Investigation of 2-dimensional fluid flow using finite difference flow method of Navier-Stokes equation

TL;DR

This paper introduces a novel finite difference method for solving 2D Navier-Stokes equations, utilizing unknown functions in stream and pressure functions, demonstrated through cavity flow benchmark simulations.

Contribution

A new numerical approach for 2D Navier-Stokes equations using unknown functions in stream and pressure, differing from traditional vorticity-stream methods.

Findings

Effective solution of cavity flow benchmark.

The method simplifies solving coupled equations.

Demonstrates accuracy in 2D fluid flow simulation.

Abstract

The presented research paper illustrates the development of a new methodology to solve 2-dimensional (2D) Navier-Stoke equations, which Pukhnachev proposed through introducing unknown functions in the stream and pressure functions of fluid flow. The proposed novel method is distinguishable from the common vorticity-stream given in the Navier-Stokes expression because it has a stream function that corresponds to the unknown function in the elliptic expression. The equation represents a couple of scheme in algorithmic considerations because it enables two situations to be solved using one function of the subject stream without putting new conditions on the innovative function. Here, the concept of numerical algorithm is applied in a flow under a cavity to represent a benchmark task to be solved. The benchmark task gives enough representation of the subject flow.