Application Studies Of High-order Accurate Schemes To Unsteady Flows

While Numerical simulation method is used to compute unsteady Euler/N-S equations, 5-order accurate weighted compact nonlinear scheme(WCNS) has been applied to calculate unsteady flows of single-degree-of-freedom forced/free oscillation. In this paper, some essential problems of high accuracy unsteady calculation are conducted. Such as unsteady"dual-time-step"method, various difference schemes for time derivative and calculation of coupled equations. Finally, high-order accurate scheme is used to compute unsteady dynamic stability derivatives. The numerical results show that:1. When"dual-time-step"method is applied to high accuracy unsteady calculation: (a), The physical time step has a enormous effect on both calculation accuracy and efficiency; A long physical time step can also reduce convergence ability; physical time step play an important role in unsteady numerical simulation.(b), A perfect tolerance(Tol) of inner iteration is the one which can save computation time while ensure the computation accuracy.(c), Compared with 2-order schemes, high-order scheme has to compute with a relatively small CFL number which will slow down the speed of convergence in the progress of inner iteration.2. While the time derivatives is decreted with 1-order,2-order and 3-order difference schemes, the numerical results show that: 1-order scheme perform worse in calculation efficiency, while 2-order and 3-order scheme at the same level; 3-order scheme prone to non-physical oscillations(which can be weakened by a shorter physical time step or a higher Tol level); Overall, 2-order scheme shows a totally better performance in accuracy, efficency and stability.3. To numerically simulate the unsteady flows of free oscillating, loosely coupled method and tightly coupled method are adopt to solve coupled equations. The results show that: Differences of time solving accuracy between the two coupling methods are very small; If the calculation efficiency is considered, then loosely coupled method will have a totally 15% advantage over tightly coupled method.4. When the high-order accuracy scheme(WCNS) is applied to the dynamic stability derivatives calculation:, The calculation results of pitch damping derivatives and pitch stiffness based on free oscillation method are acceptable; Dynamic stability of blunted 10-degree cone is immune to oscllation amplitude, but weakened if center of gravty is moved back; For a free oscillation, the oscillation mode and calculation result are affected by Moment-of-Inertia a lot.