Direct numerical simulation of flow in channel with time-dependent wall geometry

A numerical scheme is developed to extend the scope of the spectral method without solving the covariant and contravariant forms of the Navier-Stokes equations in the curvilinear coordinates. The primitive variables are represented by the Fourier series and the Chebyshev polynomials in the computational space. The time advancement is accomplished by a high-order time-splitting method,and a corresponding high-order pressure condition at the wall is introduced to reduce the splitting error. Compared with the ...