Compatible algorithms for coupled flow and transport

By Clint N. Dawson, Shuyu Sun, Mary F. Wheeler. 2004

342 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/08efb8acc4927b3fb820d13a30a43f4c5282d12b

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Estimation of penalty parameters for symmetric interior penalty Galerkin methods (2007, methodology): “Our results also apply to the incomplete interior penalty Galerkin method [11], that differs from SIPG and NIPG in the fact that the symmetrizing stabilizing term is removed.”
Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case (2007, methodology): “By taking into account the fact that for all the DG methods considered the vector flux σ̂ is conservative and using the definition of the jump and average operators on the boundary faces, the expression in (20) can be rewritten as ADGi (ui, vi) = ∫ Ωi ∇hui · ∇hvi dx−[1−γ[[û]]] ∫ E Ii [[ui]] · {∇hvi”
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations ofElliptic Problems (2007, background): “For the non-symmetric NIPG and IIPG methods, since A(·, ·) is not longer symmetric, it does not define an inner product.”
ON ITERATIVE IMPES FORMULATION FOR TWO-PHASE FLOW WITH CAPILLARITY IN HETEROGENEOUS POROUS MEDIA (2010, background): “Iterative coupling is also popular in the simulation of single-phase and two-phase flow and reactive transport [2, 24, 27, 63–65,71].”
Numerical Solution of Richards' Equation: A Review of Advances and Challenges (2017, methodology): “…finite differences, multi-point flux approximation (MPFA) techniques, mixed finite elements, and discontinuous Galerkin methods (Chavent and Roberts, 1991; Arbogast et al., 1995; Aavatsmark et al., 1998; Campbell et al., 2002; Dawson et al., 2004; Klausen and Russell, 2004; Trangenstein, 2013).”
Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport (2006, methodology): “ð2:11Þ where sform = 1 for NIPG (the nonsymmetric interior penalty Galerkin method [30]) or OBB-DG (the Oden-Babuška-Baumann formulation of DG [23]), sform = 1 for SIPG (the symmetric interior penalty Galerkin method [49,36,38]), and sform = 0 for IIPG (the incomplete interior penalty Galerkin metho”
A posteriori error estimation and dynamic adaptivity for symmetric discontinuous Galerkin approximations of reactive transport problems (2006, background): “However, realistic simulations for simultaneous transport and chemical reaction present significant mathematical and computational challenges [10,25,61, 47,43,30,24].”
Discontinuous Galerkin methods for coupled flow and reactive transport problems (2005, methodology): “Three versions of primal discontinuous Galerkin (DG) methods were proposed to solve couple and reactive transport in porous media.”
Locally conservative, stabilized finite element methods for variably saturated flow (2008, methodology): “In general, higher order mixed spaces can be used to define local Neumann problems to meet higher order compatibility conditions [18, 47].”