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Text:    Optimal MODIFIED CONTINUOUS Galerkin CFD,  (2014)
References:       1. Wilcox, Turbulence Modeling for CFD,  (2006)
      2. Pope, Turbulent Flows,  (2000)
      3. John, Large Eddy Simulation of Turbulent Incompressible Flows,  2004)
      4. Cebeci & Smith, Analysis of Turbulent Boundary Layers,  (1974)
      5. Sekachev et al, J. Computational Physics,  (2014)
      6. Tannehill,  Anderson & Pletcher,Computational Fluid Mechanics and Heat Transfer , (1997)
 
 
Class Date Lecture Topics Courseware Prob Due    Text Chapter Reference
 
1  JAN  8  Schedule, course requirements, mathematical physics characterization of turbulence  TFD.1 - .10 P-1   1.1_1.4  1, Ch. 1
2, Ch. 6.1
2  13  RaNS tutorial, optimal continuum weak form GWSN + TS, error norm, trial space basis h/p adaption, Reynolds stress tensor models  CFD.1 - .8
 CST.1 - .3 		     8.1_8.7  
3  15  Fourier spectral theory, CFD optimal mGWSh/GWSh + TS, stability, dispersion error, numerical diffusion  CST.4 - .17    P-1  5.5_5.8
 6.2_6.4 		 
4   20  Aerodynamics, steady BL GWSh + TS, optimal accuracy/convergence, time averaged BL, MLT closure model  PNS.1 - .8 P-2   3.1_3.3
3.7, 3.12   
4.1_4.8 		  
5  22  Aerodynamics, n-D turbulent parabolic NS, TKE closure models, GWSh + TS, Re stress algebraic model, validations, hypersonic shock layer  PNS.9 - .19
  		4.9_4.14
App. B 		  
6  27  Unsteady NS, pressure projection theory, phi, sumphi, genuine pressure, optimal mGWSh + TS, stability, dispersion error  PPNS.1 - .10
  		P-3 P-2 5.1_5.4
5.9_5.11   		 
7  29  Unsteady time averaged RaNS, TKE closure model, wall function BCs, optimal mGWSh + TS, stability, dispersion error annihilation  PPNS.10 - .19    8.1_8.5   
8  FEB 3  Turbulence characterization, unsteady time averaging, Re stress tensor PDE + BCs, auto correlations, parabolic similarity theory  TFC.1 - .8  P-4   8.7_8.9
App.B.4  		  1, Ch.2 
9  5  Parabolic RaNS similarity theory, MLT closure model design, wall/farfield modifications, norms  TFC.9 - .15
  		   P-3 4.7  1, Ch.3,
4, Ch.X  
10  10  RaNS + PDE closure models, BCs, similarity, farfield  RANS.1 - .8 P-5   4.9  1, Ch. 4
11  12  RaNS + PDE closure models, farfield, low Ret alterations, computed comparisons  RANS.9 - .17
  		P-4    1, Ch. 4
12  17  Compressible NS, Favre mass-weighted time average, contravariant vectors, turbulence closure issues  CNS.1 - .6  P-6   App B.1 - B.4  1, Ch.5.1 - 5.4  
13  19  Compressible RaNS, law of the wall, PDE closure, near-field resolution  CNS.7 - .12   P-5   1, Ch. 5.6 - 5.7  
14  24  Reynolds stress tensor models, non-linear, frame indifference, algebraic, parabolic-order ASM  ASM.1 - .8 P-7   4.10_4.14   1. Ch. 6.1 - 6.2
   
15  26  Re stress transport, closure correlations, low Ret  ASM.9 - .17 P-6 8.7_8.9  1. Ch. 6  
16  MAR 3  Beyond time averaged NS, direct (DNS), space filtered (LES), BCs, detached eddy (DES)  BRaNS.1 - .8 P-8   1.3, 9.2 
10.4 		 1. Ch.8 
17  5  Mathematical physics descriptions in turbulent fluid dynamics, stastical mechanics, random variables  MMFD.1 - .9 P-9      2. Ch.2,  3
18  10  Mathematical physics, probability distributions, joint random variables, processes  MMFD.10 - .18 P-7   2. Ch. 3
19  12  Mathematical physics, random vector fields, covariance, mean flow equations, Boussinesq closure  MMFD.19 - .25   P-8   2. Ch.3,  4
  17  Spring Break      
  19  Spring Break      
20  24  DNS, LES, subgrid scale (SGS) phenomena, filtered random variable, Fourier transforms  LES.1 - .8 P-10     2. Ch. 9, 13 
21  26  LES, filtered spectra, mesh resolution, Smagorinsky SGS tensor closure, filter definitions  LES.8 - .16 P-9   2. Ch. 13 
22  31  LES closure, dynamics, implicitness, computational issues requiring resolution  LES.16 - .18
CLES.1 - .6 		    3. Ch. 1
23  APR 2  Computational LES, fundamental issues errors, notation, spaces, norms CLES.7 - .13   9.2, 9.3  3. Ch. 2, 3
24  7  Rational LES (RLES), gaussian filter Fourier transform interpolations, analytical predictions  CLES.14 - .20 P-11    9.4, 9.5  3. Ch.4
25  9  LES solution process, weak forms existence, uniqueness, discretization, asymptotic convergence, verification  CLES.21 - .29 P-10    3. Ch. 5-8, 10
26  14  RLES theory, weak solution boundedness, verification class SFS tensor model assessments  CLES.30 - .37   9.5  3. Ch. 11
27  16  RLES theory reprise, weak form algorithm, unresolved issues: auxiliary problem BCs, SFS tensor closure  CFDLES.1 - .6 P-11     9.7
 AUX1   RLES issues resolution, analytical SFS tensor/vector derivation, arLES theory filter-ordered state variable, DES BCs, laminar Re validation, mesh adequacy diagnostics
no lecture video 		 XXX.1 - .24  9.8_9.11   
 AUX2   arLES theory well-posed on bounded domains, Dirichlet BCs resolution, model-free! laminar-turbulent transition validation, mesh adequacy
no lecture video 		 XX.1 - .24  9.13_9.21   
28  21  Course summary
at the time! 		 SUM.1 - .24     
29  23   Student assessment
Take-home final exam		      
30  30   Final Exam due, mounted at 4:00pm.      
 
ADD DEADLINE: JANUARY 16 DROP DEADLINE:  JANUARY 16
STUDY PERIOD: APRIL 24 FINAL EXAM: APRIL 30
 

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