An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data

Area of Science:

• Computational geometry
• Biomedical engineering
• Scientific computing

Background:

• Accurate mesh generation is critical for reliable computational fluid dynamics (CFD) simulations, especially for complex biological geometries.
• Existing methods often struggle with scale-invariance and adapting mesh density to local feature sizes in intricate biological surfaces.
• Magnetic Resonance Imaging (MRI) provides complex, topologically challenging datasets requiring advanced meshing techniques.

Purpose of the Study:

• To develop a boundary-fitted, scale-invariant unstructured tetrahedral mesh generation algorithm.
• To enable precise registration of element size to local feature size for improved simulation accuracy.
• To generate quality grids for CFD simulations of complex biological surfaces derived from MRI data.

Main Methods:

• Determining a feature size field by casting rays normal to the surface and applying gradient-limiting operations for continuity.
• Adjusting surface mesh density proportionally to the feature size field.
• Generating a layered anisotropic volume mesh that is scale-invariant between minimum (L(min)) and maximum (L(max)) scale sizes.

Main Results:

• Successfully generated scale-invariant unstructured tetrahedral meshes.
• Demonstrated the algorithm's ability to adapt mesh element size to local feature size.
• Illustrated the application of the generated meshes for CFD simulations on complex biological surfaces.

Conclusions:

• The presented algorithm provides a robust method for generating high-quality, scale-invariant meshes for complex biological geometries.
• This approach enhances the accuracy and reliability of CFD simulations for biomedical applications.
• The algorithm is implemented in the Los Alamos grid toolbox (LaGriT) at Pacific Northwest National Laboratory (PNNL).