Using AI libraries for Incompressible Computational Fluid Dynamics (2402.17913v1)

Abstract: Recently, there has been a huge effort focused on developing highly efficient open source libraries to perform AI related computations on different computer architectures (for example, CPUs, GPUs and new AI processors). This has not only made the algorithms based on these libraries highly efficient and portable between different architectures, but also has substantially simplified the entry barrier to develop methods using AI. Here, we present a novel methodology to bring the power of both AI software and hardware into the field of numerical modelling by repurposing AI methods, such as Convolutional Neural Networks (CNNs), for the standard operations required in the field of the numerical solution of Partial Differential Equations (PDEs). The aim of this work is to bring the high performance, architecture agnosticism and ease of use into the field of the numerical solution of PDEs. We use the proposed methodology to solve the advection-diffusion equation, the non-linear Burgers equation and incompressible flow past a bluff body. For the latter, a convolutional neural network is used as a multigrid solver in order to enforce the incompressibility constraint. We show that the presented methodology can solve all these problems using repurposed AI libraries in an efficient way, and presents a new avenue to explore in the development of methods to solve PDEs and Computational Fluid Dynamics problems with implicit methods.