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Fluids 2018, 3(3), 50; https://doi.org/10.3390/fluids3030050

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

1
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
2
CSE Group, Applied Mathematics and Cybernetics, SINTEF Digital, NO-7465 Trondheim, Norway
*
Author to whom correspondence should be addressed.
Received: 16 June 2018 / Revised: 13 July 2018 / Accepted: 16 July 2018 / Published: 18 July 2018
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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Abstract

Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the major component of the computational expense. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the computation of incompressible flows. In our approach, proper orthogonal basis functions are generated to be used in solving the Poisson equation in a reduced order space. Since the time integration of the advection–diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in the full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full order and reduced order spaces. We investigate the feasibility of the proposed method by solving the Taylor–Green vortex decaying problem, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model. View Full-Text
Keywords: hybrid analytics; physics-based modeling; data-driven modeling; proper orthogonal decomposition; Poisson solver; Navier–Stokes equations hybrid analytics; physics-based modeling; data-driven modeling; proper orthogonal decomposition; Poisson solver; Navier–Stokes equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Rahman, S.M.; Rasheed, A.; San, O. A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers. Fluids 2018, 3, 50.

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