The RBF-SliDe tool is an C++ implementation of radial basis functions interpolation technique for mesh deformation. Special methods are implemented for robust mesh deformation in case of internal flow applications. Sliding boundary nodes methods, periodic boundary conditions and data reduction techniques are implemented to enhance the performance of the mesh deformation method.
As sliding boundary node methods a direct and pseudo sliding approach is available. In case of direct sliding the interpolation conditions of the RBF are altered to allow for the sliding. For the pseudo sliding the exterior boundary nodes are freely displaced and projected back onto the boundary of the domain.
When applying periodicity, the RBF itself is made periodic in order to allow for a periodic displacement of the boundaries, where these nodes are treated as they were internal nodes. The periodicity can be applied in different ways: only making the RBF periodic in the periodic direction, a periodic displacement with fixed domain vertices and a periodic displacement with sliding domain vertices (requires use of sliding method).
As a data reduction method a greedy full point algorithm is available. A double-edged selection is employed to select the control nodes not only based on error magnitude but also direction. Additionally, a multi-level adaptation of the greedy algorithm is implemented, however so far it did not yield satisfactory results for typical internal flow domains.
For the projection algorithm nanoflann, a header only of the FLANN library, is used which offers fast nearest neighbour searches for two and three-dimensional spaces using k-d trees [2].
The tool can be directly run on Windows by running the executable, as provided in the repository. The tool is run with the call $ RBF_SLIDE your_config_file.cfg, where the executable, input mesh file, deformation file and configFile are located in the current working directory. Alternatively, the executable can be placed in a separate folder and its directory can be added to the path environment variable. This allows for calling of the tool from any folder.
Additionally, the source and makefile are in the repository to be able to build from source. The C++ library Eigen is required, since it is used for matrix operations within the RBF interpolations. See https://eigen.tuxfamily.org/index.php?title=Main_Page for more details and how to use the library.
The example configuration file named configFile.cfg shows the various possible inputs and methods for the RBF-SliDe tool and a simple 25x25 square mesh is provided as an example test case.
This tool was developed as part of an MSc. thesis project by:
Floyd van Steen MSc. Student, TU Delft.
Matteo Pini Assistant Prof., Power and Propulsion, TU Delft.
Alexander van Zuijlen Assistant Prof., Aerodynamics, TU Delft.
More details regarding the tool can be found in the following document:
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F.A. van Steen. Mesh Deformation Using Radial Basis Function Interpolation for Numerical Optimisation of Internal Flow Applications. Master Thesis, TU Delft, 2023.
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Jose Luis Blanco et al. nanoflann: a C++ header-only fork of FLANN, a library for Nearest Neighbor (NN) with KD-trees. https://github.com/jlblancoc/nanoflann. 2014.
