Turbulence Calculation Based on the Extended

In the study, we proposed a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on extended Navier–Stokes (N–S) equations. With several phenomenological observations and H. J. Kreuer’s interpretation of the origin of viscosity, we make a hypothesis that the shear process in fluid flow is accompanied by eddy formation, and considering the influence of eddies on convection and diffusion, the classical N–S equations have been improved to obtain the extended N–S equations. The extended equations are closed, and the source of the velocity fluctuations being explicitly considered to be additional convection and diffusion. The extended equations are compatible with the classical N–S equations and can describe laminar and turbulent flows in a unified manner. In fluid flow simulations, the equations describing the mean flow quantities can be obtained directly from the extended N–S equations without any additional turbulence models. The flow over a cube placed in a channel was numerically investigated to verify the extended equation, the simulation results agreeing well with the Large Eddy Simulation (LES) and experimental results.