This chapter discusses the simulation of incompressible flows by computing the Navier–Stokes equations via the multiblock method. The Navier–Stokes equations in curvilinear coordinates are discretized using a second-order finite difference method on overset/composite grids, and the discretized equations are solved by the artificial compressible method. The computation utilizes the conventional Schwarz method and other techniques, including implicit residual smoothing, local dual-time stepping, and V-cycle multigrid acceleration. Grid connectivity and interface treatment are discussed. An interface method is derived to enforce mass conservation at grid interfaces, which is crucial in the simulation of an incompressible flow. The method is referred to as mass flux balance interpolation (MFBI); it is a slight modification of the standard interpolation (SI) at the interfaces, and it is straightforward to implement. Numerical experiments are conducted in cavity flow, pipe-bend flow, and flow past a cylinder to test the multiblock method. These experiments demonstrate that, compared with the SI, the MFBI removes or suppresses numerical oscillations at grid interfaces, leads to faster convergence of the Schwarz iteration, and tends to reduce conservation errors of numerical solutions.