Extraction of Crack-Free Isosurfaces from Adaptive Mesh Refinement Data

Adaptive mesh refinement (AMR) is a numerical simulation technique used in computational fluid dynamics (CFD). This technique permits efficient simulation of phenomena characterized by substantially varying scales in complexity. By using a set of nested grids of different resolutions, AMR combines the simplicity of structured rectilinear grids with the possibility to adapt to local changes in complexity within the domain of a numerical simulation that otherwise requires the use of unstructured grids. Without proper interpolation at the boundaries of the nested grids of different levels of a hierarchy, discontinuities can arise. These discontinuities can lead, for example, to cracks in an extracted isosurface. Treating locations of data values given at the cell centers of AMR grids as vertices of a dual grid allows us to use the original data values of the cell-centered AMR data in a marching-cubes (MC) isosurface extraction scheme that expects vertex centered data. The use of dual grids also induces gaps between grids of different hierarchy levels. We use an index-based tessellation approach to fill these gaps with ''stitch cells.'' By extending the standard MC approach to a finite set of stitch cells, we can define an isosurface extraction scheme that avoids cracks at level boundaries