Developing an Understanding of the Steps Involved in Solving Navier–Stokes Equations

Abstract

This article describes how Mathematica can be used to develop an understanding of the basic steps involved in solving Navier– Stokes equations using a finite-volume approach for incompressible steady-state flow. The main aim is to let students follow from a mathematical description of a given problem through to the method of solution in a transparent way. The wellknown “driven cavity” problem is used as the problem for testing the coding, and the Navier–Stokes equations are solved in vorticity-streamfunction form. Building on what the students were familiar with from a previous course, the solution algorithm for the vorticity-streamfunction equations chosen was a relaxation procedure. However, this approach converges very slowly, so another method using matrix and linear algebra concepts was also introduced to emphasize the need for efficient and optimized code.