Relaxing timestep restrictions for numerical stability in DNS

Ensuring the numerical stability of direct numerical simulations demands a careful selection of the timestep size. When evolving flows with explicit timestepping methods, the maximum numerically stable timestep is often set by the CFL condition, which can entail high computational costs. However, in our pseudospectral simulations, we routinely observe stability when taking timesteps significantly larger than the CFL limit. In this work, we present simulations of various flows to demonstrate that they remain accurate and numerically stable outside of the CFL regime. We also leverage linear stability theory to isolate the sources of unstable growth modes in each problem. Understanding when large timesteps are viable will be beneficial to the wide class of DNS applications involving explicit timestepping, such as when solving flows with nonlinear convection.