An Introduction to Multipoint Flux Approximations for Quadrilateral Grids

By Ivar Aavatsmark. 2002

558 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/cb6364ff550bcd8d5918420c4f9da00052382c17

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

Open-source MATLAB implementation of consistent discretisations on complex grids (2012, methodology): “Examples include the two-point flux-approximation method [7], the lowest-order-mixed finite-element methods [8], multipoint flux-approximation schemes [5, 6, 14] and recently developed mimetic finite-difference methods [9].”
Convergence of a symmetric MPFA method on quadrilateral grids (2007, methodology): “In the following, we will deal with the MPFA O-method in a reference space [1].”
Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics (2015, methodology): “For the flow problem, we use the multipoint flux approximation (MPFA) O-method [37] that allows for element-wise mass-conservation while leading to a consistent and convergent discretization, even for distorted grids or full permeability tensors.”
Mixed finite elements for solving 2‐D diffusion‐type equations (2010, methodology): “…operator method [Hyman et al., 1997; Berndt et al., 2001], the multipoint flux approximation method [Aavatsmark et al., 1994; Edwards and Rogers, 1994, 1998; Aavatsmark, 2002], and the mimetic finite difference method [Kuznetsov et al., 2004; Brezzi et al., 2005a, 2005b; Lipnikov et al., 2006].”
Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures (2008, methodology): “Unlike the common multi-point flux-approximation (MPFA) methods [23], which in 1D becomes two-point approximation, the MFE method relates the flux across each cell face to the potential variables in the entire domain.”
Stability and convergence of sequential methods for coupled flow and geomechanics: Drained and undrained splits (2011, methodology): “j1⁄41 Vh;ij: ð20Þ The inter-element flux can be evaluated using a two-point or a multipoint flux approximation [60].”
Multipoint flux approximation methods for quadrilateral grids (2007, methodology): “These were introduced and discussed in [2, 4, 5, 6, 8, 11, 14, 15, 18, 29, 30, 44, 53, 66].”
Physically based modeling in catchment hydrology at 50: Survey and outlook (2015, methodology): “This property is realized by control-volume based methods such as finite volumes (including multipoint flux approximations [Aavatsmark et al., 1998; Aavatsmark, 2002]) and mixed finite elements, but not by classical finite elements [Putti and Sartoretto, 2009].”
Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media (2005, methodology): “These have been developed by several authors, details may be found in [ 1 ].”
Monotone nonlinear finite‐volume method for nonisothermal two‐phase two‐component flow in porous media (2017, methodology): “with the discrete unknowns pk and the transmissibilities tk , depending on the grid and the permeability tensors [38].”
FINITE VOLUME SCHEMES FOR DIFFUSION EQUATIONS: INTRODUCTION TO AND REVIEW OF MODERN METHODS (2014, background): “S(1) = 0, where 1 is the vector with all components equal to 1), the discrete minimum principle (1.”
On the relationship between the multiscale finite-volume method and domain decomposition preconditioners (2008, methodology): “This is the case for most finite-volume methods, such as those discussed in Aavatsmark [ 2 ] and the references therein.”
Small-stencil 3D schemes for diffusive flows in porous media (2012, result): “This has been the object of several studies [20], [16, Chapter 3], [13], [1] .”
Sequential methods for coupled geomechanics and multiphase flow (2010, background): “(3.18) The inter-element flux can be evaluated using a two-point or a multipoint flux approximation (Aavatsmark, 2002).”
Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics (2011, methodology): “(18) The inter-element flux can be evaluated using a two-point, or a multipoint, flux approximation (Aavatsmark, 2002).”