Wallraff M. An investigation of multigrid algorithms for a higher order Discontinuous Galerkin RANS solver: Diss. … Dr.-Ing. / Deutsches Zentrum für Luft- und Raumfahrt, Institut für Aerodynamik und Strömungstechnik, Braunschweig. - Köln: DLR, 2015. - xxi, 153 p.: ill. - (Forschungsbericht; 2015-20). - Res. also Germ. - Bibliogr.: p.147-153. - ISSN 1434-8454  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

1 Introduction ................................................. 1 1.1 Literature review and contribution to the field ......... 3 1.2 Objective ............................................... 6 1.3 Thesis outline .......................................... 6 2 Governing equations in CFD ................................... 8 2.1 The compressible Navier-Stokes equations ................ 8 2.2 Flux formulation of the steady-state Navier-Stokes equations .............................................. 10 2.3 Reynolds-averaged Navier-Stokes equations .............. 14 2.3.1 The steady-state RANS-kω equations .............. 15 2.3.2 The steady-state RANS-SA equations .............. 19 3 Discontinuous Galerkin discretization ....................... 22 3.1 Triangulation .......................................... 22 3.2 Numerical flux function for convective terms ........... 27 3.2.1 Roe flux ........................................ 27 3.2.2 Eigenvalue decomposition of the flux Jacobian ... 28 3.3 Boundary conditions .................................... 30 3.4 Basis functions ........................................ 32 3.5 Mesh related issues .................................... 33 4 Solver methods .............................................. 36 4.1 Nonlinear multigrid methods ............................ 39 4.2 Nonlinear smoothers / single level solver .............. 40 4.2.1 Baekward-Euler .................................. 41 4.2.2 GMRes method .................................... 43 4.3 Linear multigrid algorithm ............................. 44 4.4 Linear smoothers / preconditioner ...................... 45 4.5 Startup strategy ....................................... 47 4.6 Transfer Operators ..................................... 49 4.7 Line creation .......................................... 51 4.8 Mesh agglomeration ..................................... 55 4.9 Solver overview ........................................ 58 5 Computational test cases .................................... 67 5.1 Test case introduction and framework verification ...... 67 5.1.1 L1T2 high-lift three element airfoil ............ 68 5.1.2 MDA 30P30N three element airfoil ................ 74 5.1.3 VFE-2 delta-wing ................................ 78 5.1.4 NASA Trap Wing .................................. 82 5.2 Algorithmic investigations ............................. 86 5.2.1 General settings and information ................ 88 5.2.2 Investigation of startup strategies ............. 92 5.2.3 Trade-off between nonlinear and linear iterations ..................................... 101 5.2.4 Coarse level linearization ..................... 105 5.2.5 Linear multigrid algorithm as a preconditioner ............................... 107 5.2.6 Linear multigrid algorithm as a solver ......... 116 5.2.7 Investigation of the nonlinear multigrid algorithm ...................................... 119 5.2.8 Investigation of different solver choices ...... 125 5.2.9 h-and p-independency ........................... 131 5.3 Framework benchmark ................................... 135 6 Conclusions ................................................ 140 A Convective flux Jacobian ................................... 143 В TauBench ................................................... 145 Bibliography .................................................. 147