Operator splitting for two-dimensional incompressible fluid equations
Provides theoretical convergence guarantees for operator splitting methods applied to important fluid dynamics models, but the result is incremental as it extends known analysis to a specific class of equations.
The paper proves that Godunov and Strang splitting methods converge with expected rates for two-dimensional incompressible fluid equations, including Navier-Stokes and surface quasi-geostrophic equations, given sufficiently regular initial data.
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.