Adaptive Embedded Unstructured Grid Methods.

Abstract

A simple embedded domain method for node-based unstructured grid solvers is
presented. The key modification of the original, edge-based solver is to remove all geometryparameters
(essentially the normals) belonging to edges cut by embedded surface faces. Several
techniques to improve the treatment of boundary points close to the immersed surfaces are explored.
Alternatively, higher-order boundary conditions are achieved by duplicating crossed
edges and their endpoints. Adaptive mesh refinement based on proximity to or the curvature of
the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or
automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary
work. Recent work has led to a notable improvement in speed via suitable data structures,
the option to treat dispersed particles in the context of embedded surfaces, a direct link
to Discrete Particle Methods (DPM), a volume to surface meshing technique that obtains bodyfitted
grids by post-processing adaptive embedded grids; and links to simplified CSD models.
Several examples are included that show the viability of this approach for inviscid and viscous,
compressible and incompressible, steady and unsteady flows, as well as coupled fluid-structure
problems.