Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.
['Johannes Steiner', 'Daniel Ruprecht', 'Robert Speck', 'Rolf Krause']
I am writing a research paper on a idea Convergence of Parareal for the Navier-Stokes equations depending on the Reynolds number
[{"from": "human", "value": "I am writing a research paper on a idea Convergence of Parareal for the Navier-Stokes equations depending on the Reynolds number"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal\u2019s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal\u2019s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution."}]