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