No abstract

SUMMARYWe develop a Godunov-type scheme for a non-conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial di erential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and nonequilibrium thermodynamics (two pressures, two temperatures, two densities, etc.). Its numerical resolution poses several di culties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non-conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions.

SUMMARYWe construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the ÿrst class of methods, we interpolate the solution in the space-time element. We start by calculating the ÿrst-order node residuals, then we calculate the high-order cell residual, and modify the ÿrst-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order ÿnite di erence approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.

SUMMARYFor certain initial conditions, the exact solution to the Riemann problem for the shallow water equations is not unique. We test the performance of several numerical methods on such initial data and establish that the numerical solution can pick out di erent exact solutions. Moreover, the numerical solution does not necessarily converge towards the picked-out exact solution.

We are concerned with robust and accurate forecasting of multiphase flow rates in wells and pipelines during oil and gas production. In practice, the possibility to physically measure the rates is often limited; besides, it is desirable to estimate future values of multiphase rates based on the previous behavior of the system. In this work, we demonstrate that a Long Short-Term Memory (LSTM) recurrent artificial network is able not only to accurately estimate the multiphase rates at current time (i.e., act as a virtual flow meter), but also to forecast the rates for a sequence of future time instants. For a synthetic severe slugging case, LSTM forecasts compare favorably with the results of hydrodynamical modeling. LSTM results for a realistic noizy dataset of a variable rate well test show that the model can also successfully forecast multiphase rates for a system with changing flow patterns.