Nonclassical Solutions of the Classical Problem of Viscous Incompressible Flow in a Plane Channel

Abstract

This article describes a procedure for numerical analysis of the dynamics of viscous incompressible fluids in the framework of the classical Navier-Stokes model using a system of equations that preserve the reciprocal relationship between the dynamic equations and the energy equation and ensure that the law of mass conservation is satisfied with fairly high accuracy in numerical work. We report the results of numerical analysis of time-dependent flows in sufficiently long channels with various boundary and initial conditions. The existence of nonclassical solution structures is demonstrated.