An adaptive mesh refinement technique developed for the solution of scalar problems is extended to the simulation of two-phase flow problems, as a means of reducing the computational runtime associated with such problems. The methodology, involving the adaptive partition of the domain into uniformly discretised regions, is extended to systems of equations without increase in algorithmic complexity. By application first to the simpler case of the Euler equations of gas dynamics, the technique is shown to handle shocks without loss of accuracy and to result in significant CPU runtime reductions of over 90%. Application to more complex two-phase flow problems, including the flashing flow during the decompression of a pipeline, also show dramatic increase in computational performance. (C) 2015 Elsevier Ltd. All rights reserved.