+ Fig. 1.1 Overall view of initial mesh 1
+
+ Fig. 1.2 Close-up image of mesh 1 of the leading edge of the NACA-profile
+|
+
+ Fig. 1.1 Overall view of initial mesh 1 + |
+
+
+ Fig. 1.2 Close-up image of mesh 1 of the leading edge of the NACA-profile + |
+
+ 
+ Fig. 1.3 Overall view of initial mesh 2 + |
+
+ 
+ Fig. 1.4 Close-up image of mesh 2 of the leading edge of the NACA-profile + |
+
+ Fig. 1.5 Block-structuring with the parameter BoundaryOrder=2/3/5, (BoundaryOrder-1)^3 elements are grouped together.
+
+ 
+ Fig. 1.6 Front view of the leading edge with the initial mesh configuration. All elements and edges are linear. + |
+
+ 
+ Fig. 1.7 Front view of the leading edge of the mesh with the following setting: |
+
+ 
+ Fig. 1.8 Generated curved high order mesh by agglomeration. + |
+
+ 
+ Fig. 1.9 Initial mesh 1 |
+
+ 
+ Fig. 1.10 Mesh by following parameter setting: |
+
+ 
+ Fig. 1.11 Generated curved high order mesh by agglomeration. + |
+
+ 
+ Fig. 1.12 Generated curved high order mesh by agglomeration. + |
+
+ 
+ Fig. 1.13 View of mesh 1 by following parameter setting: |
+
+ 
+ Fig. 1.14 View of mesh 1 by following parameter setting: |
+
+
+ Fig. 1.15 View of mesh 1 by following parameter setting: |
+
+ 
+ Fig. 1.16 Oblique view of mesh 1 by following parameter setting: |
+
+ Fig. 2.1 Transformation of the coordinate system.
+
+ Fig. 2.2 Visualization of the parameters which determine the shape.
+
+ Fig. 2.3 Plot of the calculation function if the parameter `stretchType` is set to 3 ($ f $ means `fac`, $ \frac{\Delta x_{max}}{\Delta x_{min}} $ means `DXmaxToDXmin`). If the value of fac increases, the peakedness will increase and the element sizes near the bonudaries will decrease.
+
+ 
+ Fig. 2.4 Non-stretched element arrangement. |
+
+ 
+ Fig. 2.5 Stretched element arrangement. The element size in the direction of the x-axis increases by a factor of 1.5. In the direction of the y-axis it increases by the factor of 2.2. |
+
+ 
+ Fig. 2.6 The `stretchType` parameter is set to 3 for the x-axis. The plot of the belonging calculation function shows that the element sizes increase immediately. In the direction of the y-axis the element size increases by the factor of 2.2. |
+
+ 
+ Fig. 2.7 The `stretchType` parameter is set to 3 for the x-axis and the y-axis. although the fac values are different the plots of the belonging calculation function looks very similar to each other. |
+
+ 
+ Fig. 2.8 Sketch of the 1 zone curved structured mesh. The full cirlce mesh ( |
+
+ 
+ Fig. 2.9 Sketch of the 1 zone curved structured mesh with a stretched element arrangement. For the x-direction the |
+
+ 
+ Fig. 2.10 Curved structured mesh + |
+
+ 
+ Fig. 2.11 Inner domain of the curved structured mesh + |
+
+ 
+ Fig. 2.12 Curved structured mesh with stretched element arrangement. + |
+
+ 
+ Fig. 2.13 Inner domain of the curved structured mesh with stretched element arrangement + |
+
+ 
+ Fig. 2.14 |
+
+ 
+ Fig. 2.15 |
+
+ 
+ Fig. 2.16 Outer circular mapping with parameter2.ini + |
+
+ 
+ Fig. 2.17 9 block mesh with stretching parameter3.ini + |
+
+ 
+ Fig. 2.18 |
+
+ 
+ Fig. 2.19 |
+
+ 
+ Fig. 2.20 |
+
+ 
+ Fig. 2.21 |
+
+ 
+ Fig. 2.22 parameter_shell.ini, |
+
+ 
+ Fig. 2.23 parameter_shell.ini, |
+
+ Fig. 2.1 From linear meshes to high order meshes.
+
+ Fig. 2.2 Sequence of constructing curved element edges from surface normals..
+
+ 
+ Fig. 2.3 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.4 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file. |
+
+ 
+ Fig. 2.5 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file. |
+
+ 
+ Fig. 2.6 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions. |
+
+ 
+ Fig. 2.7 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.8 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file. |
+
+ 
+ Fig. 2.9 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file. |
+
+ 
+ Fig. 2.10 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions. |
+
+ 
+ Fig. 2.11 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.12 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file. |
+
+ 
+ Fig. 2.13 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file. |
+
+ 
+ Fig. 2.14 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions. |
+
|
+
+ Fig. 2.15 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.15 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_04.cgns file. |
+
+ 
+ Fig. 2.16 Boundary sphere by using the sphere_surfmesh_06.cgns file. Because of the fact that this subdivision pattern was created neither with a double nor with a triple subdivision of the surface mesh the parameter boundaryOrder has to be adapted accordingly. |
+
+ 
+ Fig. 2.17 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file. |
+
|
+
+ Fig. 2.18 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.19 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file. |
+
+ 
+ Fig. 2.20 Boundary sphere by using the sphere_surfmesh_10.cgns file. Because of the fact that this subdivision pattern was created neither with a double nor with a triple subdivision of the surface mesh the parameter boundaryOrder has to be adapted accordingly. |
+
+ 
+ Fig. 2.21 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_16.cgns file. |
+
|
+
+ Fig. 2.22 Boundary sphere without using a curving technique. + |
+
+ 
+ Fig. 2.23 Boundary sphere with a single subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file. |
+
+ 
+ Fig. 2.24 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_16.cgns file. |
+
+ 
+ Fig. 2.25 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_36.cgns file. |
+
+ Fig. 2.26 Curved mesh file created by Gmsh..
+
+ Fig. 1.1 Screenshot of the folder structure of a CGNS mesh.
+
+ 
+ Fig. 1.2 HOPR output of spheremesh01.cgns + |
+
+ 
+ Fig. 1.3 HOPR output of spheremesh01.cgns with extracted edges. + |
+
+ 
+ Fig. 1.4 Element surfaces (6) of spheremesh01.cgns the boundary condition sphere was assigned to. + |
+
+ 
+ Fig. 1.5 HOPR output of spheremesh02.cgns + |
+
+ 
+ Fig. 1.6 HOPR output of spheremesh02.cgns with extracted edges. + |
+
+ 
+ Fig. 1.7 Element surfaces (24) of spheremesh02.cgns the boundary condition sphere was assigned to. + |
+
+ 
+ Fig. 1.8 HOPR output of spheremesh04.cgns + |
+
+ 
+ Fig. 1.9 HOPR output of spheremesh04.cgns with extracted edges. + |
+
+ 
+ Fig. 1.10 Element surfaces (64) of spheremesh04.cgns the boundary condition sphere was assigned to. + |
+
+ 
+ Fig. 3.1 Mesh consisting of 6 tetrahedra + |
+
+ 
+ Fig. 3.2 Each tetrahedron subdivided into 4 hexahedra + |
+
+ 
+ Fig. 2.1 Standard mesh + |
+
+ 
+ Fig. 2.2 All elements refined by a factor of 2 + |
+
+ 
+ Fig. 1.1 NACA-profile with all elements curved + |
+
+ 
+ Fig. 1.2 NACA-profile with only the profile boundary curved + |
+
+ 
+ Fig. 1.3 NACA-profile with the first cell curved + |
+
+ 
+ Fig. 1.4 NACA-profile with the first three cells curved + |
+
+ Fig. 1.1 HOPR output: Mesh of multiple cartesian boxes with a stretched element arrangement.
+
+ 
+ Fig. 1.2 Sketch of the current problem + |
+
+ 
+ Fig. 1.3 Cartesian Box Boundary Conditions ini-File + |
+
+Fig. 1.4 Mesh of the cartesian box
+
+ 
+ Fig. 1.5 Boundary condition 1 (BC_wall) is assigned to surface 1 + |
+
+ 
+ Fig. 1.6 Boundary condition 2 (BC_inflow) is assigned to surface 2 + |
+
+ 
+ Fig. 1.7 Boundary condition 3 (BC_outflow) is assigned to surface 3 + |
+
+ 
+ Fig. 1.8 Boundary condition 4 (BC_yplus) is assigned to surface 4 + |
+
+ 
+ Fig. 1.9 Boundary condition 5 (BC_xminus) is assigned to surface 5 + |
+
+ 
+ Fig. 1.10 Boundary condition 6 (BC_zplus) is assigned to surface 6 + |
+
+ 
+ Fig. 1.11 Sketch of Example 1 + |
+
+ 
+ Fig. 1.12 Cartesian Box example 1 Boundary Conditions ini-File + |
+
+Fig. 1.13 Mesh of the cartesian box
+
+ 
+ Fig. 1.14 Boundary condition 1 (BC_wall) is assigned to surface 1-4 + |
+
+ 
+ Fig. 1.15 Boundary condition 2 (BC_inflow) is assigned to surface 5 + |
+
+ 
+ Fig. 1.16 Boundary condition 3 (BC_inflow) is assigned to surface 6 + |
+
+ 
+ Fig. 1.17 Sketch of Example 2 + |
+
+ 
+ Fig. 1.18 Cartesian Box example 2 Boundary Conditions ini-File + |
+
+ Fig. 1.19 Mesh of the cartesian box
+
+ 
+ Fig. 1.20 Boundary condition 1 (BC_wall) is assigned to surfaces 1, 3 and 6 + |
+
+ 
+ Fig. 1.21 Boundary condition 2 (BC_inflow) is assigned to surface 5 + |
+
+ 
+ Fig. 1.22 Boundary condition 3 (BC_outflow) is assigned to surface 2 and 4 + |
+
+ Fig. 1.23 Sketch of the current problem; For a greater clarity in this figure the displacement vectors are shown shorter than they are. In truth the vector arrows are as long as the side length of the cartesian box.
+
+ Fig. 1.24 Cartbox periodic ini-File.
+
+ Fig. 1.25 Sketch of the current problem; For a greater clarity in this figure the displacement vectors are shown shorter than they are. In truth the vector arrows are as long as the side length of the cartesian box.
+
+ Fig. 1.26 Mesh of the multiple cartesian boxes.
+
+ 
+ Fig. 1.27 Boundary condition 1 (BC_slipwall) is assigned to surface 1 of the first box + |
+
+ 
+ Fig. 1.28 Boundary condition 2 (BC_upperwall) is assigned to surface 6 of the second and the third box + |
+
+ 
+ Fig. 1.29 Boundary condition 3 (BC_lowerwall) is assigned to surface 3 of the first box and to surface 1 of the third box + |
+
+ 
+ Fig. 1.30 Boundary condition 4 (BC_inflow) is assigned to surface 5 of the first and the second box + |
+
+ 
+ Fig. 1.31 Boundary condition 5 (BC_outflow) is assigned to surface 3 of the third box + |
+
+ 
+ Fig. 1.32 Periodic boundary condition 6 (BC_yminus) is assigned to surface 2 of the first, the second and the third box + |
+
+ 
+ Fig. 1.33 Periodic boundary condition 7 (BC_yplus) is assigned to surface 4 of the first, the second and the third box + |
+
+ Fig. 1.34 "Stretch parameters" `factor` and `l0`
+
+ 
+ Fig. 1.35 Non-stretched element arrangement |
+
+ 
+ Fig. 1.36 Stretched element arrangement. The element size in the direction of the x-axis increases by a factor of 1.5. In the direction of the y-axis it decreases by the factor of -1.2. |
+
+ 
+ Fig. 1.37 Stretched element arrangement. The first element in the direction of the x-axis has a length of 0.5 and a length of 0.2 in the direction of the y-axis. The parameter factor is adjusted. |
+
+ 
+ Fig. 1.38 Stretched element arrangement with a combination of factor and l0. The parameter l0 defines the side lengths of the first element. The following element sizes are multiplied by the compontens of the parameter factor. The number of elements N which is defined by the parameter nElems is not retained. |
+
+ Fig. 1.39 Sketch of a mesh with multiple cartesian boxes with a stretched element arrangement. The arrows show in which direction the elements are compressed. The elements are getting smaller the closer the elements get to the cartesian x-y-plane and y-z-plane. The elements in the direction of the cartesian y-axis remain equidistant.
+
+ Fig. 1.40 Side view of the mesh of the multiple cartesian boxes with a stretched element arrangement.
+
+ Fig. 1.41 Mesh of the multiple cartesian boxes with a stretched element arrangement.
+
+ Fig. 1.1
+
+ 
+ Fig. 1.2 + |
+
+ 
+ Fig. 1.3 + |
+
+ 
+ Fig. 1.4 + |
+
+ 
+ Fig. 1.5 + |
+
+ 
+ Fig. 1.6 + |
+
+ 
+ Fig. 1.7 + |
+
+ Fig. 1.8
+
+ Fig. 1.9
+