Separating Flow Behind a Back-Step. Part I. Quasi-Hydrodynamic Equations and Computation of a Laminar Flow

TL;DR

This paper models laminar flow behind a back-step using quasi-hydrodynamic equations, demonstrating a numerical algorithm's effectiveness and relating QHD to Navier-Stokes equations.

Contribution

It introduces a phenomenological derivation of QHD equations and applies them to simulate laminar flow in a channel with a back-step, linking QHD to classical Navier-Stokes models.

Findings

Numerical results successfully model laminar flow behind a back-step.

QHD equations are shown to be related to Navier-Stokes equations.

The proposed algorithm effectively computes viscous incompressible flows.

Abstract

We demonstrate the results of the numerical modelling of a plane two-dimensional viscous incompressible flow in a channel with a back-step. As a mathematical model we take equations for a incompressible flow based on the quasi-hydrodynamic (QHD) equations. We present a phenomenological derivation of the QHD equations and show a relation of these equations to the Navier-Stokes system. We test the proposed numerical algorithm by computing of certain laminar flows