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

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 constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the majority of the computational cost. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the incompressible flow computations where the data-driven approach is 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 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 and reduced order spaces. We investigate the feasibility of the proposed method by solving various canonical test problems, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model.