3D Unsteady aerodynamics solver features

In this section, we present the numerical features of the ALE Navier-Stokes code Canari (Vuillot et al., 1993). This 3D code solves Euler and Reynolds – averaged Navier-stokes equations in multi-block structured grids.

1.1 Space and time ALE discretization for the mean flow

Unsteady Navier-Stokes computations have to be performed in a moving grid framework. An ALE (Arbitrary-Lagrangian-Eulerian) numerical scheme has therefore been developed. The spatial discretization is based on a centered finite volume approach. The fliid motion equations are written in a frame, which rotates at circular frequency D. In this frame, the grid is moving at velocity Vg :

where Q = (p, pW, pE)t is the unknown field vector, Fc[Q, Vg] the convective flix, Fd[Q, gradQ] the diffusive flix and T[Q] the source term. W is the relative velocity of the fluid and E the relative total energy in the rotating frame.

The time integration (Jameson et al.,1981) is performed using a Jameson – like four stage Runge-Kutta scheme. Second and fourth order artificial viscos­ity terms are added to the original scheme in order to obtain suitable dissipative
properties. The implicit spectral radius method of Lerat (Lerat et al., 1982) is used to increase the stability domain.