Newmark scheme

Using the variable Q = (q, q)1 gives a first order in time differential equa­tion:

AQ + BQ = F * A=(J£) B=(“-1) F=(£)

At time tn+2 , a second order in time discretization is obtained using New- mark’s scheme.

With aerodynamic forces being calculated at time /" 1 ^ , a mechanical cou­pling iteration has to be performed in order to equilibrate generalized coordi­nate at time tn+1. The following numerical scheme is implemented:

■ Modal mesh deformations computation TIMELOOP: Physical time loop

Generalized coordinates estimate at t”+1 MECALOOP: Coupled fluid – structure equilibrium loop

Grid velocity computation DUALLOOP: Dual time loop

RKLOOP: Runge – Kutta loop ■ Unsteady Aerodynamic dual step END RKLOOP END DUALLOOP

Generalized coordinates and metric updating at tn+1 END MECALOOP if convergence criterium is reached

END TIMELOOP