\r\nfor simulating complex flow and transport phenomena related to

\r\nnatural gas transportation in pipelines. Such kind of problems

\r\nare of high interest in the field of petroleum and environmental

\r\nengineering. Modeling and understanding natural gas flow and

\r\ntransformation processes during transportation is important for the

\r\nsake of physical realism and the design and operation of pipeline

\r\nsystems. In our approach a two fluid flow model based on a system

\r\nof coupled hyperbolic conservation laws is considered for describing

\r\nnatural gas flow undergoing hydratization. The accurate numerical

\r\napproximation of two-phase gas flow remains subject of strong

\r\ninterest in the scientific community. Such hyperbolic problems are

\r\ncharacterized by solutions with steep gradients or discontinuities, and

\r\ntheir approximation by standard finite element techniques typically

\r\ngives rise to spurious oscillations and numerical artefacts. Recently,

\r\nstabilized and discontinuous Galerkin finite element techniques

\r\nhave attracted researchers’ interest. They are highly adapted to the

\r\nhyperbolic nature of our two-phase flow model. In the presentation

\r\na streamline upwind Petrov-Galerkin approach and a discontinuous

\r\nGalerkin finite element method for the numerical approximation of

\r\nour flow model of two coupled systems of Euler equations are

\r\npresented. Then the efficiency and reliability of stabilized continuous

\r\nand discontinous finite element methods for the approximation is

\r\ncarefully analyzed and the potential of the either classes of numerical

\r\nschemes is investigated. In particular, standard benchmark problems

\r\nof two-phase flow like the shock tube problem are used for the

\r\ncomparative numerical study.", "references": null, "publisher": "World Academy of Science, Engineering and Technology", "index": "International Science Index 129, 2017" }