HOHQMesh

HOHQMesh, the High Order Hex-Quad Mesher, is an open-source mesh generator that automatically creates quadrilateral/hexahedral meshes with high-order boundary information. To get an impression of what kind of meshes HOHQMesh can generate, please see the gallery.

What you can do with HOHQMesh

To use HOHQMesh to generate all-quadrilateral meshes with arbitrary order boundary elements you use a control file to

• Define a MODEL consisting of

  • An optional closed outer boundary curve made up of one or more connected curved segments defined by primitives like straight line segments, circular arcs, elliptic arcs, splines, or equations
  • Zero or more closed inner boundary curves defined in the same way
  • Zero or more internal boundary curves that define boundaries for multiple material applications
  • An optional bottom topography defined either in functional form or from a file to use to refine a 2D mesh around bottom features. (For example for shallow water equation computations.)

• Tell it how to mesh the model with a CONTROL_INPUT section by

  • Setting run parameters that specify where to write the results, specify the mesh and plot file formats and set the polynomial order of the boundary curves
  • Setting a background grid size to specify the largest element size desired
  • Setting how the mesh should be smoothed
  • Defining optional refinement regions to allow manual refinement of the mesh to emphasize specific regions not indicated by the boundary curves or topography.

HOHQMesh will automatically generate a mesh with curved elements sized according to the geometry, like the curvature of the boundary curves and bottom topography, and the distance between boundary curves. It will generate a mesh that is symmetric about a symmetry line if segments of the outer boundary are defined as symmetry boundaries.

Additionally, you can generate an all hexahedral mesh from the two-dimensional mesh by extruding a quadrilateral mesh by

• Simple extrusion along a coordinate direction
• Simple rotation about an axis
• Sweeping a quadrilateral mesh along a curve and optionally scaling the width along the way

One can have the bottom of a hexahedral mesh follow a prescribed topography defined in functional form or from data. A 3D mesh can also be sized according to the curvature of the bottom topography.

Getting started

HOHQMesh can be used via HOHQMesh.jl, a Julia package that provides an interface to HOHQMesh and that supplies precompiled executables for Linux, macOS, Windows, and FreeBSD. If you would like to use HOHQMesh directly from the command line, please continue reading the next sections for instructions on how to obtain the sources and compile HOHQMesh yourself.

Prerequisites

To build and install HOHQMesh, you need the following tools:

• A Fortran compiler (we recommend GFortran)
• GNU Make
• CMake (optional; only for CMake-based builds)

Building on Linux and macOS should be straightforward, building on Windows requires MSYS2.

Install with Spack

You can install HOHQMesh using the Spack package manager. To install the HOHQMesh with Spack, git clone https://github.com/spack/spack.git ~/spack source ~/spack/share/spack/setup-env.sh spack install hohqmesh@main This will install HOHQMesh and all of its dependencies (including FTObjectLibrary) from source code. Once installed, HOHQMesh can be added to your environment using spack load hohqmesh

Obtaining the sources

You can download the latest HOHQMesh release from GitHub. Make sure to get the tarball named HOHQMesh-vVERSION.tar.gz, as it already contains the required sources for the FTObjectLibrary dependency, and unpack it with tar xf HOHQMesh-vVERSION.tar.gz. Alternatively, you can build HOHQMesh directly from the latest sources in the main branch. In this case, you need enter the clone directory and execute bash ./Utilities/bootstrap before proceeding, which will download the FTObjectLibrary sources for you. This step is required only once.

Building

There are two ways to build HOHQMesh from source: Using plain make or by using CMake. The make-based build is conceptually simpler but only works as an in-source build, thus populating your HOHQMesh root directory with build artifacts. The CMake-based build is slightly more involved but also allows you to do out-of-source builds.

HOHQMesh is tested to run with the gfortran and ifort compilers. We recommend the gfortran compiler. Our experience on the test suite is that it runs about 50% slower with the ifort compiler.

Using plain make

Enter the HOHQMesh directory and execute shell make This will build HOHQMesh using the gfortran compiler by default. The compiler choice can be overridden by passing FC=<pathToCompiler> to make. You can further pass the -jN option to make (with N being a non-negative integer), which will use N parallel processes.

For example, to build HOHQMesh specifically with the Fortran compiler gfortran-10 and with 4 parallel processes, execute bash make -j 4 FC=gfortran-10

Using CMake

For a CMake-based build, you first need to build the FTObjectLibrary, install it, and then build HOHQMesh itself. If you followed the steps for obtaining the sources above, all required files are already present.

For convenience, we will assume that you are executing the following from within the HOHQMesh root directory. However, after modifying the paths appropriately, you can use these steps also from anywhere else:

```shell

Build and install FTObjectLibrary

mkdir build-ftol && cd build-ftol cmake ../Contrib/FTObjectLibrary/ -DCMAKEINSTALLPREFIX=../install cmake --build . cmake --install . cd ..

Build and install HOHQMesh

mkdir build-hm && cd build-hm CMAKEPREFIXPATH=../install cmake .. -DCMAKEINSTALLPREFIX=../install cmake --build . cmake --install . cd ..

Copy HOHQMesh executable to root directory

cp install/bin/HOHQMesh . ```

The HOHQMesh executable can be moved around freely and does not rely on any other files in the install prefix or in the build directories (which can thus be deleted safely if so desired).

By default, HOHQMesh (and FTObjectLibrary) will be built by the standard Fortran compiler configured for CMake. The compiler choice can be overridden by setting the environment variable FC=<pathToCompiler> when invoking the configure step of CMake, e.g., FC=gfortran-10 cmake ...

Testing

After building HOHQMesh, you can verify that everything works as expected by running the internal test suite. To execute the tests, type bash ./HOHQMesh -test -path <pathToBenchmarks> where <pathToBenchmarks> is the path to the HOHQMesh directory. If you are inside the HOHQMesh directory, you can also omit the -path option, as it defaults to ..

Generating a mesh

To mesh a control file, type bash ./HOHQMesh -f <pathToControlFile> where -f allows you to provide the path to the control file for which you want to create your mesh.

For example, if you are inside the HOHQMesh root directory, you can run shell ./HOHQMESH -f Examples/2D/GingerbreadMan/GingerbreadMan.control to generate a mesh for a gingerbread man geometry. This will produce three files, Examples/2D/GingerbreadMan/GingerbreadManMesh.mesh Examples/2D/GingerbreadMan/GingerbreadManPlot.tec Examples/2D/GingerbreadMan/GingerbreadManStats.txt where the .mesh file stores the actual mesh, the .tec file is a Tecplot-compatible visualization file, and the .txt file contains statistical information on the mesh quality.

The Tecplot file can be visualized, e.g., using the open-source software ParaView, which has a built-in Tecplot reader. In the case of the gingerbread man, the resulting mesh should look like the example found in the online mesh gallery.

Getting help

To get a list of the command line options available in HOHQMesh, type bash ./HOHQMesh -help

Documentation

Complete details on how to use HOHQMesh, including the preparation of input files, the different formats of the resulting mesh files, and visualization instructions, can be found in the online documentation.

Referencing

If you use HOHQMesh in your own research, please cite the following article: bibtex @article{kopriva2024hohqmesh:joss, title={{HOHQM}esh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements}, author={David A. Kopriva and Andrew R. Winters and Michael Schlottke-Lakemper and Joseph A. Schoonover and Hendrik Ranocha}, year={2024}, journal={Journal of Open Source Software}, doi={10.21105/joss.07476}, volume = {9}, number = {104}, pages = {7476}, publisher = {The Open Journal} } In addition, you can also directly refer to this repository as bibtex @misc{kopriva2024hohqmesh:repo, title={{HOHQM}esh: An All Quadrilateral/Hexahedral Unstructured Mesh Generator for High Order Elements}, author={Kopriva, David A and Winters, Andrew R and Schlottke-Lakemper, Michael and Schoonover, Joseph A and Ranocha, Hendrik}, year={2024}, howpublished={\url{https://github.com/trixi-framework/HOHQMesh}}, doi={10.5281/zenodo.13959058} }

Authors

HOHQMesh was initiated by David A. Kopriva, who is also the principal developer. The full list of contributors can be found in AUTHORS.md.

License and contributing

HOHQMesh is licensed under the MIT license (see LICENSE.md).