PROJECT PROPOSAL

CS 422 NUMERICAL SIMULATION

Numerical Simulation of Navier Stokes Equation

V.Vinoth (1100335), VNVM Abhinav (1100139), Rahul Agrawal (1100325)

Abstract:

The main focus of this project is to demonstrate numerical methods for solving Navier Stokes

equation by summarizing the discretisation of the Navier Stokes equation followed by

experimenting various algorithms for numerically solving the discretised form of the partial

differential equation. The Navier Stokes equation describes the viscous flow of a fluid using a set of

differential equations. Simply put, they are derived from applying Newtons second law on fluid

motion along with the assumption that stress in the fluid is dependent on a diffusing viscous term and

a pressure gradient thus making it applicable to viscous flows.

Navier-Stokes equations have been extensively used in simulating and describing various physical

phenomena varying from modelling ocean currents to studying blood-flow in the arteries hence

making them versatile for a myriad range of applications. Hence finding an efficient way of solving

these equations numerically is of great interest and it has been pursued by researchers for a long time

now. A specific mention here [1] should be given on usage of algorithms like Jacobi, Gauss-Seidel

and SOR for solving the discritised form of the Navier-Stokes equation. The current project aims on

elaborating these algorithms analytically and implementing them on a software platform like Matlab.

We hope to solve the Navier-Stokes equation for simple problems like flow through a pipe or over

a plane surface using numerical methods mentioned above and also with algorithms which might be

discussed in the course. If feasible, the project could be extended to studying the stability of these

algorithms and comparing them for performances in terms of program run-time or computing power.