Numerical Simulations of Strong Shock and Disturbance Interactions Using High-Order Shock-Fitting Algorithms

High order methods that can solve flows involving 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. For numerical simulation of compressible flows, shock capturing schemes have been the most popular choice. However, most of such methods are inherently dissipative and may incur numerical oscillations near the shock. Present paper focuses on developing and implementing new algorithms based on shock-fitting and front-tracking 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. Conventionally, shock fitting is implemented on moving grid while shock forms a boundary of the computational domain. However, shock-fitted grid generation can be tedious for large and complex motions of the shock-front. Hence, we have also worked on developing a fixed grid set-up for shock-fitting method where shock is tracked using Lagrangian points and is free to move across underlying fixed grid. Using these shock-fitting algorithms we have solved one and two dimensional interactions of shock and vorticity/entropy disturbance waves and results have been found to be very satisfactory. We have also carried out a rate of convergence study to establish that, unlike shock-capturing schemes, the shock-fitting methods are high-order accurate near the shock. Although problems considered in this paper are relatively simple, the quality of results obtained from shock-fitting method provides good motivation to pursue it further for the problems of shock-turbulence interactions. In future, fixed grid shock-fitting methodology will be further developed with Immersed interface method of Zhong [1, 2] and more robust front-tracking algorithms so that more complex shock-turbulence interaction problems can be considered.