Mesh Curving by Post-Deformation

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Parameter File

This is the parameter file, which is also found in


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.

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


The undeformed and deformed mesh is shown in picture 1 and 2.

The order of the curved element mapping can be chosen arbitrarily

useCurveds   =T 
Picture 1: MeshPostDeform=0
Picture 2: 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


We choose a periodic boundary condition in z direction.

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


see Picture 3.

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 picture 4.

Picture 3: Outer circular mapping with parameter2.ini
Picture 4: 9 block mesh with stretching parameter3.ini

Output Visualization

If there is a need for assistance of visualizing the HOPR output visit Visualization.

Next Tutorial Section : Curved Torus