Spatial transition point from laminar flow to turbulence in a circular pipe with bellmouth inlet by solving a weakly-stochastic navier-stokes equation

In order to simulate the spatial transition point from laminar flow to turbulence in a closed pipe, we proposed the numerical method called “stochastic determinism” that based on the stochastic Navier-Stokes equation. The important point is that the stochasticity level is decided by inlet disturbance intensity. The finite difference method based on the multi-level formulation is also included which can calculate spatial derivatives of physical quantities and integrated quantities accurately. In this report, an incompressible flow in straight pipe with bellmouth inlet is computed. The difference in transition length between our computation and experimental results by Kanda were reduced by decreasing inlet disturbances in our computation.