Cellular Nonlinear Network for fluid dynamics: towards geophysical flows modeling

Abstract

This work proposes an application of Cellular Nonlinear Networks (CNNs) to fluid dynamics, implemented towards the application to geophysical flows. We revisit the CNN paradigm for the solution of Partial Differential Equations with a focus of some main physical properties of geophysical flows. We address numerical aspects of the obtained model, including the treatment of boundary conditions, stability and correctness of the results. This is done by applying our method to canonical testcases and comparing the results with accepted benchmark data and analytical solutions from the literature. The parallelizability of the method is also assessed by means of benchmarking tests on a multi-core processor. We validate the model by simulating classical geophysical flows. The results that we present show the capability of the model to reproduce typical velocity profiles of viscous flows, making it promising for applications that require the simulation of such materials