Developing an Understanding of the Steps Involved in Solving Navier– Stokes Equations
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Date
2015
Authors
Adair, Desmond
Jaeger, Martin
Journal Title
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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
Description
Keywords
Navier– Stokes equations, Mathematica
Citation
Desmond Adair, Martin Jaeger; 2015; Developing an Understanding of the Steps Involved in Solving Navier– Stokes Equations; The Mathematica Journal