Domain decomposition methods in computational fluid dynamics

The divide‐and‐conquer paradigm of iterative domain decomposition or substructuring has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi‐uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the non‐linear iteration. Multiple discretizations (second‐order in the operator and first‐order in the preconditioner) and locally uniform mesh refinement pay dividends separately and can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.