Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts
This work addresses the numerical simulation of turbulent flows in ducts using fractional models, which is of interest to fluid dynamics researchers, but the contribution appears incremental.
The paper numerically investigates a space-fractional model for turbulent fluid flow in rectangular ducts, using finite-difference approximations and the conjugate gradient method. Results show mean velocity fields at different Reynolds numbers, but no concrete performance numbers are provided.
The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steady-state flow in a duct is considered under the condition that the turbulent diffusion is governed by a fractional power of the Laplace operator. To study numerically flows in rectangular channels, finite-difference approximations are employed. For approximate solving the corresponding boundary value problem, the iterative method of conjugate gradients is used. At each iteration, the problem with a fractional power of the grid Laplace operator is solved. Predictions of turbulent flows in ducts at different Reynolds numbers are presented via mean velocity fields.