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

Sk Rahman,Omer San,Adil Rasheed

doi:10.3390/fluids3030050

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.

Highlights

In the latest age of digitalization, industries demand technologies and algorithms that would make near real-time predictions, control and monitoring in the context of Digital Twin a possibility
We use this ROM based Poisson solver in our hybrid analytics ROM (HA-ROM) framework to illustrate the feasibility of the model for solving the two-dimensional Taylor–Green vortex (TGV) case
The two-dimensional TGV problem has a known exact analytic solution of the unsteady, incompressible Navier–Stokes equations, which can be used to validate the results obtained from the HA-ROM model

Summary

Introduction

In the latest age of digitalization, industries demand technologies and algorithms that would make near real-time predictions, control and monitoring in the context of Digital Twin a possibility. Purely data-driven artificial intelligence and machine learning algorithms were looked upon as the most attractive enabling technologies for Digital Twins. Owing to their blackbox nature, they have not yet found whole-hearted acceptance within the engineering community specially in critical applications. This has led to the development of a new field of research called the “Hybrid Analytics” that combines the interpretability, robust foundation and understanding of a physics-based modeling approach with the accuracy, computational efficiency, and automatic pattern-identification capabilities of advanced data-driven machine learning and artificial intelligence algorithms. The current work is an effort to demonstrate one way of conducting hybrid analytics involving a combination of an unsupervised machine learning

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