Honors Program
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.
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.
Comments
To appear on https://arxiv.org.
Copyright Luke Galvan 2021.