1 Introduction ................................................. 1
1.1 Starting point .......................................... 1
1.2 A closer look at the DGM from a CAA point of view ....... 2
1.3 Objective and approach .................................. 6
1.4 Organization of thesis .................................. 6
2 Method ....................................................... 7
2.1 Acoustic Perturbation Equations ......................... 7
2.1.1 Basics ........................................... 7
2.1.2 Particularly employed form of APE ................ 7
2.2 FRPM method ............................................. 8
2.2.1 Introduction ..................................... 8
2.2.2 Theory ........................................... 9
2.2.3 Discretization .................................. 10
2.2.4 Favorable characteristics ....................... 11
2.3 Discretization of APE via DGM .......................... 12
2.3.1 Approximate representation of field variables ... 12
2.3.2 Elementwise integration of weighted residuals ... 14
2.3.3 Surface integrals ............................... 14
2.3.4 Line integrals .................................. 16
2.3.5 Semi-discrete DG formulation .................... 19
2.3.6 Time integration ................................ 20
2.3.7 Alternative mean-flow/flux representations ...... 21
2.4 Implementation ......................................... 24
2.4.1 DG code ......................................... 24
2.4.2 Further software ................................ 27
3 Results ..................................................... 29
3.1 Plane sound wave in medium at rest ..................... 29
3.1.1 Introduction .................................... 29
3.1.2 Computational setup ............................. 29
3.1.3 Evaluation of order of accuracy ................. 31
3.1.4 Results ......................................... 31
3.1.5 Summary of results .............................. 34
3.2 Monopole in plane wall ................................. 37
3.2.1 Introduction .................................... 37
3.2.2 Computational setup ............................. 37
3.2.3 Results ......................................... 38
3.2.4 Summary of DG results ........................... 40
3.2.5 PIANO computations .............................. 40
3.3 Monopole in boundary layer ............................. 44
3.3.1 Introduction .................................... 44
3.3.2 Computational setup ............................. 44
3.3.3 Results ......................................... 46
3.3.4 Summary of results .............................. 51
3.3.5 Performance of alternative approaches ........... 51
3.4 Flat plate trailing edge noise ......................... 56
3.4.1 Introduction .................................... 56
3.4.2 Computational setup ............................. 56
3.4.3 Results ......................................... 59
3.4.4 Summary and outlook ............................. 64
3.5 Airframe noise of high-lift systems .................... 65
3.5.1 Introduction .................................... 65
3.5.2 Calculation of spectra .......................... 65
3.5.3 FREQUENZ geometry ............................... 66
3.5.4 TIMPAN geometries ............................... 77
3.5.5 30P30N geometry ................................. 81
3.5.6 Summary of results .............................. 87
4 Summary, conclusions, outlook ............................... 89
4.1 Summary ................................................ 89
4.2 Conclusions ............................................ 90
4.3 Outlook ................................................ 90
Nomenclature ................................................ 92
Bibliography ................................................ 98
A Coordinate systems ......................................... 107
A.1 Global Σ coordinate system ............................ 107
A.2 Local Σ(m) coordinate system .......................... 108
A.3 Local Σj(m) coordinate system ......................... 108
A.4 Coord, transformation between Σ and Σ(m) .............. 109
B Reference shape functions .................................. 111
B.1 Two dimensions ........................................ 1ll
B.2 One dimension ......................................... 1ll
C Edge normal flux coefficients .............................. 113
D Farfield boundary .......................................... 115
E LEE convergence tests ...................................... 117
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