Unverstät Stuttgart Drekte numersche Smulaton von Strömungslärm n komplexen Geometren Claus-Deter Munz Gregor Gassner, Floran Hndenlang, Andreas Brkefeld, Andrea Beck, Marc Staudenmaer, Thomas Bolemann, Muhammed Attack, Tm Kraus Insttut für Aerodynamk und Gasdynamk, Unverstät Stuttgart Berln 2011
1. Drect Smulaton and Hybrd Approach Hybrd approach Flow smulaton s seperated from sound propagaton flow smulaton acoustc source term modellng sound propagaton Advantages Low Mach number flow ncompressble smulaton RANS smulatons and turbulence data - RPM ndependent from flow smulaton Dsadvantage Modelng of acoustc source terms wth uncertantes LES flow smulaton produce huge data fles Workflow
1. Drect Smulaton and Hybrd Approach Drect smulaton Acoustcs s smulated wthn the flud flow flow smulaton together wth acoustc propagaton Advantages Smulaton based on the frst prncple: Naver-Stokes Resoluton of all relevant scales: DES, LES, DNS Dsadvantages Mach number M > 0.1 LES smulaton very expensve Sophstcated numercs flexble grds, hgh order
1. Drect Smulaton and Hybrd Approach Our opnon: LES becomes more and more mportant LES needs hgh order methods to be good and effcent same methods as for nose propagaton lnearzed equatons need nearly the same effort Our objectves: Basc research hgh order schemes and under-resolved turbulence drect smulaton of acoustcs Applcatons computatons for valdaton real applcatons
2. Dscontnuous Galerkn Schemes Fnte volume schemes Integral conservaton equaton (hyperbolc terms) u n+ 1 = ntegral mean values u n - t Q Q f( u Evoluton equaton for ntegral mean values Dscontnuous Galerkn schemes Q φ k u u h t dx (x, t) Q = u f(u) (x, t) φ = k N k=1 dx û,k + (t)φ degrees of freedom Q,k φ k (x) h ) n dx flux through the boundary, couplng to the neghbors f(u) n dx for x Q = bass functons: polynomals 0
2. Dscontnuous Galerkn Schemes Spectral scheme n every grd cell: Flexblty of grd and local order of accuracy Automatc p-adaptvty (1 N 5) Ma=0.3, Re=300 570.460 DOF decreased to 350.000 DOF by p-adaptvty
2. Dscontnuous Galerkn Schemes Research Codes HALO most general code general polymorphc grds cells tme consstent local tme steppng modal bass wth nodal ntegraton FLEXI pure hexahedrons nodal wth tensor product bass Runge Kutta tme dscretzaton Integraton ponts = nterpolaton ponts N u h, j,k 1 j 2 k 3, j,k=1 (x, t) = û (t)φ ( ξ ) φ ( ξ )φ ( ξ ) reduces work from O( N kdney shaped nozzle geometry, curved grd cells at curved boundares for x E O( N) K. Black 2000, Fagherazz et al. 2004, Graldo et al. 2002, 2008, Koprva, 2009 3 ) to Lagrangean polynomals
2. Dscontnuous Galerkn Schemes Spectral element based on quads/hex cells Q wth mappng x = X(ξ) Complex geometres possble curved grd cells!
2. Dscontnuous Galerkn Schemes Computatonal effort on a Cartesan grd for Naver-Stokes Method spec. CPU tme (Nehalem)/dof compact FD (O6) 4 Modal DG (HALO) (O6) 10 DGSEM (FLEXI) ( O6) 2 Koprva, Gassner: On the quadrature and weak form choces n collocaton type dscontnuous Galerkn spectral element methods, JSC 2011 Parallel effcency Sem-dscrete varatonal formulaton d dt û (t) = R V (û (t)) + R S (û (t),û + (t)) values from the neghbors volume ntegrals surface ntegrals Data passng s hdden behnd the volume ntegrals, drect neghbors
2. Dscontnuous Galerkn Schemes Parallel Effcency IBM Blue Gene system JUGENE (1 Petaflop peak) Strong scalng from 8 up to 32,768 processors
2. Dscontnuous Galerkn Schemes Strong scalng up to 131,072 processors (N=7, 27 Elem/Proc):
3. Under-resolved Turbulence Basc research: Hgh order methods and turbulence modellng Taylor Green Vortex: Homogeneous Isotropc Decayng Turbulence Re=5000, M=0.1 Computaton: 2x10 8 DOF, 2x10 5 tme steps, 3x10 4 processors
3. Under-resolved Turbulence Potental of hgh order DG scheme for under-resolved Turbulence Dsspaton Rate Taylor Green vortex (comparson wth DNS) Same number of DOF (64³): comparson O2 and O16 DG O2 too dsspatve, O16 accurate but unstable due to alasng!
3. Under-resolved Turbulence Vortex detecton crterum λ 2 ( Taylor Green Vortex: Re=1600) O2 (64³ DOF) O16 (64³ DOF) DNS (384³)
3. Under-resolved Turbulence Stablzed hgh order dscontnuous Galerkn scheme Re=800 Re=1600 Overall Dsspaton = Molecular Dsspaton + Numercal Dsspaton Numercal dsspaton ncreases for hgher Re (Remann solver!)
Comparson to State of the Art Methods Same resoluton (64³ DOF), ncreasng Reynoldsnumber Stablzed hgh order DG results work very well and are perfect schemes for acoustc propagaton
4. Conclusons and Current Work Hgh order DG schemes seems to be an nterestng canddate for hgh fdelty turbulence models Acoustc propagaton s automatcally captured Heterogeneous doman decomposton couplng to an acoustc solver outsde the flow regon? Nonlnear Euler equatons need nearly as much CPU tme as the lnearzed Euler equatons Current work: Valdaton for jet flow Mach 0.9 jet n cooperaton wth C. Bogey, Lyon, Test SGS and acoustcs??? Open source codes?
2. Dscontnuous Galerkn Schemes NosSol Acoustc solver acoustc propagaton on trangles lnearzed Euler equatons or APE PIANO PIANO NosSol wth sources from FRPM patch slat nose smulaton n PIANO+ project
2. Dscontnuous Galerkn Schemes Slat Nose Smulaton Pressure feld at t=2.0
4. Conclusons and Current Work Acknowledgements Support by EU-project IDIHOM (Industralzaton of Hgh Order Methods) BMBF-project STE-DG (Hgh Performance Computng) Cluster of Excellence: Smulaton Technology (SmTech) MetStroem - DFG
3. Under-resolved Turbulence LES modelng combned wth hgh order schemes
3. Under-resolved Turbulence Wde range of spatal and temporal scales Grd convergence of knetc energy spectra wth -5/3 Kolmogorov range