Exact(8)
The cut cells near the immersed boundary are identified using a fictitious level set function.
On the other hand cut cells only appear in a small region of the domain.
Cartesian meshes for domains with complicated boundaries give rise to cut cells with arbitrarily small volumes.
A quadrature technique is proposed for accurately integrating on general cut cells.
These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells.
Even though very small cut cells can appear when moving an object through the fixed grid, the method is stable.
When cut cells are used for the representation of orography in numerical weather prediction models this leads to very small cells.
The presented method is as stable and accurate as the underlying split-explicit method but furthermore it can compute with cut cells with nearly no additional effort.
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