Study on a grid interface algorithm for solutions of incompressible Navier–Stokes equations

Grid interface treatment is a crucial issue in solving unsteady, three-dimensional, incompressible Navier–Stokes equations by domain decomposition methods. Recently, a mass flux based interpolation (MFBI) interface algorithm was proposed for Chimera grids [Tang HS, Jones SC, Sotiropoulos F. An overset grid method for 3D unsteady incompressible flows. J Comput Phys, 2003;191:567–600] and it has been successfully applied to a variety of flows. MFBI determines velocity and pressure at grid interfaces by mass conservation and interpolation, and it is easy to implement. Compared with the commonly used standard interpolation, which directly interpolates velocity as well as pressure, the proposed interface algorithm gives fewer solution oscillations and faster convergence rates. This paper makes a study on MFBI. Starting with discussions about grid connectivity, it is shown that MFBI is second-order accurate for mass flux across grid interface. It is also derived that the scheme provides second-order accuracy for momentum flux. In addition, another version of MFBI is presented. At last, numerical examples are presented to demonstrate that MFBI honors mass flux balance at grid interfaces and it leads to second-order accurate solutions.