THESE de DOCTORAT - cerfacs

List of Figures
1.1 Main sources of aircraft noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2 Acoustic solvers: The Euler acoustic solver is used beforehand to provide proper
boundary conditions to the low Mach number acoustic solver. . . . . . . . . . . 19
3.1 A triangular element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 A set of six triangular cells embedded in a mesh grid . . . . . . . . . . . . . . . . 44
3.3 A set of three triangular cells at the boundary of the computational domain . . 44
3.4 Typical Matrices for a non-structured 3D problem [93]. Non-zero entries are
shown as dark points. Here C T is the transpose of C. The dyadic product CC T
is shown to display the non-zero elements of C j . . . . . . . . . . . . . . . . . . . 46
3.5 Reduction of the linear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Hessenberg decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 The GMRES Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.8 The embedded GMRES Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.1 Monopoles placed at y and listener placed at x . . . . . . . . . . . . . . . . . . . 59
4.2 Outputs of AVSP-f. Monopole case . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Acoustic field produced by a monopole. p ′ = | ˆp| cos(arg( ˆp)) . . . . . . . . . . . 60
4.4 Analytical solution vs Numerical solution. . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Outputs of AVSP-f. Dipole case . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.6 Acoustic field produced by a dipole. p ′ = | ˆp| cos(arg( ˆp)) . . . . . . . . . . . . . 62
4.7 Analytical solution vs Numerical solution. . . . . . . . . . . . . . . . . . . . . . . 63
4.8 Outputs of AVSP-f. Three monopoles out of phase . . . . . . . . . . . . . . . . . 64
4.9 Acoustic field produced by three monopoles out of phase. p ′ = | ˆp| cos(arg( ˆp)) . 64
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