Adaptive grids as parametrized scale-free networks

TL;DR

This paper introduces a model for adaptive numerical grids based on scale-free network principles, linking grid resolution to physical properties like viscosity and velocity gradients to improve differential problem solving.

Contribution

It proposes a novel approach that integrates scale-free network theory into adaptive grid design for numerical simulations, enabling dynamic resolution adjustment based on physical variables.

Findings

Demonstrates the feasibility of using scale-free networks for adaptive grid modeling

Provides examples showing potential for complex fluid dynamics applications

Suggests further development for more intricate scenarios

Abstract

In this paper we present a possible model of adaptive grids for numerical resolution of differential problems, using physical or geometrical properties, as viscosity or velocity gradient of a moving fluid. The relation between the values of grid step and these entities is based on the mathematical scheme offered by the model of scale-free networks, due to Barabasi, so that the step can be connected to the other variables by a constitutive relation. Some examples and an application are discussed, showing that this approach can be further developed for treatment of more complex situations.