A New Fourier Spectral Method for the Direct Numerical Simulationof Three-dimensional, Spatially GrowingCompressible Boundary Layer Transition

Abstract

In a conventional numerical scheme, the computational domain is truncated from a large physical system, leaving the inflow/outflow boundary conditions difficult to specify. In this study, a "spatial window function" is introduced to truncate the computational domain from the physical domain in the streamwise direction. The standard compressible Navier-Stokes equations are transformed into a set of equations with periodicity in this direction. Fourier spectral methods then can be used in the streamwise direction to solve this set of equationsefficiently. No numerical inflow/outflow boundary conditions are needed. Theories regarding the convergence property of this new scheme and design principles for the window function are developed. The accuracy of the scheme is shown to be mainly related to the window function. By properly designing the window function, spectral accuracy can be obtained. Issues concerning the numerical implementation of this scheme are also discussed.