# The Application of Computer Algebra for the Discretization and
Coding of the Navier--Stokes Equations

* V.V. Goldman *

*J.A. van Hulzen*

Department of Computer Science, University of Twente,

* P.O. Box 217, 7500 AE Enschede, The Netherlands*

*A.E. Mynett*

*A.S. Posthuma*

and *H.J. van Zuylen*

* Delft Hydraulics, P.O. Box 177, Rotterdamseweg 185*

* 2600 MH Delft, The Netherlands*

### Abstract:

For the solution of flow problems, the Navier--Stokes equations provide
a suitable mathematical framework. For most situations, only the
numerical solution of these equations is possible. The equations
have to be discretized; i.e., mapped on a grid, after which a solution can
be formulated in terms of the unknown variables: the mass flux components
at particular locations in the flow.
Then the discrete Navier--Stokes equations are linearized with respect
to these unknown
variables, after which a linear system of equations has to be solved.
The FORTRAN code to build the matrix of coefficients is quite
complex, due to the strong logical coherence and the large number of
transformations and approximations applied. Therefore the code is
error-prone and difficult to maintain.

A solution was found by generating the code and maintaining it on a
higher level of abstraction. Computer algebra was applied using the
REDUCE package with GENTRAN and
SCOPE. Instead of
maintaining the source code, the knowledge needed to build the source
code is documented and used to generate the source code. Maintenance is
done on the documented knowledge.

Computer Algebra in Industry 2 Edited by A.M. Cohen, L. van Gastel and
S.M. Verduyn Lunel

© 1995 John Wiley & Sons Ltd

Reproduced by permission of John Wiley & Sons Ltd, 1995

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Applications

*Computer Algebra in Industry 2*

Thierry van Effelterre

Last Update: June 24, 1997.