Finite volume method 1- Closed surface 2- Rigid motion of the blade 3- Geometric Conservation Law
Calculations of the surface fluxes
IMPLICIT DUAL-TIME METHOD Redefinition of the Residual term Spatial discretisation Time discretisation
Time-stepping SCHEME 1- Multi-stage Runge-Kutta scheme 2- Unfactored-factored method Use of acceleration techniques CFL number
RESULTS from previous reports JAMESON - Runge-Kutta ROE - FUN method Preference for the ROE-FUN method: - BETTER respect of the physic (convection) - FASTER convergence
FUN METHOD Factorisation in the spanwise direction 2 LINEAR SYSTEMS
ANALYSES of the FUN method SMALL SIZE of the matrices LARGE NUMBER of pseudo-time steps to get a high convergence. Problems to damp out the small errors frequencies
Objectif: SPEED the code UP 1- CODING 2- ALGORITHM UNFACtored method
CODING UNROLLING of repetitive operations Transformation of the matrices (5x5) into a vector (25x1)
ALGORITHM Implementation of the UNFACtored method Modification of the LHS block matrix size where the flow variables are stored Consideration of the 3 Dimensions
REFERENCE TESTS - LANN WING : unsteady case (3D) - EC/ONERA 7A 4-bladed Model Rotor Model Rotor in transonic hover flight Single block grid
UNSTEADY Case - LANN wing y/b=0.475 y/b=0.825 Sectional Force Coefficients Pitching moment coeff.
UNSTEADY Case - LANN wing y/b=0.475 y/b=0.825 Mean Steady PressureFirst Harmonic Pressure
Convergence behaviour STEADY run UNSTEADY run
Periodic OH grid, 84 x 60 x 32 7A Model Rotor in hover flight
Pressure Coefficient distribution, Normal force Coeff.
COMMENTARIES UNFACtored method Higher CFL number Faster convergence Higher average computing time / iterations
CONCLUSIONS GOOD agreement with the FUN method Calculations 5 times faster This method requires some other tests. It looks ATTRACTIVE for the unsteady cases
FUTURE WORK Use of the UNFACtored method for the CHIMERA grid Implementation of the WENO method relevant to a future AEROACOUSTIC module: Blade Vortex Interaction (BVI) MPI implementation to enable the studies of large and important cases.