Motivation: Investigate a flow solver using overlapping grids for simulating turbulent flow past a body at high Reynolds number.
In preparation for studying the wake behind a three dimensional body, I studied the wake behind a circular cylinder. A circular cylinder
is the most simple two-dimensional body. Despite its geometric simplicity, a range of complicated physics are present including boundary layer
flow, separated flow, thin shear layers and an unsteady to turbulent wake. Qualtitative feature such as the emergence of a vortex street at low
Reynolds number are able to be used for validation in addition to more quantitative measures like the drag coefficient and shedding frequency.
The flow solver used is called cg and was developed using the Overture framework developed at Lawrence Livermore National Laboratory (LLNL). More
information on Overture and cg is available at their LLNL homepage:
Overture homepage. Overlapping grids, also called chimera or overset grids, are
advantageous as they allow one to concentrate resolution where it is needed. They are also useful for problems with complicated geometries.
For flow past bodies they allow one to use an efficient cartesian grid for the outer flow and mid-to-late wake region in addition to a more natural
body-fitted grid at the body itself to capture the small scales in the boundary layer and near wake region. Counterbalancing these desirable qualities,
overlapping grids are notorious for requiring complicated interpolation schemes for transferring data between overlapping grids, especially as the grids
become more complex with multiple grids overlapping in a single region.
Despite the use of complicated interpolation schemes, difficulties in accurately transferring data between complicated grid boundaries,
especially in ensuring mass conservation, are often present.
Initial results from 2-D simulations for steady flow past a cylinder were promising but
difficulties with numerical instability at the overlapping grid boundaries in 3-D for large Reynolds numbers proved unsurmountable.
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| Sample overlapping grid for simulating flow past a circular cylinder. Note that different colors indicate a different grid, a total of six grids are being used to provide resolution where needed. | Vorticity field for flow past a cylinder at Re=500 (2D simulation). The regular vortex pattern behind the cylinder is referred to as a vortex street. |