A Geometry-Adaptive Mesh Refinement Framework for Immersed Boundary Methods on Hybrid Unstructured Meshes

Abstract

In this work, we describe a new preprocessing tool for geometry-adaptive mesh refinement on hybrid unstructured meshes with a target application on immersed boundary methods. The tool has as input an unstructured, hybrid, and conforming mesh generated by an external mesh generation software, and the main goal is to refine this mesh around immersed geometries in such a way that the CFD solver using the immersed boundary method can simulate flow problems in an accurate and efficient manner. The input background mesh can be made of different types of elements, like tetrahedra, hexahedra, prisms, and pyramids, which, unlike Cartesian meshes, permit for a more flexible mesh. Hybrid unstructured meshes enable one to use the immersed boundary technology in a new class of flow problems where the full geometry is decomposed into a fixed geometry part and a changing geometry part. A body-fitted mesh is generated for the fixed geometry while for the changing one is used the immersed boundary method. We simulate several flow problems to test the new meshes, including subsonic flow past a cylinder and subsonic flow past an NACA0012 airfoil, both using finite volume and discontinuous Galerkin methods and solving the Navier-Stokes equations. As an industrial example of our mesh generation, we consider the simulation of a multi-element airfoil: in this case, a mesh generation software generates an unstructured conforming background mesh for the slat and main airfoil, while the flap is placed as immersed geometry in this body-fitted mesh. As accurate and efficient results are sought, this mesh is refined around the flap and then the subsonic flow at high-lift flow conditions is simulated with a finite volume method coupled with an immersed boundary method and using the Reynolds-averaged Navier-Stokes equations.

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BibTeX RIS

BibTeX

@misc{rosa2026geometryadaptive,
  title = {{A Geometry-Adaptive Mesh Refinement Framework for Immersed Boundary Methods on Hybrid Unstructured Meshes}},
  author = {Jonatan Núñez-de la Rosa and Esteban Ferrer and Eusebio Valero},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.27580},
  eprint = {2607.27580},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.27580},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - A Geometry-Adaptive Mesh Refinement Framework for Immersed Boundary Methods on Hybrid Unstructured Meshes
AU  - Jonatan Núñez-de la Rosa
AU  - Esteban Ferrer
AU  - Eusebio Valero
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2607.27580
UR  - https://arxiv.org/abs/2607.27580
AB  - In this work, we describe a new preprocessing tool for geometry-adaptive mesh refinement on hybrid unstructured meshes with a target application on immersed boundary methods. The tool has as input an unstructured, hybrid, and conforming mesh generated by an external mesh generation software, and the main goal is to refine this mesh around immersed geometries in such a way that the CFD solver using the immersed boundary method can simulate flow problems in an accurate and efficient manner. The input background mesh can be made of different types of elements, like tetrahedra, hexahedra, prisms, and pyramids, which, unlike Cartesian meshes, permit for a more flexible mesh. Hybrid unstructured meshes enable one to use the immersed boundary technology in a new class of flow problems where the full geometry is decomposed into a fixed geometry part and a changing geometry part. A body-fitted mesh is generated for the fixed geometry while for the changing one is used the immersed boundary method. We simulate several flow problems to test the new meshes, including subsonic flow past a cylinder and subsonic flow past an NACA0012 airfoil, both using finite volume and discontinuous Galerkin methods and solving the Navier-Stokes equations. As an industrial example of our mesh generation, we consider the simulation of a multi-element airfoil: in this case, a mesh generation software generates an unstructured conforming background mesh for the slat and main airfoil, while the flap is placed as immersed geometry in this body-fitted mesh. As accurate and efficient results are sought, this mesh is refined around the flap and then the subsonic flow at high-lift flow conditions is simulated with a finite volume method coupled with an immersed boundary method and using the Reynolds-averaged Navier-Stokes equations.
ER  -

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