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.