Kinetic Treatment of Linear Stability of Finite Thickness Shocks

The bi-modal distribution of translational velocities inside shock layers and their effect on stability and unsteadiness of the flow has been previously demonstrated. Linear stability of one dimensional finite thickness shocks is investigated using kinetic methods for both base flows and linear stability equations in this study. In this work we use a kinetic method to analyze the modal linear stability characteristics of such shocks. A linearized formulation of the Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) operator is utilized with Chebyshev collocation points for the spatial discretization and Gauss-Hermite points for the micro-velocity nodes. Our in-house kinetic Linear Stability Theory (kLST) code uses sparse matrices and implicitly restarted Arnoldi algorithm for the solution of large matrices that establishes the eigenvalue problem. The code is validated against the classical compressible Couette flow cases in equilibrium conditions against the Navier-Stokes (NS) based solutions. Application of the kLST to a weak shock at M=1.2 showed good agreement against the NS based solutions as well. For higher Mach numbers with the increase in the non-equilibrium within the shock layer the difference between the NS based solution and kLST results shall increase. The higher Mach number results are in progress and will be presented at the time of the meeting.