Symmetry consideration in the problem of wave modes of thin viscous liquid layer flow

TL;DR

This paper investigates symmetry properties in the equations governing nonlinear wave modes in viscous liquid film flow, demonstrating how symmetry considerations can improve numerical solution efficiency.

Contribution

It reveals symmetry invariance in the equations and boundary conditions, and shows how exploiting this symmetry enhances computational efficiency in solving the problem.

Findings

Equations are invariant under parity transformation.

Steady-state solutions exhibit the detected symmetry.

Using symmetry improves numerical calculation efficiency.

Abstract

The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with boundary conditions are invariant under parity transformation. It is numerically shown that for moderate Reynolds numbers the steady-state travelling solutions of the equations have the detected symmetry. It is demonstrated that using this symmetry for the numerical solution of the problem by Galerkin methods significantly increases the efficiency of calculations.