Analysis of a Fractional-Step Method on Overset Grids

A fractional-step method for solving the incompressible Navier–Stokes equations on overset grids is derived as a matrix factorization of the spatially and temporally discretized system of equations. The algorithm is applied to several test problems using second-order-accurate finite-volume flux differencing on staggered grid systems and a hybrid implicit/explicit time advancement scheme. Spatial order of accuracy is shown to depend on the behavior of the overset grid overlap during grid refinement. The temporal order of accuracy of the time advancement algorithm on a single grid is maintained on the overset grid.