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A TVD scheme for 3d unstructured grids applied to compositional reservoir simulation

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      Abstract

      Abstract In reducing the grid orientation effect for the numerical solution of partial differential equations, interpolation functions play an important role when the advective transport of the governing equations is considered. This is due to the fact that, in general, the unknowns are evaluated in the vertices of the elements and such properties must be extrapolated to inner parts of the elements. First-order schemes, such as upwind, are the easiest methods to use for performing the extrapolation of the properties. However, such methods introduce a large amount of numerical diffusion in the solution. A few higher-order interpolation schemes, on the other hand, are capable of providing solutions free of numerical diffusion, increasing the accuracy of the method and reducing the computational efforts required. In this work, we investigate the TVD interpolation scheme for three-dimensional unstructured grids in conjunction with Element-based Finite Volume Method (EbFVM) using four types of elements: hexahedron, tetrahedron, prism and pyramid.

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      Most cited references 37

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      Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method

       Bram Van Leer (1979)
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        Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations

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          High resolution schemes for hyperbolic conservation laws

           Ami Harten (1983)
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            Author and article information

            Affiliations
            Ceará orgnameUniversidade Federal do Ceará orgdiv1Department of Metallurgical Engineering and Materials Science Brazil
            Austin orgnameUniversity of Texas orgdiv1Center for Petroleum and Geosystems Engineering United States
            Ceará orgnameUniversidade Federal do Ceará orgdiv1Laboratory of Computational Fluid Dynamics Brazil
            Contributors
            Role: ND
            Role: ND
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            Journal
            bjce
            Brazilian Journal of Chemical Engineering
            Braz. J. Chem. Eng.
            Brazilian Society of Chemical Engineering (São Paulo, SP, Brazil )
            0104-6632
            1678-4383
            October 2017
            : 34
            : 4
            : 1161-1174
            S0104-66322017000401161
            10.1590/0104-6632.20170344s20160272

            This work is licensed under a Creative Commons Attribution 4.0 International License.

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            Figures: 0, Tables: 0, Equations: 0, References: 37, Pages: 14
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            Product Information: SciELO Brazil

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