 | Schoenawa S. Higher-order discontinuous Galerkin discretizations of two-equation models of turbulence: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Aerodynamik und Strömungstechnik, Braunschweig. - Köln: DLR, 2015. - xiii, 131 p.: ill. - (Forschungsbericht; 2015-06). - Bibliogr.: p.121-128. - ISSN 1434-8454
|
Acronyms ....................................................... xi
List of Notations ............................................ xiii
List of Figures ............................................... xix
List of Tables .............................................. xxiii
1 Introduction ................................................. 1
1.1 Previous Work ........................................... 1
1.1.1 Turbulence modeling .............................. 3
1.1.2 Discontinuous Galerkin Methods ................... 6
1.2 Objective and contributions ............................. 8
1.3 Overview ................................................ 9
2 Governing equations ......................................... 11
2.1 The Navier-Stokes equations ............................ 12
2.1.1 The steady-state Navier-Stokes equations ........ 13
2.1.2 Boundary conditions ............................. 16
2.2 Derivation of the Reynolds-averaged Navier-Stokes
equations .............................................. 19
2.3 Two-equation turbulence models ......................... 22
2.3.1 Wilcox' k-ui turbulence model ................... 28
2.3.2 Menter's baseline turbulence model .............. 30
2.3.3 Menter's shear-stress transport turbulence
model ........................................... 31
2.3.4 Readability condition for k and и ............... 32
2.3.5 Boundary conditions ............................. 34
2.4 Transition ............................................. 36
3 Discontinuous Galerkin discretization ....................... 37
3.1 Basics of discontinuous Galerkin methods ............... 39
3.2 Discretization of the Reynolds-averaged Navier-Stokes
equations .............................................. 42
3.3 Artificial viscosity for shock-capturing ............... 47
3.4 Nonlinear and linear solver ............................ 48
4 Higher-order computation of the wall distance ............... 51
4.1 The brute-force approach ............................... 52
4.2 Finite Element discretization of the eikonal equation .. 55
4.3 Numerical results ...................................... 59
4.3.1 2D test cases ................................... 59
4.3.2 3D test cases ................................... 62
4.3.3 Conclusion ...................................... 66
5 Modifications, stabilizations and extensions of the SST
turbulence model in the higher-order context ................ 69
5.1 Modification of the blending function near walls ....... 71
5.2 Artificial viscosity for stabilizing the turbulent
kinetic energy k near the boundary layer edge .......... 75
5.3 Boundary condition for the specific dissipation rate ... 81
6 Numerical results ........................................... 87
6.1 Flat plate ............................................. 89
6.1.1 Influence of the smoothing scheme for k ......... 91
6.1.2 Influence of the turbulence model ............... 94
6.2 Transonic flow around the RAE 2822 airfoil ............. 96
6.2.1 Case 9 .......................................... 98
6.2.2 Case 10 ........................................ 102
6.3 VFE-2 delta wing ...................................... 106
6.4 Common Research Model ................................. 112
7 Conclusion ................................................. 117
Bibliography .................................................. 121
A. Computational meshes ....................................... 129
|
|
