Nalu supports simulations using an overset mesh methodology to model complex geometries. Currently the codebase utilizes a native STK based overset grid assembly algorithm for all overset assembly. STK searches are performed to remove elements which intersect bounding shapes. Three shapes are supported:
- Axis-aligned bounding boxes (AABB),
- Oriented bounding boxes (OBB), and
- Oriented cylinders (OC).
AABB directly uses efficient STK search routines to remove elements which have an AABB that intersects the overset mesh's AABB. OBB instead removes elements which have nodes within an oriented bounding box that follows an overset block's movement. OC behaves similarly where now a cylindrical volume is removed that follows the block's motion. The oriented cutting shapes provide more consistent overlap for moving cases and are generally suggested over the AABB strategy for such cases.
The overset descriptions begins with the basic background mesh (block 1) and overset mesh (block 2) depicted in Figure overset-block-one-two. Also shown in this figure is the reduction outer surface of block 2 (light blue). Elements within this reduced overset block will be determined by a parallel search. The collection of elements within this bounding box will be skinned to form a surface on which constraint nodes are placed. Elements within this volume are set in a new internally managed inactive block. These mesh entities are fully removed from the overall matrix for each dof. Elements within this volume are provided a masking integer element varibale of unity to select out of the visualizattion tool. Therefore, constraint nodes live at the external boundary of block 2 and along the reduced surface. The parallel search provides the mapping of constraint node and owning element from which the state can be constructed.
Two-block use case describing background mesh (block 1) and overset mesh (block 2).
After the full search and overset initialization, this simple example yields the original block 1 and 2, the newly created inactive block 3, the original surface of the overset mesh and the new skinned surface (101) of the inactive block (Figure overset-block-one-two-cut).
Three-block and two surface, post over set initialization.
A simple heat conduction example is provided in Figure overset-hc where the circular boundary is set at a temperature of 500 with all external boundaries set to adiabatic.
A simple heat conduction example providing the overset mesh and donor constraint nodes.
As noted before, every constraint node lies within an owning element. Sufficient overlap is required to make the system well posed. A fully implicit procedure is provided by writing the constraint node value as a linear constraint of the owning element (Figure overset-nodes).
Constraint nodes for background and overset mesh for which a fully implicit constraint equation is written.
For completeness, the constraint equation for any dof ϕo is simply,
ϕo − ∑Nkϕk = 0.
As noted, full sensitivities are provided in the linear system by constructing a row entry with the columns of the nodes within the owning element and the constraint node itself.
Finally, a mixed hex/tet mesh configuration example (overset mesh is tet while background is hex) is provided in Figure overset-sphere.
Flow past a three-dimensional sphere using a hybrid topology (hex/tet) mesh configuration.