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The paper presents first a linear stability analysis for the time-parallelParareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method asfine propagator, confirming that dominant imaginary eigenvalues negativelyaffect Parareal's convergence. This suggests that when Parareal is applied tothe nonlinear Navier-Stokes equations, problems for small viscosities couldarise. Numerical results for a driven cavity benchmark are presented,confirming that Parareal's convergence can indeed deteriorate as viscositydecreases and the flow becomes increasingly dominated by convection. The effectis found to strongly depend on the spatial resolution.

Convergence of Parareal for the Navier-Stokes equations depending on the Reynolds number