A Computational Investigation of a Continuum Model for Flocking Dynamics

Authors

• Luke Galvan, University of Nebraska - LincolnFollow

Date of this Version

2021

Document Type

Thesis

Citation

Galvan, L. 2021. A Computational Investigation of a Continuum Model for Flocking Dynamics. Undergraduate Honors Thesis. University of Nebraska - Lincoln.

Comments

To appear on https://arxiv.org.

Copyright Luke Galvan 2021.

Abstract

We computationally investigate the 2D pressureless Euler equations with a commutator forcing. In 1D, regularity for singular kernels $\phi_{\alpha}(x) = |x|^{-(n+\alpha)}$ was shown on the full range of $\alpha \in (0,2]$. The simulations we present introduce a novel psuedospectral algorithm for efficiently handing the nonlocal nonlinearity present in the system. The computational investigations include: spectral vanishing viscosity with special attention to $\alpha=2$, testing possible 2D conserved quantities, monitoring properties of flocking solutions such as Disorder and alignment, and testing an external wind force implemented by mathematical derivations from a microscopic setting. There is also brief discussion of future work including an plan of rigorously proving local well-posedness for the 2D system.