Fu Future Direction in Turbulence Modeling: Oleg V. Vasilyev & - PowerPoint PPT Presentation

Fu Future Direction in Turbulence Modeling: Oleg V. Vasilyev & AliReza Nejadmalayeri Department of Mechanical Engineering University of Colorado Boulder Department of Mechanical Engineering F Multi-Scale Modeling Multi-Scale Modeling u t u r e D i r e c t i o n s i n C F D R e s e a r c h , A u g u s t 8 , 2 0 1 2 1 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Fu Dynamic Two-way Coupling of Fu Future Direction in Turbulence Modeling: Numerical Methods and Physical Models Oleg V. Vasilyev & AliReza Nejadmalayeri Department of Mechanical Engineering University of Colorado Boulder Department of Mechanical Engineering F Multi-Scale Modeling Multi-Scale Modeling u t u r e D i r e c t i o n s i n C F D R e s e a r c h , A u g u s t 8 , 2 0 1 2 1 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Fu Dynamic Two-way Coupling of m(q)-LES Fu Future Direction in Turbulence Modeling: Numerical Methods and Physical Models Adaptive LES with Model Refinement Oleg V. Vasilyev & AliReza Nejadmalayeri Department of Mechanical Engineering University of Colorado Boulder Department of Mechanical Engineering F Multi-Scale Modeling Multi-Scale Modeling u t u r e D i r e c t i o n s i n C F D R e s e a r c h , A u g u s t 8 , 2 0 1 2 1 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? Parallel adaptive high order numerical methods New/improved turbulence models Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? Parallel adaptive high order numerical methods Not New/improved turbulence models Not Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? Parallel adaptive high order numerical methods Not New/improved turbulence models Not Reasons: • Spatial/temporal intermittency of turbulent flows is not used • Inhomegeneous fidelity - a-priori large/small scale separation - under-resolves energetic structures - over-resolves in between them Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? Parallel adaptive high order numerical methods Not New/improved turbulence models Not Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? Parallel adaptive high order numerical methods New/improved turbulence models Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? New direction/philosophy/paradigm : Parallel adaptive high order numerical methods New/improved turbulence models Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Future Directions in CFD Research? New direction/philosophy/paradigm : Direct physics-based coupling of Parallel adaptive high order numerical methods & New/improved turbulence models that takes advantage of spatio-temporal intermittency of turbulent flows Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 2 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

What does direct coupling bring? • the active control of the fidelity/accuracy of the simulation • near optimal spatially adaptive computational mesh • the “desired” flow-physics is captured by considerably smaller number of spatial modes • considerably smaller Reynolds scaling exponent, Re α , α < 9 / 4 • robust general mathematical framework for spatial/temporal model -refinement ( m -refinement) that can be extended to LES with AMR approach • mathematical framework for epistemic uncertainty quantification Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 3 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Wavelet-based Turbulence Modeling Hierarchy Wavelet thresholding filter: 2 n � 1 + 1 d µ,j k ψ µ,j X X X X c 0 l φ 0 > ✏ i ( x ) = l ( x ) + k ( x ) u l 2 L 0 j =0 µ =1 k 2 K j | d j k | � ✏ k u k Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 4 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Wavelet-based Turbulence Modeling Hierarchy Wavelet thresholding filter: 2 n � 1 + 1 d µ,j k ψ µ,j X X X X c 0 l φ 0 > ✏ i ( x ) = l ( x ) + k ( x ) u l 2 L 0 j =0 µ =1 k 2 K j | d j k | � ✏ k u k Physical Space Wave Number Space Local Local Support Support -5 x 10 1.5 5 1 4 0.5 3 X) K) � ( � ( 0 2 � � � -0.5 1 -1 0 0 0.2 0.4 0.6 0.8 1 0 20 40 60 80 100 � X Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 4 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Wavelet-based Turbulence Modeling Hierarchy Wavelet thresholding filter: 2 n � 1 + 1 d µ,j k ψ µ,j X X X X c 0 l φ 0 > ✏ i ( x ) = l ( x ) + k ( x ) u l 2 L 0 j =0 µ =1 k 2 K j | d j k | � ✏ k u k Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 4 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Wavelet-based Turbulence Modeling Hierarchy Wavelet thresholding filter: 2 n � 1 + 1 d µ,j k ψ µ,j X X X X c 0 l φ 0 i ( x ) = > ✏ l ( x ) + k ( x ) u l 2 L 0 j =0 µ =1 k 2 K j | d j k | � ✏ k u k ≤ ✏ ( x , t ) u ( x , t ) = u > ✏ ( x , t ) + u Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 4 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12

Wavelet-based Turbulence Modeling Hierarchy Wavelet thresholding filter: 2 n � 1 + 1 d µ,j k ψ µ,j X X X X c 0 l φ 0 > ✏ i ( x ) = l ( x ) + k ( x ) u l 2 L 0 j =0 µ =1 k 2 K j | d j k | � ✏ k u k Choice of : ✏ • WDNS - ✏ ⌧ 1 ≤ ✏ ( x , t ) u ( x , t ) = u > ✏ ( x , t ) + u • CVS * - ✏ ≈ ✏ opt • SCALES † - ✏ > ✏ opt *Coherent Vortex SImulation (CVS): Farge M, Schneider K, Kevlahan N. Phys. Fluids 11:2187–201, 1999. † Stochastic Coherent Adaptive Large Eddy Simulations (SCALES): Goldstein, D.E. and Vasilyev, O.V., Phys. Fluids 16: 2497-2513, 2004. Department of Mechanical Engineering C o u p l i n g o f N u m e r Multi-Scale Modeling Multi-Scale Modeling i c a l M e t h o d s a n d P h y s i c a l M o d e l s , A u g u s t 8 , 2 0 1 2 4 & Simulation Laboratory & Simulation Laboratory Wednesday, August 8, 12