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263d367..913fb5d 100644 --- a/docs/documentation/index.md +++ b/docs/documentation/index.md @@ -29,6 +29,18 @@ caption: Developer Guide developerguide/index.md ``` +```{toctree} +--- +maxdepth: 4 +caption: Tutorials +--- +tutorials/index_inbuiltmeshgenerators.md +tutorials/index_externalmeshes.md +tutorials/index_agglomeration.md +tutorials/index_postprocessing.md +tutorials/index_visualization.md +``` + ```{toctree} --- maxdepth: 1 diff --git a/docs/documentation/tutorials/blockstructuredmeshes.md b/docs/documentation/tutorials/blockstructuredmeshes.md new file mode 100644 index 0000000..360a86e --- /dev/null +++ b/docs/documentation/tutorials/blockstructuredmeshes.md @@ -0,0 +1,251 @@ +# Block-Structured Meshes +This tutorial shows how to agglomerate block-structured grids with linear elements to get a curved mesh consisting of fully curved hexahedral elements. + +The parameter file can be found in + + tutorials/3-01-agglomeration_NACA/parameter.ini + +## Restrictions on the block-structured mesh readin + +- If meshes are used to create curved elements, a **unique factor** should be present in the i,j,k element count of **all blocks**!! +- Boundary Conditions: + - Attention: **One block face** can only be associated to **one boundary condition**. Block faces with mixed BCs or BC and internal faces a likely to produce wrong mesh topology!! + **Split blocks** in this case, else you will get problems in the mesh connect step! + - Each boundary conditions must be specified in the inifile by its name and an associated Boundary Type: + + BoundaryName = wall_1 + BoundaryType = (/4,0,0,0/) + BoundaryName = wall_2 + BoundaryType = (/4,0,0,0/) + + +You can combine multiple BCs by using only a common part of the boundary name string (here for example `BoundaryName=wall`) + +## Initial Meshes + +The use of block-structured meshes enables the generation of fully three-dimensional curved elements by agglomeration of a specific block of elements, leading to a very simple and robust curving technique. In order to illustrate block-structuring and agglomeration, enabled by the new parameter `MeshIsAlreadyCurved`, two initally fine meshes of a NACA-profile are provided as CGNS files, mesh 1 without boundary layer refinement and mesh 2 with boundary layer refinement: + +
Mesh1: NACA0012_icem_32elems.cgns
+ + + + + + +
+
+ ../_images/Aggl-nv-fern.jpg +
+

Fig. 1.1 Overall view of initial mesh 1

+
+
+
+
+ ../_images/Aggl-nv-nah.jpg +
+

Fig. 1.2 Close-up image of mesh 1 of the leading edge of the NACA-profile

+
+
+
+ +
Mesh2: NACA0012_icem_viscous_32elems.cgns
+ + + + + + +
+
+ ../_images/Aggl-v-fern.jpg +
+

Fig. 1.3 Overall view of initial mesh 2

+
+
+
+
+ ../_images/Aggl-v-nah.jpg +
+

Fig. 1.4 Close-up image of mesh 2 of the leading edge of the NACA-profile

+
+
+
+ +All of the following figures were created with mesh 1. + +

Agglomeration Curving Technique

+When using agglomeration, the important parameters are + + MeshIsAlreadyCurved=T + useCurved=T + BoundaryOrder=5 + +and they lead to a coarsening in all three dimensions of the structured mesh, using the internal points as interpolation points for the curved mapping. The number of elements in each direction of the structured block must be a multiple number of `BoundaryOrder-1`!!! This situation is explained on an exemplary mesh in Fig. 1.5. For `BoundaryOrder = 2` the initial linear mesh is found and no agglomeration is done. + +
+ ../_images/Nskip.jpg +
+

Fig. 1.5 Block-structuring with the parameter BoundaryOrder=2/3/5, (BoundaryOrder-1)^3 elements are grouped together.

+
+
+ +In addtion, the parameter `nskip` to coarsen the initial mesh. + +## Description of Parameters + +Below all new parameters that are associated with agglomeration are explained. A description of all parameters can be found in {ref}`userguide/parameters:List of Parameters`. + +```{table} Block-Structured Meshes: Description of Parameters. +--- +name: tab:Block-Structured Meshes Description of Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `MeshIsAlreadyCurved` | `T` | T (True): Enables the agglomeration
F (False): Disables the agglomeration | + | `nskip` | `2` | Coarsen block-structured meshes:
1: no skip
2: use every second point
... | + | `nskipZ` | `2` | Only if the mesh is extruded in z-direction, a different nskip can be given in z-direction. | +``` + + + + + + + +
+
+ ../_images/Aggl-c1.jpg +
+

Fig. 1.6 Front view of the leading edge with the initial mesh configuration. All elements and edges are linear.

+
+
+
+
+ ../_images/Aggl-c2.jpg +
+

Fig. 1.7 Front view of the leading edge of the mesh with the following setting: BoundaryOrder = 5. One block consists of 4x4x4 = 64 elements. The blocks' edges (blue lines) are the boundary of the curved elements. The initial structured mesh is shown in grey. All nodes/connections of the white lines are interpolation points

+
+
+
+
+ ../_images/Aggl-c3.jpg +
+

Fig. 1.8 Generated curved high order mesh by agglomeration.

+
+
+
+ +

Coarsening

+For coarsening two new parameters are provided: `nskip` applies to all structured directions equally, and `nskipZ` can be used for z-extruded meshes.
+ +`nskip` Variations:
+ + + + + + + + +
+
+ ../_images/Aggl-nv-skip0.jpg +
+

Fig. 1.9 Initial mesh 1 nskip =1

+
+
+
+
+ ../_images/Aggl-nv-skip2.jpg +
+

Fig. 1.10 Mesh by following parameter setting: nskip =2

+
+
+
+
+ ../_images/Aggl-nv-skip4.jpg +
+

Fig. 1.11 Generated curved high order mesh by agglomeration.

+
+
+
+
+ ../_images/Aggl-nv-skip8.jpg +
+

Fig. 1.12 Generated curved high order mesh by agglomeration.

+
+
+
+ +The mesh on the left side shows the initial mesh with an initial element, shown in grey. The parameter `nskip=1` uses every point of the initial mesh. The mesh in the middle shows the mesh if `nskip` is set to 2. That means that one node in each direction of the respective coordinate system is skipped and that the size of the new element reaches to the next node. The skipped nodes will not be used for the mesh anymore, also not for curving. +The parameter `nskipZ` is has the same function as `nskip` but only for the z-direction. As a consequence of a setting of this parameter the skip level in z-direction by the parameter `nskip` will be repealed.
+ +In section Output Visualization a few different parameter settings are illustrated for the NACA-profile. Take into account that the block-structuring will only work if the value for the parameter(s) `nskip` (and `nskipZ`) is a common divisor of the number of all mesh elements for each axis!!!> + +`nskip`-`nskipZ` Combinations: + + + + + + + + +
+
+ ../_images/Aggl-nv-skip2z-.jpg +
+

Fig. 1.13 View of mesh 1 by following parameter setting: nskip = 2 !nskipZ = ..

+
+
+
+
+ ../_images/Aggl-nv-skip2z1.jpg +
+

Fig. 1.14 View of mesh 1 by following parameter setting: nskip = 2 nskipZ = 1

+
+
+
+
+ ../_images/Aggl-nv-skip2z-.jpg +
+

Fig. 1.15 View of mesh 1 by following parameter setting: nskip = 2 nskipZ = 2

+
+
+
+
+ ../_images/Aggl-nv-skip2z2.jpg +
+

Fig. 1.16 Oblique view of mesh 1 by following parameter setting: nskip = 2 nskipZ = 4

+
+
+
+ +

Correction for z-extruded Meshes

+ +This function does not only apply to block-structured meshes, but to all meshes which are extruded along the z-direction! There are five more new parameters by which one can change special properties of z-extruded meshes like for example length, starting point. + +```{table} Correction for z-extruded Meshes: Description of Parameters. +--- +name: tab:Correction for z-extruded Meshes Description of Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `doZcorrection` | `F` | T (True): Can only be applied to z-extruded meshes: All elements are aligned exactly along z-direction to suppress grid generator errors
F (False): Correction is disabled | + | `nElemsZ` | `1` | The number of elements in z-direction (after agglomeration!) | + | `zstart` | `0.` | Set minimum z-coordinate | + | `zLength` | `1.0` | Set length of domain in z-direction | + | `zperiodic` | `T` | T (True): The Boundary conditions (here `z_plus` and `z_minus`) are set to periodic ones.
F (False): Default. No change of the boundary condition. | +``` + +The boundary periodicity can be set here to be applied after the mesh connectivity process. The boundary condition type of the z-faces should then be set to >1,(because of tolerance issues, problems during connectivity process are found if the boundary conditions are set to periodic) and then periodicity is then applied afterwards in the z-correction process. + +## Output Visualization + +The figures here were visualizations of the mesh `NACA0012_icem_32elems.cgns`. Therefore, the files `NACA0012_VISCOUS_Debugmesh.vtu` (Fig. 1.1 - Fig. 1.4, Fig. 1.9 - Fig. 1.16) and `NACA0012_VISCOUS_SplineVol.vtu` (Fig. 1.6 - Fig. 1.8) were used. The volume visualization can become quickly a large file. The number of elements can be reduced by the parameter + + Visu_sJ_limit= 0.1 ! for DebugvisuLevel=2, only write elements with a scaled Jacobian < given limit + +that skips elements with a scaled Jacobian > limit.
+ +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. \ No newline at end of file diff --git a/docs/documentation/tutorials/curvedmeshes.md b/docs/documentation/tutorials/curvedmeshes.md new file mode 100644 index 0000000..f49c886 --- /dev/null +++ b/docs/documentation/tutorials/curvedmeshes.md @@ -0,0 +1,398 @@ +# Curved Meshes +## Curved Structured Mesh +This tutorial shows how to generate a curved structured mesh with an equidistant or with a stretched element arrangement alternatively. +The parameter file can be found in + + tutorials/1-05-curved_structured/parameter.ini + + +### Curved Structured Mesh: Description of Parameters +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. + +
+ ../_images/Carttocurve.jpg +
+

Fig. 2.1 Transformation of the coordinate system.

+
+
+ +- `nZones=1` +- `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 Fig. 2.2. 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. + +
+ ../_images/CurveCOS.jpg +
+

Fig. 2.2 Visualization of the parameters which determine the shape.

+
+
+ +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 {ref}`userguide/parameters:List of Parameters`. + +```{table} Curved Structured Mesh: Description of Parameter. +--- +name: tab:Curved_Structured_Mesh_Description_of_Parameter +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `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]` | +``` + +### Curved Structured Mesh: Stretching Functions +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 {ref}`userguide/parameters:List of Parameters`. +```{table} Curved Structured Mesh: Stretching Functions. +--- +name: tab:Curved_Structured_Mesh_Stretching_Functions +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `stretchTypetype` | ` (/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
1: Stretching with a factor
2: Stretching with a legnth ratio
3: Stretching with a bell function. | + | `fac ` | `(/1.5,2.2,10/)` | Stretching factor of the elements in the direction of the turned local cylindrical coordinate axis. A value >1 means an increase of the element size in the direction of the coordinate axis, however, a value of the intervall (0,1) 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. | +``` + +

Calculation Formulas

+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`: + + $$ {\Delta x_{i+1} = f \cdot \Delta x_{i} f = \left(\frac{\Delta x_{max}}{\Delta x_{min}} \right)^{1/(nElems - 1)} }$$ + +- Calculation of the element size for `stretchType = 3`:
+ + $$ \Delta x(\xi) \sim 1 + \left( \frac{\Delta x_{max}}{\Delta x_{min}}-1\right)\cdot \left( \frac{\exp[-(\xi \cdot f)^2] - \exp[-f^2]}{\exp[0] - \exp[-f^2]}\right) $$ + +
+ ../_images/Stretching-math.jpg +
+

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.

+
+
+ + +

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. + + + + + + + + +
+
+ ../_images/Stretch-curve_ex1.jpg +
+

Fig. 2.4 Non-stretched element arrangement.
nElems =(/8,6,4/)
+ stretchType =(/1,1,0/)
+ fac =(/1,1,0./)
+ DXmaxToDXmin =(/100.,100.,1/)

+
+
+
+
+ ../_images/Stretch-curve_ex2.jpg +
+

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.
nElems =(/8,6,4/)
+ stretchType =(/1,1,0/)
+ fac =(/1.5,2.2,0./)
+ DXmaxToDXmin =(/100.,100.,1/)

+
+
+
+
+ ../_images/Stretch-curve_ex3.jpg +
+

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.
nElems =(/8,6,4/)
+ stretchType =(/3,1,0/)
+ fac =(/1.5,2.2,0./)
+ DXmaxToDXmin =(/100.,100.,1/)

+
+
+
+
+ ../_images/Stretch-curve_ex4.jpg +
+

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.
nElems =(/8,6,4/)
+ stretchType =(/3,3,0/)
+ fac =(/1.5,2.2,0./)
+ DXmaxToDXmin =(/100.,100.,1/)

+
+
+
+
+
+ + +### Curved Structured Mesh: Sketchs + +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 Fig. 2.8. 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 Fig. 2.9. 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. + + + + + + +
+
+ ../_images/Cylinder.jpg +
+

Fig. 2.8 Sketch of the 1 zone curved structured mesh. The full cirlce mesh (WhichMapping=4) shall consist of twelve elements in x-direction, eight elements in y-direction and four elements in z-direction, all equidistant.

+
+
+
+
+ ../_images/Cylinder2.jpg +
+

Fig. 2.9 Sketch of the 1 zone curved structured mesh with a stretched element arrangement. For the x-direction the stretchType parameter was set to 3. The parameter DXmaxToDXmin was set to 6 and the parameter fac to 1.5. For the y-direction the stretchType parameter was set to 1 and the elements were stretched by the factor 2.2. The elements in z-direction remain equidistant.

+
+
+
+ +### Curved Structured Mesh: Outout Visualization +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. + +

Curved Structured Mesh without Stretched Elements

+ + + + + + +
+
+ ../_images/Curvedtotal.jpg +
+

Fig. 2.10 Curved structured mesh

+
+
+
+
+ ../_images/Curvedinner.jpg +
+

Fig. 2.11 Inner domain of the curved structured mesh

+
+
+
+ +

Curved Structured Mesh with Stretched Elements

+ + + + + + +
+
+ ../_images/Curvedstretchedtotal.jpg +
+

Fig. 2.12 Curved structured mesh with stretched element arrangement.

+
+
+
+
+ ../_images/Curvedstretchedinner.jpg +
+

Fig. 2.13 Inner domain of the curved structured mesh with stretched element arrangement

+
+
+
+ +## Mesh Curving by Post-Deformation +This tutorial shows how to generate a curved multi-block mesh, composed of several structured boxes, which are first assembled and then globally mapped to a curved domain +The parameter file can be found in + + tutorials/1-06-curved-postdeform/parameter.ini + +### Mesh Curving by Post-Deformation: User-defined Variables +User-defined varibles can be used to parametrize the parameterfile. + +User-defined variables are searched and replaced in **all other lines(!)** of the parameterfile (all strings between the = and ! sign are searched). They are either an Integer or Real value and defined in the parameterfile as + + DEFVAR=(INT): i0 = 002 ! no. elems in inner square i0xi0 + DEFVAR=(REAL): ri = 0.5 ! inner square dim + +Note that each variable is searched and replaced one after the other, so that names should be absolutely unique. In the example, a variable called ri0 would not be allowed. + +### Mesh Curving by Post-Deformation: Post-Deformation from a box to a cylinder +The idea is to build first a simple box using the internal mesh procedures explained in Multiple Cartesian Boxes and then use a deformation function to obtain a cylinder. The post-deformation parameter is + + MeshPostDeform=1 + +The undeformed and deformed mesh is shown in Fig. 2.14 and Fig. 2.15. + +The order of the curved element mapping can be chosen arbitrarily + + useCurveds =T + BoundaryOrder=5 + + + + + + +
+
+ ../_images/Nopost.jpg +
+

Fig. 2.14 MeshPostDeform=0 +

+
+
+
+
+ ../_images/Withpost.jpg +
+

Fig. 2.15 MeshPostDeform=1

+
+
+
+ +The mapping function maps the xy [-1;1]^2 coordinates to a circular domain of radius 1, but smoothed towards the center to avoid a singular mesh. The radius can be scaled with the parameter + + MeshPostDeform_R0=1.0 + +We choose a periodic boundary condition in z direction. + +### Mesh Curving by Post-Deformation: Parameter Variations +In a variant of the parameterfile, parameter2.ini, the extend of the domain in xy is [-2;2]^2 and is mapped to a circular domain with a radius of 2. The part of the domain inside [-1;1]^2 is mapped like in the example above, but ouside of [-1;1]^2, the mapping is perfectly circular. A final radius of 1 is then achieved by setting the scaling factor to + + MeshPostDeform_R0=0.5 + +see Fig. 2.16. + +In another variant of the parameterfile, parameter3.ini, a mesh with 9 zones in built, and refined at a specific radius, using the stretching functions explained in Stretching Functions, see Fig. 2.17. + + + + + + +
+
+ ../_images/Cylinder_param2.jpg +
+

Fig. 2.16 Outer circular mapping with parameter2.ini

+
+
+
+
+ ../_images/Cylinder_param3.jpg +
+

Fig. 2.17 9 block mesh with stretching parameter3.ini

+
+
+
+ +### Mesh Curving by Post-Deformation: Output Visualization +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. + +## Curved Torus +The same Post-Deformation applied to generate a torus +The parameter file can be found in + + tutorials/1-07-curved-torus/parameter.ini + +### Curved Torus: Post-Deformation from a box to a torus +Analogously to the previous tutorial Mesh Curving by Post-Deformation, we deform a box to a torus with a circular cross section. We only add the main radius of the torus as a parameter + + MeshPostDeform = 1 ! deforms [-1,1]^2 to a cylinder with radius Postdeform_R0 + PostDeform_R0 = s0 ! here domain is [-2,2]^2 mapped to a cylinder with radius 0.5*2 = 1 + PostDeform_Rtorus = rz ! z must be inside [0,1] and periodic + +Since the connectivity of the mesh is created before the deformation, the boundary condition in z direction must be periodic on the undeformed mesh. The torus then has the correct connectivity. + + + + + + +
+
+ ../_images/Nopost_torus.jpg +
+

Fig. 2.18 MeshPostDeform=0

+
+
+
+
+ ../_images/Torusmesh_q0.jpg +
+

Fig. 2.19 MeshPostDeform=1

+
+
+
+ + +## Curved Sphere +The same Post-Deformation applied to generate a mesh of a sphere and a sphherical shell +The parameter file can be found in + + tutorials/1-08-curved-sphere/parameter.ini + +### Curved Sphere: Post-Deformation from a box to a sphere +Analogously to the tutorial Mesh Curving by Post-Deformation, we deform a box to a sphere. + + MeshPostDeform=2 + PostDeform_R0=0.5 + +The initial box consists of 1 central zone and 6 neighbor zones, and forms a cube of [-2;2]^3 , being mapped to a sphere of radius 2. Again, PostDeform_R0 can be used to scale the radius. The mapping of the domain inside [-1;1]^3 is again smoothed to avoid singular elements, and outside [-1,1]^3 is perfectly spherical, see Fig. 2.20 and Fig. 2.21 . + + + + + + +
+
+ ../_images/Nopost_sphere.jpg +
+

Fig. 2.20 MeshPostDeform=0

+
+
+
+
+ ../_images/Withpost_sphere.jpg +
+

Fig. 2.21 MeshPostDeform=2

+
+
+
+ +### Curved Sphere: Spherical shell +In a variant of the parameterfile, parameter_shell.ini, only 6 domains without the central domain are used and a spherical shell is generated. The boundary conditions have to be changed, and the central hole has a size of [-1,1]^3, see Fig. 2.22 and Fig. 2.23, where also the inner boundary face is shown. + + + + + + +
+
+ ../_images/Nopost_shell.jpg +
+

Fig. 2.22 parameter_shell.ini, MeshPostDeform=0

+
+
+
+
+ ../_images/Withpost_shell.jpg +
+

Fig. 2.23 parameter_shell.ini, MeshPostDeform=2

+
+
+
\ No newline at end of file diff --git a/docs/documentation/tutorials/externalmesheswithcurvedboundaries.md b/docs/documentation/tutorials/externalmesheswithcurvedboundaries.md new file mode 100644 index 0000000..df09097 --- /dev/null +++ b/docs/documentation/tutorials/externalmesheswithcurvedboundaries.md @@ -0,0 +1,346 @@ +# External Meshes with Curved Boundaries +This tutorial shows how several methods can be applied to curve the boundary faces of the elements. + +The parameter file can be found in + + tutorials/2-02-external_mesh_sphere/parameter.ini + +## Mesh Curving Techniques +In the development of the next generation of numerical methods for CFD, high order methods are promising a substantial increase in efficiency and accuracy. While the particular high order methods can be very distinct, they have in common that they must rely on a high-order approximation of curved geometries to maintain their high-order of accuracy. The generation of curved meshes is thus a topic whose importance cannot be overstated, if one truly wants to apply high order methods to problems with industrial relevance. Especially aerospace applications heavily rely on complex geometries and pose high requirements to the quality of geometry representation. + +
+ ../_images/Curving.jpg +
+

Fig. 2.1 From linear meshes to high order meshes.

+
+
+ +HOPR provides several strategies to produce high order meshes, relying on linear meshes, which are the standard of today's state-of-the-art meshing software and can be generated by commercial mesh generation tools. The two main strategies can be selected with the parameter `curvingMethod`. Therefore, the parameter `useCurveds` has to set to `T`. +```{table} Mesh Curving Techniques Parameter. +--- +name: tab:Mesh Curving Techniques Parameter +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `curvingMethod` | `1` | 0: No curving method activated.
1: Curving with normal vectors at surface points.
3: Curving with subdivided surface mesh. | +``` + +## Curving Using Normal Vectors +Using normal vectors at the surface points, one can reconstruct the curved boundary face. Normal vectors can either be reconstructed from the existing coarse mesh, given in a point-normal file or prescribed analytically. The way of providing the normal vectors can be selected with the parameter `NormalsType`. For each setting a different number of new but self-explanatory parameters are mandatory. These parameters are listed below. + +It has to be taken into account that for generating the curved boundary splines the parameter `boundaryOrder` has always to set to 4 for a normal vector approach. Otherwise HOPR will maybe not work correctly. + +
+ ../_images/Normalvectors.jpg +
+

Fig. 2.2 Sequence of constructing curved element edges from surface normals..

+
+
+ +

Description of Parameters

+ +Below all parameters which are mandatory for this curving technique are explained. A description of all parameters can be found in {ref}`userguide/parameters:List of Parameters`. + +```{table} Curving Using Normal Vectors: Description of Parameters. +--- +name: tab:Curving Using Normal Vectors Description of Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `NormalsType` | `1` | Source of the normal:
1: Reconstructed from coarse surface mesh (no additional parameters, `CurveIndex` of BC must be >0).
2: `NormalVectFile` (point normal vector file) needed
3: Analytical normals from surface point positions | + | `NormalVectFile` | ` filename` | Number of association between BC `CurveIndex` and analytical normal. Mandatory if `NormalsType=3` | + | `nExactNormals` | `1` | Number of association between BC `CurveIndex` and analytical normal. Mandatory if `NormalsType=3` | + | `ExactNormals` | `(/1,1/)` | (/ BC `curveIndex`, number of analytical formula/). Build in formulas (see src/mesh/curved.f90):
1: Sphere with origin (0,0,0)
2: Cylinder around z-axis Mandatory if `NormalsType=3` | + | `boundaryOrder` | ` 4` | Not used here, fixed to cubic polynomial | + +``` +

Output Visualization

+The figures below show the visualizations of the boundary sphere (`BoundaryType=(/4,1,0,0/)`) of the meshes `spheremesh01.cgns` (Fig. 2.4 - Fig. 2.6), `spheremesh02.cgns` (Fig. 2.8 - Fig. 2.10) and `spheremesh04.cgns` (Fig. 2.12 - Fig. 2.14) for the three different normal vector approaches. Therefore, the `SPHERE_CURVED_SplineSurf.vtu` file was used. Furthermore, for the second normal vector approach (`NormalsType=2`) the point normal vector file `normals_out_000001.dat` was used (called filename in the captions). +For the purpose of comparison the surfaces of the original meshes the boundary sphere were assigned to are also shown (Fig. 2.3, Fig. 2.7, Fig. 2.11) and were visualized with the `SPHERE_CURVED_Debugmesh_BC.vtu` file. + +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. + +
spheremesh01
+ + + + + + + + +
+
+ ../_images/Exmesh-sm1.jpg +
+

Fig. 2.3 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-01j.jpg +
+

Fig. 2.4 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file.
NormalsType = 1

+
+
+
+
+ ../_images/Exmesh-011.jpg +
+

Fig. 2.5 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file.
NormalsType = 2
NormalVectFile = filename

+
+
+
+
+ ../_images/Exmesh-012.jpg +
+

Fig. 2.6 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions.
NormalsType = 3
nExactNormals = 1

ExactNormals = (/1,1/)

+
+
+
+ +
spheremesh02
+ + + + + + + + +
+
+ ../_images/Exmesh-sm2.jpg +
+

Fig. 2.7 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-02j.jpg +
+

Fig. 2.8 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file.
NormalsType = 1

+
+
+
+
+ ../_images/Exmesh-021.jpg +
+

Fig. 2.9 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file.
NormalsType = 2
NormalVectFile = filename

+
+
+
+
+ ../_images/Exmesh-022.jpg +
+

Fig. 2.10 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions.
NormalsType = 3
nExactNormals = 1
ExactNormals = (/1,1/)

+
+
+
+ +
spheremesh04
+ + + + + + + + +
+
+ ../_images/Exmesh-sm4.jpg +
+

Fig. 2.11 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-04j.jpg +
+

Fig. 2.12 Boundary sphere with curved surfaces. These are generated by splines with normal vectors which are reconstructed from the coarse mesh file.
NormalsType = 1

+
+
+
+
+ ../_images/Exmesh-041.jpg +
+

Fig. 2.13 Boundary sphere with curved surfaces. These are generated by normal vectors coming from a mandatory point normal vector file.
NormalsType = 2
NormalVectFile = filename

+
+
+
+
+ ../_images/Exmesh-042.jpg +
+

Fig. 2.14 Boundary sphere with curved surfaces. These are generated by analytical normals from surface point positions.
NormalsType = 3
nExactNormals = 1
ExactNormals = (/1,1/)

+
+
+
+ +## Curving Using Subdivided Surface Mesh +Here, we need an additional surface mesh file, which contains a surface mesh (in CGNS format) generated by a mesh generator from the initial coarse surface mesh by subdivision. The additional surface points are lying on the CAD geometry and are then used as interpolation points for the polynomial description of the element face. + +

Description of Parameters

+ +Below all parameters which are mandatory for this curving technique are explained. A description of all parameters can be found in {ref}`userguide/parameters:List of Parameters`. +```{table} Curving Using Subdivided Surface Mesh: Description of Parameters. +--- +name: tab:Curving Using Subdivided Surface Mesh Description of Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `SplitElemFile` | `filename` | Name of suvdivided surface mesh. Mandatory if `curvingMethod=3` | + | `boundaryOrder` | `5` | Order of spline-reconstruction for curved surfaces, corresponding to the number of subdivisions
1 x subdivided: `boundaryOrder=3`
2 x subdivided: `boundaryOrder=5`
3 x subdivided: `boundaryOrder=9`... | +``` +

Output Visualization

+ +The figures below show the visualization of the `SPHERE_Debugmesh_BC.vtu` file by using the mesh file `spheremesh01.cgns` (Fig. 2.3 - Fig. 2.6), `spheremesh02.cgns` (Fig. 2.7 - Fig. 2.10) and `spheremesh01.cgns` (Fig. 2.11 - +Fig. 2.14). In addition, for each file three examples with a different subdivision of the surface mesh are given. + +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. + +
spheremesh01
+ + + + + + + + +
+
+ ../_images/Exmesh-sm1.jpg +
+

Fig. 2.15 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-sm14.jpg +
+

Fig. 2.15 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_04.cgns file.
boundaryOrder = 5

+
+
+
+
+ ../_images/Exmesh-sm16.jpg +
+

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.
boundaryOrder = 7

+
+
+
+
+ ../_images/Exmesh-sm18.jpg +
+

Fig. 2.17 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file.
boundaryOrder = 9

+
+
+
+ +
spheremesh02
+ + + + + + + + +
+
+ ../_images/Exmesh-sm2.jpg +
+

Fig. 2.18 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-sm28.jpg +
+

Fig. 2.19 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file.
boundaryOrder = 5

+
+
+
+
+ ../_images/Exmesh-sm210.jpg +
+

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.
boundaryOrder = 6

+
+
+
+
+ ../_images/Exmesh-sm216.jpg +
+

Fig. 2.21 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_16.cgns file.
boundaryOrder = 9

+
+
+
+ +
spheremesh04
+ + + + + + + + +
+
+ ../_images/Exmesh-sm4.jpg +
+

Fig. 2.22 Boundary sphere without using a curving technique.

+
+
+
+
+ ../_images/Exmesh-sm48.jpg +
+

Fig. 2.23 Boundary sphere with a single subdivision of the surface mesh by using the sphere_surfmesh_08.cgns file.
boundaryOrder = 3

+
+
+
+
+ ../_images/Exmesh-sm416.jpg +
+

Fig. 2.24 Boundary sphere with a double subdivision of the surface mesh by using the sphere_surfmesh_16.cgns file.
boundaryOrder = 5

+
+
+
+
+ ../_images/Exmesh-sm436.jpg +
+

Fig. 2.25 Boundary sphere with a triple subdivision of the surface mesh by using the sphere_surfmesh_36.cgns file.
boundaryOrder = 9

+
+
+
+ +## Use of pre-curved meshes +In some situations the input mesh is already curved, e.g. when HOPRs own meshes are used for input or if the mesh generator already provides curved meshes (e.g. Gmsh). HOPR will read these meshes and directly use their high-order information. Existing high-order meshes from other sources can thus be directly translated into the HOPR format. Furthemore HOPR's various mesh post-processing capabilities can be applied to these meshes and the mesh curving can optionally also be redone by using the normal vector and the subdivision approach described above. + +

Description of Parameters

+Below the mandatory parameters for reading a Gmsh mesh file are described. Note that in case of Gmsh meshes HOPR only supports linear pyramids and prisms, while tetrahedra and hexahedra are supported up to order 4. A description of all parameters can be found in {ref}`userguide/parameters:List of Parameters`. + +```{table} Use of pre-curved meshes: Description of Parameters. +--- +name: tab:Use of pre-curved meshes Description of Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `Filename` | `cylinder.msh` | Name of mesh file. | + | `boundaryOrder` | `4` | Order of the geometry approximation in the mesh, i.e. the number of interpolation points per direction. Note: Gmsh denotes the polynomial degree by the term "order". | +``` + +

Output Visualization

+ +The figures below show the visualization of the `CYLINDER_SplineVol.dat` file by using the mesh file `cylinder.msh`. + +
cylinder
+ +
+ ../_images/Cylinder_gmsh.png +
+

Fig. 2.26 Curved mesh file created by Gmsh..

+
+
diff --git a/docs/documentation/tutorials/externalmesheswithoutcurvedboundaries.md b/docs/documentation/tutorials/externalmesheswithoutcurvedboundaries.md new file mode 100644 index 0000000..35edf80 --- /dev/null +++ b/docs/documentation/tutorials/externalmesheswithoutcurvedboundaries.md @@ -0,0 +1,162 @@ +# External Meshes without Curved Boundaries +This tutorial shows how to read in externally generated unstructured and structured meshes with straight-edged elements. + +The parameter file can be found in + + tutorials/2-01-external_mesh_sphere/parameter.ini + +## External Mesh +The external mesh which shall read in have to be available in the directory of the executed parameter file as CGNS file. This file is read-in by introducing the parameter `filename`. As one can see from the `parameter.ini`'s excerpt and Fig. 1.1, the parameters of the parameter file have to be adapted to the definitions in the CGNS mesh file. This means that the parameters Mode, `nZones`, `BoundaryName` and `BoundaryType` can not be set freely anymore because the structure of the external mesh must be retained. In this case, the external mesh `spheremesh02` is available as CGNS file and consists of three zones. Therefore, the settings of the parameters are `Mode=3`, `nZones=3`, `filename=spheremesh02.cgns`. + +Another important fact is that for external meshes no `BCIndex` parameter is needed which assigns normally bondary conditions to the surfaces of the mesh. The reason for this is that the boundary conditions are assigned to their belonging surfaces by their names. The boundary condition, for example, of `Zone_1` of the CGNS file (`BC_sphere`) has to be defined as `BoundaryName=sphere` in the parameter file. + + !================================================================= ! + ! MESH + !================================================================= ! + Mode =3 ! 1 Cartesian 3 CGNS 4 STAR-CD V3 + nZones =3 ! number of zones + filename=spheremesh02.cgns ! name of mesh file + ... + ... + + !================================================================= ! + ! CURVED + !================================================================= ! + useCurveds=F ! T to generate curved boundaries + + + !================================================================= ! + ! BOUNDARY CONDITIONS + !================================================================= ! + BoundaryName=sphere ! BC_Name must be defined in mesh file + BoundaryType=(/4,1,0,0/) + BoundaryName=inflow + BoundaryType=(/2,0,0,0/) + BoundaryName=outflow + BoundaryType=(/2,0,0,0/) + BoundaryName=mantel + BoundaryType=(/2,0,0,0/) + + +
+ ../_images/CGNSviewer_spheremesh04.png +
+

Fig. 1.1 Screenshot of the folder structure of a CGNS mesh.

+
+
+ +Furthermore, the `BoundaryType` parameter has to be adapted to the definitions in the CGNS mesh file. If a boundary of the external mesh is curved the `curveIndex` component (2nd component) of the `BoundaryType` parameter has to be an value unequal to zero. Wether curved boundaries shall be generated or not can be controlled by the parameter `useCurveds`. In this tutorial `useCurveds=F`. The case `useCurveds=T` is the topic of the next tutorial which explaines how to use mesh curving techniques to get curved boundaries for your mesh. + +All new parameters of the parameter file of this tutorial are explained below. + +```{table} External Mesh Parameters. +--- +name: tab:External Mesh Parameters +--- + | Parameters |Setting | Description | + | :------ | :----------: | :--------------------------- | + | `filename` | `spheremesh.cgns` | The name of the external mesh file. The belonging files have to be available in the directory of the executed parameter file as CGNS files. | + | `meshscale` | ` 0.001` | Scales all input meshes by a factor | + | `SpaceQuandt` | ` 1000` | Characteristic length of the mesh | + | `useCurveds` | `T` | T (True): If curved boundaries are defined
F (False): If no curved boundaries are defined . | +``` + +A description of all parameters of the parameterfile can be found in {ref}`userguide/parameters:List of Parameters`. + +## Output Visualization +If there is a need for assistance of visualizing the HOPR output visit {ref}`tutorials/index_visualization:Visualization`. + +The figures below show the visualizations of the `SPHERE_Debugmesh.vtu` file. In Addition, a visualization of the surfaces the first boundary condition sphere was assigned to (the `curveIndex` of the `BoundaryType` parameter is set to 1) of the `SPHERE_Debugmesh_BC.vtu` file is shown for each external mesh (see Fig. 1.4, Fig. 1.7, Fig. 1.10) + +

spheremesh01

+ + + + + + + +
+
+ ../_images/Exmeshwo_spheremesh01_surfaces.jpg +
+

Fig. 1.2 HOPR output of spheremesh01.cgns

+
+
+
+
+ ../_images/Exmeshwo_spheremesh01_mesh.jpg +
+

Fig. 1.3 HOPR output of spheremesh01.cgns with extracted edges.

+
+
+
+
+ ../_images/Exmeshwo_spheremesh01_innerbc.jpg +
+

Fig. 1.4 Element surfaces (6) of spheremesh01.cgns the boundary condition sphere was assigned to.

+
+
+
+ +

spheremesh02

+ + + + + + + +
+
+ ../_images/Exmeshwo_spheremesh02_surfaces.jpg +
+

Fig. 1.5 HOPR output of spheremesh02.cgns

+
+
+
+
+ ../_images/Exmeshwo_spheremesh02_mesh.jpg +
+

Fig. 1.6 HOPR output of spheremesh02.cgns with extracted edges.

+
+
+
+
+ ../_images/Exmeshwo_spheremesh02_innerbc.jpg +
+

Fig. 1.7 Element surfaces (24) of spheremesh02.cgns the boundary condition sphere was assigned to.

+
+
+
+ +

spheremesh04

+ + + + + + + +
+
+ ../_images/Exmeshwo_spheremesh04_surfaces.jpg +
+

Fig. 1.8 HOPR output of spheremesh04.cgns

+
+
+
+
+ ../_images/Exmeshwo_spheremesh04_mesh.jpg +
+

Fig. 1.9 HOPR output of spheremesh04.cgns with extracted edges.

+
+
+
+
+ ../_images/Exmeshwo_spheremesh04_innerbc.jpg +
+

Fig. 1.10 Element surfaces (64) of spheremesh04.cgns the boundary condition sphere was assigned to.

+
+
+
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