Numerical studies of shock amplified flow instabilities by a hybrid Lagrange-Euler pseudo-spectral method

The generation and evolution of Rayleigh-Taylor instabilities, their degeneration to Kelvin-Helmholtz shear instabilities, and the resulting chaotic mass mixing in two-fluid-interface systems are investigated theoretically. A numerical simulation technique is developed which determines the spatial position of the interfaces and the time evolution of the advancing shock wave by a Lagrangian finite-difference procedure and follows the advection transversely spreading the instability by an Eulerian pseudospectral method operating only in the spanwise material-homogeneous regions between the advancing Lagrange material interfaces. A two-step Lorenz procedure and the predictor-corrector scheme of MacCormack (1969) are compared as integration schemes in sample calculations simulating instability-growth experiments. The results are presented graphically and discussed briefly. The MacCormack procedure is found to give results in good agreement with theory and experiment.