scholarly journals Unstable Periodically Forced Navier–Stokes Solutions–Towards Nonlinear First-Principle Reduced-Order Modeling of Actuator Performance

2018 ◽  
pp. 117-145
Author(s):  
Marek Morzyński ◽  
Wojciech Szeliga ◽  
Bernd R. Noack
Keyword(s):  
Reduced Order Modeling ◽  
Navier Stokes ◽  
First Principle ◽  
Reduced Order ◽  
Actuator Performance

Machine learning–based reduced-order modeling of hydrodynamic forces using pressure mode decomposition

2021 ◽  
pp. 095441002199986
Author(s):  
Hassan F Ahmed ◽  
Hamayun Farooq ◽  
Imran Akhtar ◽  
Zafar Bangash
Keyword(s):  
Machine Learning ◽  
Short Term Memory ◽  
Stokes Equations ◽  
Decomposition Analysis ◽  
Hydrodynamic Forces ◽  
Reduced Order Modeling ◽  
Navier Stokes ◽  
Reduced Order ◽  
Mode Decomposition ◽  
Lift And Drag

In this article, we introduce a machine learning–based reduced-order modeling (ML-ROM) framework through the integration of proper orthogonal decomposition (POD) and deep neural networks (DNNs), in addition to long short-term memory (LSTM) networks. The DNN is utilized to upscale POD temporal coefficients and their respective spatial modes to account for the dynamics represented by the truncated modes. In the second part of the algorithm, temporal evolution of the POD coefficients is obtained by recursively predicting their future states using an LSTM network. The proposed model (ML-ROM) is tested for flow past a circular cylinder characterized by the Navier–Stokes equations. We perform pressure mode decomposition analysis on the flow data using both POD and ML-ROM to predict hydrodynamic forces and demonstrate the accuracy of the proposed strategy for modeling lift and drag coefficients.

scholarly journals Investigation of the Effects of Length to Depth Ratio on Open Supersonic Cavities Using CFD and Proper Orthogonal Decomposition

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yilmaz ◽  
Ece Ayli ◽  
Selin Aradag
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Navier Stokes ◽  
Reduced Order ◽  
Modeling Approach ◽  
Depth Ratio ◽  
Minimum Number ◽  
Proper Orthogonal

Simulations of supersonic turbulent flow over an open rectangular cavity are performed to observe the effects of length to depth ratio (L/D) of the cavity on the flow structure. Two-dimensional compressible time-dependent Reynolds-averaged Navier-Stokes equations with k-ωturbulence model are solved. A reduced order modeling approach, Proper Orthogonal Decomposition (POD) method, is used to further analyze the flow. Results are obtained for cavities with severalL/Dratios at a Mach number of 1.5. Mostly, sound pressure levels (SPL) are used for comparison. After a reduced order modeling approach, the number of modes necessary to represent the systems is observed for each case. The necessary minimum number of modes to define the system increases as the flow becomes more complex with the increase in theL/Dratio. This study provides a basis for the control of flow over supersonic open cavities by providing a reduced order model for flow control, and it also gives an insight to cavity flow physics by comparing several simulation results with different length to depth ratios.

POD and CVT-based reduced-order modeling of Navier–Stokes flows

2006 ◽  
Vol 196 (1-3) ◽  
pp. 337-355 ◽  
Author(s):  
John Burkardt ◽  
Max Gunzburger ◽  
Hyung-Chun Lee
Keyword(s):  
Reduced Order Modeling ◽  
Navier Stokes ◽  
Stokes Flows ◽  
Reduced Order

Comparison of a Multi-Dimensional Model With a Reduced Order Pseudo Three-Dimensional Model for Simulation of Solid Oxide Fuel Cells

2006 ◽  
Author(s):  
Suryanarayana Pakalapati ◽  
Ibrahim Yavuz ◽  
Francisco Elizalde-Blancas ◽  
Ismail Celik ◽  
Mehrdad Shahnam
Keyword(s):  
Fuel Cell ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reduced Order Modeling ◽  
Navier Stokes ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Reduced Order ◽  
Three Dimensional Models ◽  
Commercial Solver

Numerical modeling has helped the SOFC research for over a decade in which period the models grew in complexity and detail. Multi-dimensional detailed models such as FLUENT’s SOFC module calculate three dimensional distributions of velocity, temperature, concentration and electric potential inside all components of the fuel cell. Such models while being very helpful in understanding the processes inside the fuel cell may prove to be very expensive for transient simulations and simulations of multi-cell stacks. Hence reduced order modeling is still used for such applications. However, reduced order modeling entails reduction of detail and consequent loss in accuracy. In this paper a multi-dimensional SOFC code, FLUENT’s SOFC module, is compared with a reduced order pseudo three-dimensional model, DREAM SOFC. FLUENT’s SOFC module is a commercial solver built on the popular CFD solver FLUENT. DREAM SOFC is an in house code developed at Computational Fluid Dynamics and Applied Multi Physics (CFD&AMP) Center at West Virginia University. It is a combination of a one dimensional model for channels and three-dimensional models for the rest of the components in a SOFC. This approach avoids having to solve Navier-Stokes equations inside channels but still retains the three-dimensionality inside important components. Same test cases with similar conditions are simulated with these codes and results are compared with each other.

scholarly journals Effective Mori-Zwanzig equation for the reduced-order modeling of stochastic systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuanran Zhu ◽  
Huan Lei
Keyword(s):  
Stochastic Systems ◽  
Nonequilibrium State ◽  
Reduced Order Modeling ◽  
Data Driven ◽  
Chain Model ◽  
First Principle ◽  
Stochastic Dynamical Systems ◽  
Memory Kernel ◽  
Reduced Order ◽  
Kernel Approximation

<p style='text-indent:20px;'>Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for observables of stochastic dynamical systems, we show that the obtained semigroup estimates for the EMZ equation can be used to derive prior estimates of the observable statistics for systems in the equilibrium and nonequilibrium state. In addition, we introduce both first-principle and data-driven methods to approximate the EMZ memory kernel and prove the convergence of the data-driven parametrization schemes using the regularity estimate of the memory kernel. The analysis results are validated numerically via the Monte-Carlo simulation of the Langevin dynamics for a Fermi-Pasta-Ulam chain model. With the same example, we also show the effectiveness of the proposed memory kernel approximation methods.</p>

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

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