TIME-DOMAIN AND FREQUENCY-DOMAIN NUMERICAL-SIMULATION OF LINEARIZED EULER EQUATIONS

Linearized Euler solvers based on a high-resolution numerical scheme a re presented. The approach is to linearize the numerical-flux vector a s opposed to carrying through the complete linearization analysis with the dependent-variable vector written as a sum of a mean flow and a s mall perturbation. This allows the linearized equations to be maintain ed in conservation-law form in the time domain. A harmonic assumption regarding the nature of the unsteady perturbations results in a set of time-independent equations in the frequency domain. The linearized eq uations are used to compute unsteady flows in cascades arising from bl ade vibrations. The time-domain equations are solved in a time-accurat e manner and the frequency-domain equations are solved using a local t ime-stepping procedure. Numerical solutions are compared to theoretica l results, to other linearized computations, and to numerical solution s of the nonlinear Euler equations. The frequency-domain computations were found to be at least an order of magnitude faster than the corres ponding time-domain computations.