High-Order Shock-Fitting and front-tracking Methods for Numerical Simulation of Shock-Disturbance Interactions

High-order methods that can resolve interactions of flow-disturbances with shock waves are critical for reliable numerical simulation of strong-shock and turbulence interaction problems. Such problems are not well understood due to limitations of numerical methods. Most of the popular shock-capturing methods are inherently dissipative and may incur numerical oscillations near the shock. Present paper is continuation of our previous work [1] on development and implementation of new algorithms based on shock-fitting and fronttracking methodology which can solve the flow with high-order accuracy near as well as away from the shocks. The shock-fitting algorithm avoids dissipation and possible numerical oscillations incurred in shock-capturing methods by treating shocks sharply. We explore two ways for shock-fitting: conventional moving grid set-up and a new fixed grid set-up with front tracking. In conventional shock-fitting method, a moving grid is fitted to the shock while in the newly developed fixed grid set-up shock is tracked using Lagrangian points and is free to move across underlying fixed grid. High order front-tracking method gives satisfactory results for 2-D shock disturbance interaction problem. We also studied various methods to find shock velocity. It was found that conventional method of advancing the shock using characteristics based shock-acceleration relation gives more accurate results than other methods considered. Shock-turbulence interaction problems may produce nonlinearities like secondary shocks in the post-shock flow. Hence, we have combined our shock-fitting methodology with shock-capturing methods. Convergence analysis was carried out for combined shock-fitting and WENO methods for an unsteady shock disturbance problem and expected fifth order accuracy was achieved. It was found that, where applicable, shock-fitting algorithm provides superior results to those obtained from purely shock-capturing schemes.