An efficient linear wavepacket tracking method for hypersonic boundary-layer stability prediction

Abstract

A new linear wavepacket tracking method is presented that can ultimately be used for efficient transition prediction of hypersonic boundary-layers. The wavepacket tracking method employs higher-order accurate adaptive mesh refinement to track wavepackets that are introduced in the boundary-layer via pulse disturbances. The evolution of these wavepackets is used to extract boundary-layer stability characteristics, such as amplitude curves, growth rates and N-Factor curves, which are commonly used for transition prediction. The efficiency and accuracy of the wavepacket tracking method, for determining the stability characteristics of the flow, strongly depends on the numerical implementation details, such as the refinement criteria, the tracking parameter and refinement function used for adaptive mesh refinement. While the computational expense at one time step of continuous forcing approaches, commonly employed in direct numerical simulations of transitional flows, scales with the size of the geometry of interest, the computational expense for the current adaptive mesh refinement wavepacket tracking method scales with the size of the wavepacket. A detailed description of the adaptive mesh refinement wavepacket tracking (AMR-WPT) method and its computational expense is provided and the method is validated against stability analysis results extracted from direct numerical simulations on static meshes and linear stability theory for a supersonic shear layer and different hypersonic boundary-layer flows.