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SUMMARYIn this paper, a mathematical model for three-phase ow in pipelines is developed and a novel algorithm for solving the resulting system of partial di erential equations is presented. The numerical solution is based on an adaptive mesh reÿnement technique. Signiÿcant gains in the numerical performance have been achieved by using this technique combined with high-resolution schemes like FCT. This approach is highly beneÿcial in terms of speed while preserving accuracy. An explicit adaptive numerical solver adaptive conservation law solver (ACLS) has been developed in fortran90 using object-oriented methods, which give a modular and exible code. Some numerical tests are performed to show the good behaviour of this solver and to compare the numerical results against the experimental data.

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