Solution of the Navier Stokes model in 1D using finite differences schemes

Abstract

The Navier Stokes equations are ones that describe the behavior of fluids. The computational solution of these allows for a way of understanding and predicting them while being cost-effective. The fundamental equations arise from the principles of conservation of energy, momentum, and mass described in New ton’s second law, the first law of thermodynamics, and the continuity equation respectively. The obtained system of equations can be used for different fluid simulations under different circumstances such as Newtonian, compressible, or isothermal flow fluids. The objectives of this project are to describe the problem and the origin of the equations; to approximate the solution to the Navier Stokes system in one dimension through a finite differences discretization scheme used in numerical analysis to solve PDE; to mathematically analyse the selected approach in terms of error and convergence; to present examples using different boundaries conditions.