Coupling Machine Learning Local Predictions with a Computational Fluid Dynamics Solver to Accelerate Transient Buoyant Plume Simulations

TL;DR

The paper tackles the computational burden of unsteady incompressible CFD by introducing a hybrid solver that injects cell-level pressure corrections predicted by local features as initial guesses for the Poisson solve. It trains a lightweight neural network offline on 2D buoyant plume data to predict the pressure change $p^n_i-p^{n-1}_i$ from local states, and integrates these predictions into the PISO pressure-velocity coupling. Results show a mean 94% improvement in the initial Poisson guess and substantial acceleration of the first pressure corrector across solvers (approximately 3.0 for Gauss-Seidel, 1.6 for PCG-DIC, and 1.3 for GAMG-GS), while maintaining accuracy. The work demonstrates the viability of domain-specific hybrid solvers for CFD and points to future extensions to 3D, unstructured meshes, and turbulent flows, with further time-budget accounting and representation-learning opportunities.

Abstract

Data-driven methods demonstrate considerable potential for accelerating the inherently expensive computational fluid dynamics (CFD) solvers. Nevertheless, pure machine-learning surrogate models face challenges in ensuring physical consistency and scaling up to address real-world problems. This study presents a versatile and scalable hybrid methodology, combining CFD and machine learning, to accelerate long-term incompressible fluid flow simulations without compromising accuracy. A neural network was trained offline using simulated data of various two-dimensional transient buoyant plume flows. The objective was to leverage local features to predict the temporal changes in the pressure field in comparable scenarios. Due to cell-level predictions, the methodology was successfully applied to diverse geometries without additional training. Pressure estimates were employed as initial values to accelerate the pressure-velocity coupling procedure. The results demonstrated an average improvement of 94% in the initial guess for solving the Poisson equation. The first pressure corrector acceleration reached a mean factor of 3, depending on the iterative solver employed. Our work reveals that machine learning estimates at the cell level can enhance the efficiency of CFD iterative linear solvers while maintaining accuracy. Although the scalability of the methodology to more complex cases has yet to be demonstrated, this study underscores the prospective value of domain-specific hybrid solvers for CFD.

Figures (8)

• Figure 1: Simplified flowchart of the Pressure Implicit with Splitting of Operators (PISO) algorithm variant employed to address the buoyant plume case. We considered an incompressible flow with a fixed orthogonal mesh and without turbulence modeling.
• Figure 2: Illustration of the prediction workflow. At a given time step $t_n$, we aim to predict the pressure field $p^n$. (a) Local physics-based features are computed for the entire domain, enabling the model to estimate the pressure field. (b) Features are calculated similarly for each cell $i$ of the domain. Some features incorporate information from the cell's neighborhood. The model infers the cell pressure variation from one time step to the next.
• Figure 3: Supervised learning diagram. The machine learning model $f_{\theta}$ provides a prediction $\boldsymbol{\hat{y}} \approx \boldsymbol{y}$ from an input vector $\boldsymbol{x}$. A database $(X_{train}, Y_{train})$ is used to train the model. The training process aims to find optimal parameters $\theta$, according to some metric $\mathcal{L}$, to approximate the function $f$ mapping inputs $\boldsymbol{x}$ to outputs $\boldsymbol{y}$.
• Figure 4: Reference case simulation at two different time steps. Inside the domain, colors represent the concentration of a passive scalar introduced at the inflow. The orthogonal projections of the velocity vectors at the boundaries are displayed to visualize the airflow rates. For this reference simulation, we set $L_{\mathbf{x}_1} = L_{\mathbf{x}_2} = 1 \meter$, $T_{inlet}=T_0+10$, and $U_{inlet}=0.125\meter.\Sec^{-1}$.
• Figure 5: Database extract. Visualization of $6$ simulations at the same time step $t=6\Sec$. The domain size, initial conditions, and obstacles were randomly sampled. The legend (colors, vectors) is the same as in Figure \ref{['fig:ref_case']}.