Operator splitting for two-dimensional incompressible fluid equations

TL;DR

This paper analyzes the convergence of operator splitting algorithms, specifically Godunov and Strang methods, for 2D incompressible fluid equations including Navier-Stokes, showing they converge at expected rates under regular initial data.

Contribution

It provides the first rigorous convergence analysis of splitting methods for a broad class of 2D fluid equations, including Navier-Stokes and surface quasi-geostrophic equations.

Findings

Godunov and Strang splitting methods converge with expected rates

Convergence holds for sufficiently regular initial data

Applicable to a class of 2D fluid equations including Navier-Stokes

Abstract

We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.