Development of semi-implicit Runge-Kutta schemes and application to a turbulent channel flow

In this paper, two semi-implicit Runge-Kutta algorithms are developed for the simula-tion of wall-bounded flows. Using these schemes, the time integration is performed in an implicit way in the wall-normal direction, and in an explicit way in the other directions, in order to relax the time step constraint due to the fine mesh size at the wall. Based on ana-lysis in the Fourier space and on results obtained for acoustic test cases, the semi-implicit schemes are shown to be of order 3 and to provide low dissipation and low dispersion. The accuracy of the schemes is compared with that of other schemes of the litterature. They are found to be at least as accurate as the standard Runge-Kutta algorithm of order 4. An LES of a turbulent channel flow at a friction Reynolds number of 360 and a Mach number of 0.1 is also carried out with one of the semi-implicit algorithms. In this case, a reduction of the computational time by a factor 1.33 with respect to an explicit scheme is obtained. Wall pressure and velocity spectra from the LES are presented to give insights into the turbulent structures developing in the flow. In particular, acoustic components are identified in the wavenumber-frequency spectra of wall pressure fluctuations. I