A relaxation multiresolution scheme for accelerating realistic two‐phase flows calculations in pipelines

We wish to demonstrate that it is judicious to combine various existing computational techniques that appeared for academic cases in seemingly unrelated areas, namely, semi‐implicit relaxation schemes for hyperbolic systems and adaptive multiresolution algorithms, in order to achieve fast and accurate simulations of realistic two‐phase flows problems in oil transportation. By ‘realistic’ we mean problems that are modelled by partial differential equation (PDE) systems closed by sophisticated thermodynamics and hydrodynamics laws, set out over a terrain‐induced geometry and associated with time‐dependent boundary conditions. Although the combination of these techniques is not a straightforward matter, it is made possible via a careful examination of the objectives of the simulation problem and suitable adaptations of which we shall give the details. Significant benchmarks demonstrate the efficiency of the proposed method. Copyright © 2006 John Wiley & Sons, Ltd.