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Klieber, W. and Rivière, B. (2006) Adaptive Simulations of Two-Phase Flow by Discontinuous Galerkin Methods. Computer Methods in Applied Mechanics and Engineering, 196, 404-419.
http://dx.doi.org/10.1016/j.cma.2006.05.007

has been cited by the following article:

• TITLE: Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

  AUTHORS: Jiangyong Hou, Wenjing Yan, Jie Chen

  KEYWORDS: Velocity Projection, Upwind Scheme, Penalty Discontinuous Galerkin Methods, Two Phase Flow in Porous Media

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.4 No.2, June 17, 2015

  ABSTRACT: The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.