# Numerical Modeling of the 1-D Two-Phase Flow in Pipelines by Using the Two-Fluid Model and a Very High Order (VHO) Flux Reconstruction (FR) Scheme

## Palavras-chave:

1-D Fluid Flow in Pipelines, Four-Equation Single-Pressure Two-Fluid Model, SIMPLE algorithm, Flux reconstruction (FR), Finite Volume Method## Resumo

Flow models for 1-D two-phase flows in pipelines are commonly implemented using first-order

schemes. Despite being simple and robust, these schemes introduce a large amount of numerical diffusion due to

low order truncation errors, causing a high loss of accuracy. In the present work, for the first time in literature, we

propose the use of the very high-order (VHO) flux-reconstruction (FR) method to improve the accuracy and

efficiency of one-dimensional two-phase flow simulations in pipelines. The FR is implemented to solve the mass

and momentum conservation equations of the isentropic four-equation single-pressure two-fluid model. The

pressure correction equation is obtained through the mass conservation and a semi-implicit pressure-based method

SIMPLE-like is used to perform the coupling. The pressure equation is solved through the Two-Point Flux

Approximation (TPFA) finite volume technique. To test and numerically validate our formulation, we present two

benchmark problems. For the problems we have solved, our results are very promising.