A New Algorithm for Shock Sensor Calculation at Supersonic Speeds on a 3D-Unstructured Grid

ABSTRACT In this paper, 3-Dsupersonic flow around two types of wings is solved using a new algorithm for shock sensor calculation. A dual-time-stepping implicit method with 2nd-order accuracy is used for time integration of the equations. In each real time step, the non-linear system of equations is solved by iterating in pseudo-time, using a multi-step integration method. A cell-center finite volume scheme is applied to discretize the solution domain. Governing equations are discretized using 2nd-order central scheme of Jameson. Undesirable oscillations are prevented using artificial dissipation terms containing 2nd and 4th-order derivative terms. The second-order derivative term is proportional to shock sensor, which is a function of pressure gradient in general and is devised to capture shock waves correctly. Appropriate calculation of shock sensor is very important especially for the solution of 3-D supersonic flow on unstructured grids. In this study, a simple efficient algorithm is proposed for shock sensor calculation to stabilize solution in supersonic 3-D flows on unstructured grids. The new algorithm, implemented at an in-house code, is evaluated by comparison of its results with wind tunnel test data and upwindtype differencing scheme of Roe for a tailplane model tested at Royal Aircraft Establishment. The results show that supersonic flow with shock waves has been accurately captured.

摘要 本文采用一种新型激波传感器（shock sensor）计算算法，求解两类机翼绕流的三维超音速流动。针对控制方程组的时间积分，本文采用具备二阶精度的双时间步隐式方法。在每个实时间步内，通过伪时间迭代求解非线性方程组，所用数值方法为多步积分格式。本文采用单元中心有限体积格式离散求解域，控制方程的离散采用Jameson二阶中心格式。通过引入包含二阶与四阶导数项的人工耗散项，可抑制非物理振荡；其中二阶导数项与激波传感器成正比，而激波传感器通常为压力梯度的函数，其设计目的为准确捕捉激波。激波传感器的合理计算尤为关键，尤其针对非结构网格上的三维超音速流动求解。本研究提出一种简洁高效的激波传感器计算算法，用于稳定非结构网格上的三维超音速流动求解过程。该新算法已集成至自研代码中，通过与英国皇家航空研究院（Royal Aircraft Establishment）测试的平尾模型的风洞试验数据，以及Roe迎风格式（upwind-type differencing scheme）的计算结果进行对比，完成了算法验证。结果表明，该算法可准确捕捉含激波的超音速流动。