Deterministic and stochastic computations of mysterious internal flows: based on a nonlinear local correction method with global conservativity

The present paper shows a new approach for solving two types of fluid problems, which has recently emerged and has been an unsolved mysteriously for over 100 years. The first problem emerged recently is a very small amount of numerical errors comparable to pollutant emissions such as unburned hydrocarbon fuel (HC) and NOx at order of ppm or less. A new nonlinear numerical method of global and local corrections for the deterministic compressible Navier-Stokes equation for multi-components of gases is proposed and tested to overcome this first problem, while accurately evaluating fluid-dynamic instability related to turbulence and thermal efficiency as result of spatially-integrated thermodynamic quantities, related to total amount of CO2 exhausted, in power systems including combustion engines. It is stressed that the present nonlinear correction method applied for the stochastic Navier-Stokes equation is also effective for the second mysterious problem which has been unsolved for over 100 years, which is the spatial transition point from laminar to turbulent flows in pipes.