An implicit finite volume method for arbitrary transport equations

Dalton James Eric Harvie


A finite volume framework is described for solving multiphysics transport problems. The method operates in a unique way. The transport equations and associated boundary conditions are input by the user using pseudo-mathematical expressions. A Perl program parses these equations and, via the computer algebra system Maxima, `metaprograms' a Fortran code that solves the problem on an unstructured mesh using the Newton--Raphson method. The strength of the technique is that a fully implicit numerical formulation is generated and modified easily, for an arbitrary set of equations. The implemented algorithm (`arb') is available for download and licensed under the GNU General Public License.

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finite volume; transport equations

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.