Design of a high-performance unsteady Naiver–Stokes solver using a flexible-cycle additive-correction multigrid technique

A multigrid technique, based on a flexible-cycle additive-correction multigrid (FCAC-MG) scheme, is utilized to design a high-performance solver for the unsteady incompressible Navier–Stokes (N–S) equations. The unsteady incompressible N–S solver discussed here incorporates the fractional step method and finite volume discretization over a staggered Cartesian grid. The current research indicates that the FCAC-MG acceleration technique is highly efficient, reliable and robust, which makes it feasible for CPU-intensive computations, such as large eddy simulation (LES) and direct numerical simulation (DNS). The high efficiency and the robustness of the solver are achieved through developing the FCAC-MG acceleration technique as well as flow-physics oriented solving strategies. The flow solver based on the FCAC-MG technique is applied to both temporal and spatial turbulence simulations using both LES and DNS. The residuals of the large-scale algebraic equation system are guaranteed to be continuously driven down to the level of the computer machine round-off error on each time marching step, which warrants strong conservations of mass and momentum satisfied over all the control volumes. In addition, the flow solver developed in the current research possesses the potential capability for handling complex geometry flows since the performance of the solver does not rely on the use of special type of operations on the large-scale algebraic equation system, unlike the cyclic reduction algorithm, but instead it is driven by a flow-physics oriented solving strategy. LES for flows in a square duct, a square annular duct and a confined square coaxial jet are performed to present the advantages of the FCAC-MG technique and the flow-physics oriented solving strategy. The analyses of the simulation results for these three flow configurations provide strong evidence that the flow solver based on FCAC-MG method is capable of capturing the major characteristics of turbulence physics and correctly predicting the relevant turbulent flow phenomena.