Parallel computation of unsteady incompressible viscous flows around moving rigid bodies using an immersed object method with overlapping grids

A novel immersed object method is developed for simulating two-dimensional unsteady incompressible viscous flows around arbitrarily moving rigid bodies. It has been implemented in a parallel unstructured finite volume incompressible Navier–Stokes solver, based on the artificial compressibility (AC) approach using a higher-order characteristics-based upwind scheme and matrix-free implicit dual time-stepping. In the immersed object method, an object is immersed in the flow field, and it is supposed to contain frozen fluid, which moves like a solid body. This is realized by introducing source terms in the momentum equations during the AC sub-iterations. An internal mesh within the object is employed to search and locate all the Eulerian nodes within the object in every time step for imposing the source terms. Unlike many existing methods, this method does not require complex searching, extrapolation and interpolation to find the intersections of the object boundary with the unstructured background mesh and assign flow condition onto the object boundary. If it is necessary to capture the boundary layer accurately, then a dense overlapping grid can then be constructed around the object for further refined calculation. The immersed object method has been used to simulate steady and unsteady incompressible viscous flows over a stationary circular cylinder, rotating square cylinder and moving disk in cavity. The results agree well with published numerical solutions and experimental measurements.