Numerical blowup in two-dimensional Boussinesq equations

TL;DR

This study uses high-resolution numerical simulations to investigate potential finite-time singularities in the 2D Boussinesq equations, revealing signals of blowup at unprecedented resolutions.

Contribution

The paper introduces a three-stage numerical relay approach and achieves the highest resolution to date for studying singularities in these equations.

Findings

Signals of numerical blowup observed at high resolutions

High-resolution simulations suggest finite-time singularity potential

Methodology advances understanding of Boussinesq equation behavior

Abstract

In this paper, we perform a three-stage numerical relay to investigate the finite time singularity in the two-dimensional Boussinesq approximation equations. The initial asymmetric condition is the middle-stage output of a $2048^2$ run, the highest resolution in our study is $40960^2$, and some signals of numerical blowup are observed.