Development of an incompressible Navier-Stokes solver and its application to the calculation of separated flows

Using the method of pseudo-compressibility and dual time stepping, a unified formulation is presented to solve the two-dimensional, incompressible Navier-Stokes equations for both steady-state and time-dependent flow problems. The resulting equation is rigorously hyperbolic, and the steady-state equation obtained as a special case with infinite physical time step is identical to the one derived for steady state only. The algorithm uses second-order central differencing for viscous terms, and both central differencing and upwind differencing for the convective terms. The equations are solved using an LU-SGS scheme, a point symmetric-Gauss-Seidel (SGS) relaxation scheme and a line SGS relaxation scheme. The LU-SGS scheme originally proposed in a factored form is reformulated as a relaxation scheme, and the efficiency of the relaxation schemes are improved by performing multiple forward and backward sweeps. Numerical experiments are done and multiple sweeps yield better convergence than a single sweep for LU-SGS and point SGS schemes. The performance of each scheme with optimal number of sweeps is compared, and the point SGS scheme is found to be most efficient. The accuracy of the code has been verified by comparison with other computations and experiments for both stationary and time-dependent flow problems. The present method is used to calculate some steady-state and time-dependent flow problems. The first application is to calculate the flowfield around an airfoil with a spoiler in a time-accurate manner, and the unsteady vortex shedding from the spoiler tip and airfoil trailing edge is well simulated. The incompressible Navier-Stokes solver is also used to predict ice growth on an airfoil by replacing the compressible solver in the ice accretion prediction code for low Mach number flows. Less than one third of the computer time for the compressible solver is required with the incompressible code for typical cases. The time savings, thanks to the use of the incompressible solver, will enable more frequent update of the flowfield and eventually help predict the ice accretion accurately.