High-Fidelity Versatile Incompressible Flow Solver for Direct Numerical Simulations and Linear Stability Investigations

A high-fidelity versatile incompressible Navier-Stokes code was developed that is applicable for both Direct Numerical Simulations (DNS) and linear global stability investigations. The solver is based on a vorticity-velocity formulation of the Navier-Stokes equations for curvilinear orthogonal grids. It is programmed in Fortran 90 and employs parallelization using a hybrid MPI-OpenMP. The code incorporates advanced numerical algorithms, specially designed for simulations of transitional and turbulent flows. The solver includes linear stability modules based on the linearized Navier-Stokes equations (LNSE) that are tailored for primary and secondary instability investigations. No further assumptions are necessary (other than small amplitudes) with respect to the baseflow, and the primary wave as are required for conventional Linear Stability Theory (LST) and/or for Parabolic Stability Equations (PSE) analyses. Furthermore, since here the linear stability analysis is based on an initial value problem for LNSE, it is applicable for both convective and absolute/global instability with respect to both primary and secondary instability. An additional major advantage of the developed versatile solver is that linear/non-linear effects can be consistently evaluated by turning off/on the nonlinear terms. The new solver was employed for DNS of the flow for a wing section at a chord Reynolds number of Re = 200k. The capability of the linear stability modules was demonstrated by investigating the primary and secondary (convective & absolute) instability mechanisms for boundary layers and the flow past a circular cylinder.