Higher Resolution Hybrid And Vt Finite-Volume Formulations For 3-Component 2-Phase Flow On Unstructured Grids

References

1. H.A.Friis, M.G.Edwards & J.Mykkeltveit
   , 2008. Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell Centered Triangular Grids, SIAM J. Sci. Comput. Vol 31, Issue 2, pp. 1192–1220, Doi 10.1137/070692182.
   https://doi.org/10.1137/070692182 [Google Scholar]
2. T.Barth & D.C.Jespersen
   , 1989. The design and application of upwind schemes on unstructured meshes, AIAA paper 89–0366.
   [Google Scholar]
3. M.G.Edwards
   , 2006. Higher-resolution hyperbolic-coupled-elliptic flux-continuous CVD schemes on structured and unstructured grids in 2-D, International Journal for Numerical Methods in Fluids, 51, 1059–1077.
   [Google Scholar]
4. Y.W.Xie & M.G.Edwards
   , 2017. Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids, Computational Geosciences, 21, 921–936.
   [Google Scholar]
5. D.W.Peaceman
   , 1977. Fundamentals of Numerical Reservoir Simulation. Elsevier, Amsterdam/New York.
   [Google Scholar]
6. Y.Brenier & J.Jaffré
   , 1991. Upstream differencing for multiphase flow in resorvoir simulation, SIAM J. Numer. Anal., 28, 685–696.
   [Google Scholar]
7. R.J.Leveque
   , 2004. Finite-Volume Methods for Hyperbolic Problems, Cambridge university press.
   [Google Scholar]
8. M.G.Edwards
   , 2010. Global and Local Central Non-upwind Finite Volume Schemes for Hyperbolic Conservation Laws in Porous Media, Int. J. Numer. Meth. Fluids Vol 64, Issue 7, 793–811.
   [Google Scholar]
9. S.H.Lee, Y.Efendiev & H.A.Tchelepi
   , 2015. Hybrid upwind discretization of nonlinear two-phase flow with gravity, Advances in Water Resources, 27–38, 82, http://dx.doi.Org/10.1016/j.advwatres.2015.04.007.
   [Google Scholar]
10. G.Strang
    , 1968. On the construction and comparison of difference schemes, SIAM Journal on Numerical Analysis5.3, 506–517.
    [Google Scholar]
11. P.Siegel, R.Mosé, P.Ackerer, & J.Jaffré
    , 1997. Solution of the advection–diffusion equation using a combination of discontinuous and mixed finite elements, International Journal for Numerical Methods in Fluids, Wiley Online Library, 24, 595–613.
    [Google Scholar]
12. D.Nayagum, G.Schäfer, & R.Mosé
    , 2004. Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements, Computational Geosciences, 8, 49–73.
    [Google Scholar]
13. K.Aziz and A.Settari
    , 1979. Petroleum Reservoir Simulation, pub Elsevier.
    [Google Scholar]
14. J. A.Trangenstein
    , 2008. Numerical solution of hyperbolic conservation laws, Cambridge University Press.
    [Google Scholar]
15. J. B.Bell, P.Colella, & J. A.Trangenstein
    , 1989. Higher order Godunov methods for general systems of hyperbolic conservation laws, Journal of Computational Physics, 82, 362–397.
    [Google Scholar]