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Communication Dans Un Congrès Année : 2023

Autoencoder-accelerated computational homogenization of unsteady flows in porous media

Modesar Shakoor
Chung Hae Park

Résumé

As an alternative to empirical approaches such as Darcy's law and its extensions, a computational homogenization approach has recently been developed for modeling flows in porous media (1,2). In this approach, equations of Navier-Stokes type are solved using the Finite Element (FE) method at the coarse scale of the domain instead of Darcy's law. These equations involve force and stress derivatives tensors instead of the permeability tensor. In the steady case, these tensors can be computed beforehand in a pre-processing step using simulations at the fine scale of the porous medium. In the unsteady case, fine scale domains are introduced at each point of the coarse scale domain, and simulations at the two scales are strongly coupled. The resulting FExFE or FE2 scheme entails a significant computational cost. It has the advantage, however, of predicting simultaneously the flow at the two scales. This approach has been demonstrated to be reliable and robust, especially for problems involving a very small pore characteristic length and a Reynolds number below 100. It has been shown to be interesting for modeling unsteady flows in porous media as well as flows involving both a porous part and a purely fluid part such as a channel. These results are promising for applications to reservoir engineering or composites manufacturing. The associated computational cost, however, is limiting. In this work, a nonlinear Reduced Order Model (ROM) inspired from a previous work on brittle fracture (3) is developed for solving the fine scale problems. The dimension of the fine scale velocity fields is reduced using an autoencoder, which is a specific kind of deep neural network that is tailored for nonlinear dimension reduction. A recurrent neural network is then developed to predict the fine scale flow in the reduced space. This recurrent neural network is integrated in an FExROM multiscale scheme where the coarse scale problem is still solved using the FE method, but all fine scale problems are solved using the nonlinear ROM combining an autoencoder and a recurrent neural network. This presentation will introduce this original approach for modeling unsteady flows in porous media, with an emphasis on the nonlinear ROM. The integration of this ROM within the multiscale FE code will be detailed, especially regarding the computation of the derivatives tensors. The capabilities of the proposed FExROM multiscale method will be demonstrated for problems of increasing size. (1) Blanco, P. J., Clausse, A., & Feijoo, R. A. (2017). Homogenization of the Navier-Stokes equations by means of the Multi-scale Virtual Power Principle. Computer Methods in Applied Mechanics and Engineering, 315, 760-779. https://doi.org/10.1016/j.cma.2016.11.022 (2) Shakoor, M., & Park, C. H. (2023). Computational homogenization of unsteady flows with obstacles. International Journal for Numerical Methods in Fluids, 95(4), 499-527. https://doi.org/10.1002/d.5158 (3) Shinde, K., Itier, V., Mennesson, J., Vasiukov, D., & Shakoor, M. (2023). Dimensionality reduction through convolutional autoencoders for fracture patterns prediction. Applied Mathematical Modelling, 114, 94-113. https://doi.org/10.1016/j.apm.2022.09.034
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Dates et versions

hal-04320724 , version 1 (04-12-2023)

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Paternité

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  • HAL Id : hal-04320724 , version 1

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Modesar Shakoor, Chung Hae Park. Autoencoder-accelerated computational homogenization of unsteady flows in porous media. MORTech 2023 – 6th International Workshop on Model Reduction Techniques, Nov 2023, Saclay, France. ⟨hal-04320724⟩
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