Overset (Chimera) Grid
Mechanism: overlapping grids that exchange values
Overview
I want to analyse a rotating propeller together with the hull, but I'm stuck on how to connect the moving and stationary meshes.
Overset (Chimera) grids let you avoid connecting them at all. Build a grid around the propeller and a separate one for the hull and background, and simply overlap them. In the overlap, values from one grid are interpolated and passed to the other. Cells inside bodies or in excess overlap are blanked out as holes. Grids can move freely and each part can have a high-quality grid — the price is a new error source: interpolation.
Cell roles
| Type | Role |
|---|---|
| Field (active) cells | Solve the governing equations as usual |
| Holes (blanked cells) | Removed from the computation, e.g. inside bodies |
| Receptors (fringe cells) | At hole edges and grid outer boundaries, receive interpolated values |
| Donors | Cells on the other grid that supply values to receptors |
| Orphans | Receptors with no valid donor — a source of error or divergence |
Interpolation and its error
$w_i$ are interpolation weights, $k$ the wavenumber of the flow variation and $h$ the donor spacing. Linear interpolation error falls with the square of spacing, quadratic with the cube. Crucially, the error is set by the donor spacing, not the receptor's.
Popularised by Space Shuttle analyses
The overset idea was proposed in the United States in the 1980s and proved itself on the Space Shuttle launch configuration — orbiter, external tank and two solid rocket boosters side by side. Building good structured grids for each component and simply overlapping them avoided the hard job of meshing the whole assembly as one. It later became a standard method for moving-body problems such as helicopter rotors, store separation and ship propellers.
Worked example: size of the interpolation error
Resolution and error
A sine wave $\sin(2\pi x)$ was interpolated from the donor grid onto 20,000 receptor points and the maximum error (relative to amplitude) recorded:
| Donor points per wavelength | Linear | Quadratic |
|---|---|---|
| 5 | 18.2 % | 11.4 % |
| 10 | 4.9 % | 1.6 % |
| 20 | 1.2 % | 0.20 % |
| 40 | 0.31 % | 0.025 % |
Donor-to-receptor size ratio
With the fine receptor grid at 20 points per wavelength, linear-interpolation error grows as the donor grid coarsens:
| Size ratio (donor/receptor) | Max error |
|---|---|
| 1 | 1.2 % |
| 2 | 4.9 % |
| 4 | 18.2 % |
However fine the receptor grid, a coarse donor keeps the error large.
Exactly. A common mistake is a fine body grid with a coarse background grid. Vortices and wakes leaving the body degrade to the coarse grid's accuracy the moment they're handed to the background. In the overlap, keep the two grids' cell sizes within about a factor of two.
Repeated interpolation damps waves
Taking values mid-cell with linear interpolation shrinks a wave a little each time. At 10 points per wavelength the factor is 0.951 per pass, and after 20 overlap crossings only 37% of the amplitude remains; at 20 points it is 0.988 and 78% survives. When a propeller wake crosses several grids, or a rotating grid interpolates every step, this damping affects the result.
Setup and verification
Setup points
- Overlap width: overlap by at least several cells beyond the interpolation stencil. Narrow overlaps breed orphans.
- Match sizes: keep both grids within a factor of 2 in the overlap, refining the background locally there.
- Avoid steep gradients: don't place overlap boundaries in shocks, boundary layers or shear layers.
- Time step with moving grids: if a body moves more than one cell per step, hole cutting and donor relations jump abruptly. Choose a step so motion per step is below one cell.
Verification
- Check the number of orphans and eliminate them.
- Check the inflow–outflow mass balance. Interpolation is not generally conservative, so a large imbalance means the overlap setup needs revisiting.
- If the same geometry can be meshed as a single connected grid, compare once to quantify the overset-induced error.
“Spikes in the force history”
In moving-body overset runs, the force history sometimes shows periodic spikes. Usually the cause is the discontinuity when cells switch from hole to active (or back) as the body moves: if a newly activated cell's initial value doesn't match its neighbours, a small pressure jolt results. Matching sizes in the overlap, reducing the time step and keeping switching regions away from the body all make it far less noticeable.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Coarse background grid | Wakes and vortices lost at interpolation | Refine the overlap locally |
| Overlap too narrow | Orphans appear | Overlap by the stencil plus several cells |
| Overlap boundary inside the boundary layer | Wall friction and heat transfer wrong | Keep boundary layers within one grid |
| Not checking mass balance | Non-conservation goes unnoticed | Monitor inflow–outflow difference |
| Time step with too much motion | Spikes in force history | Keep motion per step below one cell |
I'd like to check interpolation error myself.
Use the interpolation simulator for interpolation order versus error, the mesh independence study tool for resolution effects and the CFD mesh quality checker for grid quality. Related methods are covered in mesh motion, adaptive mesh refinement (AMR) and inflation layers.
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