visualization
- 6 Next Tutorial Section : Mesh Curving by Post-Deformation
This is the parameter file, which is also found in
Curved Structured Mesh
To generate a curved structured mesh the following parameter settings are mandatory:
- Mode=11 (curved structured block with hexahedral elements)
- This mode activates a transformation of the cartesian coordinate system to a turned cylindrical coordinate system. The element distribution which the user can determine by the parameter nElems refers subsequently to the new coordinate system.
- MeshType=3 (for curved mesh)
The HOPR user has to choose whether he wants to generate a half or a full cylindrical mesh. Therefore the new parameter WhichMapping is provided. For specifying the general shape of the (half) cylinder three parameters are provided: R_0, R_INF and DZ. Their meaning is visualized in picture 2. It must be taken into account that the value for the inner radius (R_0) must not be zero and the value for DZ corresponds to the half thickness of the (half) cylinder.
The assignment of the boundary conditions to the surfaces refers also to the new coordinate system but are defined as before by the parameter BCIndex (z-,y-,x+,y+,x-,z+). For the case that the parameter WhichMapping is set to 4 (full cylindrical mesh) the third and fith surface (x+, x-) coincide and the corresponding components of the BCIndex vector has to set to zero.
All new abovementioned parameters are explained below. A description of all parameters of the parameter file can be found in List of Parameters.
|Meshtype||3|| 1: Cube (origin + dimensions)|
2: Bilinear (8 points CGNS notation)
3: Curved (add WhichMapping)
|WhichMapping||4|| Type of mapping using 6 boundary faces to build the curved structured mesh: |
3: Half cylinder
4: Full cylinder
|R_0||0.5||Inner radius of curved structured mesh. The Value 0 is not allowed.|
|R_INF||20||Outer radius of curved structured mesh|
|DZ||2||Dimension in z-direction: [-DZ,DZ]|
Stretching Functions for Curved Structured Meshes
Similar to straight-edged boxes one can generate curved structured meshes with a stretched element arrangement. Therefore three new parameters have to be defined in the parameter file: stretchType, fac and DXmaxToDXmin. In contrast to a cartesian box where two parameters can used individually or in combination to stretch the elements (factor, l0) here a type of stretching has to select with the parameter stretchType. For this reason and the fact that for different stretchTypes different stretching functions are required it is advisable to define all three parameters.
All three parameters are explained below. A description of all parameters of the parameter file can be found in List of Parameters.
|stretchType||(/3,1,0/)|| This parameter manages the (de)activation of the stretching functions for all axis. For this reason the parameter is a vector with three components.
0: Stretching is deactivated
|fac||(/1.5,2.2,10/)|| Stretching factor of the elements in the direction of the turned local cylindrical coordinate axis. A value means an increase of the element size in the direction of the coordinate axis, however, a value of the intervall means a decrease. The value 1 does not affect the element sizes and means an deactivation of the stretching function for this axis. The value 0 is only allowed if the stretching function for this axis is deactivated (stretchType vector component for this axis is 0). Furthermore the stretching behaviour can be mirrored by adding a negative sign to the values. If the stretchType vector component for an axis is 3, the factor will be multiplied by -1 if the half distance is reached. In addition, fac has not the significant influence on the element arrangement anymore but the parameter DXmaxToDXmin.|
In case of (/1.5,2.2,10/) each following element in x-direction is stretched by the factor 1.5, in y-direction by the factor 2.2 and in the direction of the z-axis by the factor 10 (dependent on stretchType)
|DXmaxToDXmin||(/6.,100.,1./)|| This parameter specify the frame ratio of the maximum element size to the minimum element size for the stretched element arrangement. If the stretchType vector component for an axis is 3, the element arrangement is affected significantly by DXmaxToDXmin instead of the parameter fac. |
In case of (/6,100,1/) the maximum element size in x-direction can be 6 times larger than the minimum element size. In y-direction the maximum element size can be 100 times larger than the minimum element size. The value 1, here set for ratio of the z-direction, is used typically for a deactivated stretching.
For a better understanding how the element sizes are calculated the formulas for different stretchType settings are shown below.
- Calculation of the element size for stretchType = 1:
- Calculation of the element size for stretchType = 3:
Exemplary Stretching Cases
Furthermore, three different stretching cases are presented below with a full circle (WhichMapping=4) and an element distribution nElems=(/8,6,4/). Just x- and y- values were visualized.
In the following two exemplary curved structured meshes are presented. The first mesh shall consist of twelve elements in x-direction, eight elements in y-direction and four elements in z-direction, all equidistant. The sketch of this problem is shown in picture 6. The belonging parameter file can be found in Parameterfile Curved Structured Mesh.
The second one consists of the same number of elements in each direction but instead of an equidistant element arrangement the elements shall be stretched. This sketch is presented in picture 7. To get the corresponding output by HOPR one have to edit the Parameterfile Curved Structured Mesh manually before executing because the stretching functions stretchType, fac and DXmintoDXmax are commended out.
If there is a need for assistance of visualizing the HOPR output visit Visualization.