Numerical investigation of a space-fractional model of turbulent fluid flow in rectangular ducts

TL;DR

This paper numerically investigates a novel space-fractional model for turbulent fluid flow in rectangular ducts, employing finite differences and conjugate gradient methods to analyze flow behavior at various Reynolds numbers.

Contribution

It introduces a fractional derivative-based model for turbulence and develops a numerical approach to solve the resulting boundary value problem.

Findings

Mean velocity fields predicted for different Reynolds numbers

Validation of fractional model against classical turbulence models

Numerical method effectively solves fractional Laplace boundary problems

Abstract

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.