A LSTM-enhanced surrogate model to simulate the dynamics of particle-laden fluid systems

TL;DR

A non-intrusive data-driven reduced order model (ROM) for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations and is interested in dealing both with system identification and prediction.

Abstract

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of application, the computational cost of the numerical simulations is very expensive. The use of the most modern high-performance computing infrastructures could help to mitigate such an issue but not completely fix it. In this work, we develop a non-intrusive data-driven reduced order model (ROM) for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The ROM is built using the proper orthogonal decomposition (POD) for the computation of the reduced basis space and the Long Short-Term Memory (LSTM) network for the computation of the reduced coefficients. We are interested in dealing both with system identification and prediction. The most relevant novelties rely on (i) a filtering procedure of the full-order snapshots to reduce the dimensionality of the reduced problem and (ii) a preliminary treatment of the particle phase. The accuracy of our ROM approach is assessed against the classic Goldschmidt fluidized bed benchmark problem. Finally, we also provide some insights about the efficiency of our ROM approach.

Figures (13)

• Figure 1: Input (a) and output (b) RNN architecture.
• Figure 2: Flowchart of the proposed ROM algorithm.
• Figure 3: Sketch of the computational domain at $t = t_0 = 0$. The system is at rest at the beginning of the simulation.
• Figure 4: FOM solution of the fluid volume fraction (A) and particle position (B) at times $t = 2$ s (initial column), $t = 3.5$ s (middle column) and $t = 5$ s (last column).
• Figure 5: Filtering validation - Eulerian field: PSD analysis across four distinct grid points: $P_1 = ($0, -0.07, 0.025$)$ m, $P_2 =($0, 0.07, 0.025$)$ m, $P_3 = ($0, -0.07, 0.25$)$ m and $P_4 = ($0, -0.07, 0.25$)$ m. The main figure is in logarithmic scale along $y$ axis while the inset is in logarithmic scale for both $x$ and $y$ axes. The red line shows the PSD threshold (equal to 0.005) and the cut zone is highlighted in grey.