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Andrew McCracken Supervisor: Professor Ken Badcock

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Presentation on theme: "Andrew McCracken Supervisor: Professor Ken Badcock"— Presentation transcript:

1 Accelerating Convergence of the CFD Linear Frequency Domain Method by a Preconditioned Linear Solver
Andrew McCracken Supervisor: Professor Ken Badcock University of Liverpool

2 Summary Frequency Domain Methods in CFD Linear Frequency Domain
LFD Solution Methods LFD Linear Solver Approach ILU Weighted Preconditioner Extension of Method Conclusions

3 Frequency Domain Methods in CFD
Originally developed for turbomachinery flows Models time-domain flow equations in frequency domain Quicker solution time compared with time-domain

4 Frequency Domain Methods in CFD
Useful for flutter analyses Useful for flight dynamics purposes

5 Linear Frequency Domain
Linearise assuming small perturbations: Solve resulting linear system:

6 Previous Solution Methods
LU-SGS - Semi-implicit - Face-based matrix - Can use GMRes method PETSc - Many options including implicit linear solvers - Many preconditioning options

7 Preconditioned Linear Solver
GCR Krylov solver ILU preconditioning A is second order Jacobian Approximation of P to A determined viewing solution of:

8 Preconditioned Linear Solver
Second Order Preconditioner

9 Preconditioned Linear Solver
First Order Preconditioner

10 Preconditioned Linear Solver
Good Approximation Effective conditioning Second Order Jacobian First Order Jacobian Unstable Stable Mixed-order??

11 Preconditioned Linear Solver
Mixed Order Preconditioner

12 ILU Preconditioner Formulation
Form the exact first and second order Jacobian matrices A1 and A2 Form mixed matrix Aα where α is second order weight Form preconditioner Pα from Aα

13 Test Cases 2D test cases - NACA 0012 AGARD CT2 (Euler)
- NACA 64A010 AGARD CT8 (RANS) 3D test cases - Goland Wing (Euler) - Goland Wing (RANS)

14 Convergence Goland Wing M = 0.925 α0 = 0.0° αA = 1.0° k = 0.025
Re = 15x106

15 Effect of Weighting NACA 64A010 M = 0.8 α0 = 0.0° αA = 0.5° k = 0.1
Re = 12.5x106 Pure First Order Pure Second Order

16 Goland Wing (inviscid), M = 0.8, α0 = 0.0°,αA = 1.0°, k = 0.025
Parallelisation Goland Wing (inviscid), M = 0.8, α0 = 0.0°,αA = 1.0°, k = 0.025

17 Conclusions ILU-GCR solver implemented for LFD in TAU
Weighted ILU offers greater speed up of LFD over time domain Preconditioned solver has allowed flutter analysis on an Airbus full aircraft test case Flight dynamics analysis of other large test cases has been carried out

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