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.