Data-Driven Turbulence Modeling: Physics-Informed Machine ... · and the high-fidelity simulation...
Transcript of Data-Driven Turbulence Modeling: Physics-Informed Machine ... · and the high-fidelity simulation...
![Page 1: Data-Driven Turbulence Modeling: Physics-Informed Machine ... · and the high-fidelity simulation data for the training flows. q Construct regression functions q Compute the Reynolds](https://reader035.fdocuments.net/reader035/viewer/2022081612/5f2a866b6e1b035543213765/html5/thumbnails/1.jpg)
r
www.postersessionom
Data-Driven Turbulence Modeling: Physics-Informed Machine Learning Framework Jinlong Wu, Jianxun Wang, Heng Xiao
Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University
J-X. Wang, J-L. Wu, H. Xiao, “A Physics Informed Machine Learning Approach for Reconstructing Reynolds Stress Modeling Discrepancies Based on DNS Data”, Accepted, Physics Review Fluids, 2017. J-X. Wang, J-L. Wu, J. Ling, G. Iaccarino, H. Xiao, “A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling”, Submitted, available at: arXiv:1701.07102, 2017.
Motivation
Objective and Approach
Application II. High Mach Number BL
Bibliography
For more information, please contact Heng Xiao ([email protected])or Jinlong Wu ([email protected]). More information about the authors are also available online at https://sites.google.com/a/vt.edu/hengxiao/home.
Further Information
Physics-Informed Machine Learning Framework
Application I. Flow in A Square Duct
Application III. Flow over Periodic Hills
Conclusions
The objective of this work is to demonstrate that the RANS simulated Reynolds stress of a new flow can be improved via our PIML framework with existing LES/DNS database. Three essential parts of our PIML framework is: (1) representation of Reynolds stresses discrepancies as responses; (2) identification of mean flow features as inputs and (3) construction of regression functions from training data.
Reynolds Averaged Navier-Stokes Equations:
⌧ = �u0iu
0j
Hub of RANS models
Our Motivation: q RANS modeled Reynolds stresses are known to be unreliable for many flows. q LES/DNS simulations are still infeasible for many industrial flows. q Is it possible to employ existing LES/DNS database to enhance the RANS
simulations?
⌧ = 2k
✓1
3I+A
◆= 2k
✓1
3I+V⇤VT
◆
(1) Representation of Reynolds Stresses as Responses
�⌧ ) (� log2 k,z }| {�⇠,�⌘,
z }| {�'1,�'2,�'3)
(2) Identification of Mean Flow Features
) qi (i = 1, 2, ..., 47)Integrity Basis of
(3) Construction of Regression Functions
Random Forest Neural Network
−1 0 1−1
0
1
Reb=2200
z
y
−1 0 1−1
0
1
Reb=3500
z
y
Training Flow
(Re=2200)
Test Flow
(Re=3500)
⌧zz
⌧yy
0 0.25 0.5 0.75 10.0
0.2
0.4
0.6
0.8
1.0
RANS
DNS
PIML
Procedures of PIML Framework: q Perform baseline RANS simulations on both the training flows and the test flow. q Compute the mean flow feature vector q(x) based on the RANS simulations. q Compute the discrepancies field between RANS modeled Reynolds stresses
and the high-fidelity simulation data for the training flows. q Construct regression functions q Compute the Reynolds stresses discrepancies for the test set by evaluating the regression functions.
�⌧↵ = ⌧RANS↵ � ⌧ truth↵
f↵ : q 7! �⌧↵
2-Comp 1-Comp
3-Comp
C1 C2
C3
Training Flow: q Test Flow: q M = 8, Tw = 0.53
M = 2.5, Tw = 1
general flow direction
recirculation zone
Training Flow Configuration: q Dashed Line
Test Flow Configuration: q Solid Line
In this work, we proposed a physics-informed machine learning (PIML) approach to predict RANS modeled Reynolds stresses discrepancies by utilizing DNS database. The potential impacts include: q Utilizing current high-fidelity simulations database to improve the accuracy
of RANS simulations q Assisting turbulence modelers to derive better RANS models q Inspiring other data-driven modeling approaches in computational mechanics
⌧xy
k
Ux
Re = 5600
RANS
DNS
PIML
RANS DNS PIML
⌧xy k
RANS DNS PIML
{S,⌦,rp,rk}
Tinoco et al., 55th AIAA Aerospace Sciences Meeting, AIAA2017-1208
@Ui
@t
+@(UiUi)
@xj+
1
⇢
@p
@xi� ⌫
@
2Ui
@xj@xj= r · ⌧
@Ui
@t
+@(UiUi)
@xj+
1
⇢
@p
@xi� ⌫
@
2Ui
@xj@xj= r · (⌧RANS +�⌧)