A 2D Navier-Stokes method for unsteady compressible flow calculations on moving meshes

Abstract

AbstractA moving mesh method for the computation of compressible viscous flow past deforming and moving aerofoils is described. It is based on a well established time-marching finite-volume scheme, which has been widely used for steady compressible flows. An implicit real-time discretisation is used and the equations are integrated via a dual-time scheme. This involves the introduction of derivatives of a fictitious pseudo time. The solution at each real-time step involves seeking solutions which are steady-state solutions in pseudo time. This approach decouples the stability and accuracy limitations of the scheme and permits large real-time steps to be chosen. Also well-proven convergence acceleration techniques developed for steady flows such as local-time stepping, residual averaging and multigrid may be used in the pseudo-time stepping scheme without compromising real-time accuracy. A sequence of body-conforming grids and corresponding grid speeds is required, where the inner and outer boundaries of the grid move independently. The required grids and speeds are found using a transfinite interpolation technique. Applications of the method to external compressible flows are shown, including results from a parallel version of the computer program.