Dynamic mode extrapolation to improve the efficiency of dual time stepping method

This work proposes a methodology to improve the computational efficiency of unsteady flow simulations with dual time stepping scheme. The methodology is developed on the combination of dynamic mode extrapolation and dual time stepping scheme. It accelerates the convergence speed of the inner iterations by using dynamic mode extrapolation to provide an initial solution for each physical time step. The validation and verification are demonstrated by three cases, including unsteady flow past a stationary circular cylinder at Re = 200, transonic flow over periodic and non-periodic pitching NACA 0012 airfoil and buffeting flow around NASA(SC)-0714 airfoil. For comparison, Lagrange extrapolation initial condition and natural initial condition are also applied. The results confirm that the proposed methodology is very successful in reducing computational time for both incompressible and transonic unsteady flow.