Stochastic determinism for capturing the transition point from laminar flow to turbulence

To this day, the transition from laminar flow to turbulence in channels is still an important aspect of many different phenomena such as blood flows, microfluidics, and laminar airfoils. Although a lot of researchers have tried, no methods of computational fluid dynamics can directly simulate the transition point in space for a wide range of Reynolds numbers. Previous research studies have captured only the transition in time. In this report, we present the first successful simulation of the transition point in three-dimensional space using a stochastic determinism approach based on a systematic evaluation of molecular discontinuity and proper control of numerical errors, although the results are not quantitative.