A probabilistic collocation eulerian-Lagrangian localized adjoint method on sparse grids for assessing \(\operatorname{CO}_2\) leakage through wells in randomly heterogeneous porous media

DOI10.1016/J.CMA.2014.11.034zbMath1423.76375OpenAlexW2095566405MaRDI QIDQ1736159

Hong Wang, Jinhong Jia, Michael A. Celia, Yongqiang Ren

Publication date: 29 March 2019

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.11.034

zbMATH Keywords

risk assessmentuncertainty quantificationheterogeneous porous mediaprobabilistic collocation method\(\operatorname{CO}_2\) sequestration and leakageeulerian-Lagrangian method

Mathematics Subject Classification ID

Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) Flows in porous media; filtration; seepage (76S05) Particle methods and lattice-gas methods (76M28) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (4)

A Time-Fractional Mean-Field Control Modeling Subdiffusive Advective Transport ⋮ A two-grid Eulerian-Lagrangian localized adjoint method to miscible displacement problems with dispersion term ⋮ Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation ⋮ An efficient stochastic framework to propagate the effect of the random solid-pore geometry of porous media on the pore-scale flow

Cites Work

• Unnamed Item
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• Generalized multiscale finite element method. Symmetric interior penalty coupling
• A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
• Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics
• Characteristic Petrov-Galerkin subdomain methods for two-phase immiscible flow
• On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs
• Sparse finite elements for elliptic problems with stochastic loading
• The modified method of characteristics with adjusted advection
• The corrected operator splitting approach applied to a nonlinear advection-diffusion problem
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Eulerian-Lagrangian localized adjoint methods for a nonlinear advection-diffusion equation
• Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport
• Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media
• An Eulerian-Lagrangian solution technique for single-phase compositional flow in three-dimensional porous media
• Local problem-based a posteriori error estimators for discontinuous Galerkin approximations of reactive transport
• A preliminary study on multiscale ELLAM schemes for transient advection-diffusion equations
• An Optimal-Order Error Estimate to ELLAM Schemes for Transient Advection-Diffusion Equations on Unstructured Meshes
• A Locally Conservative Eulerian--Lagrangian Method for a Model Two-Phase Flow Problem in a One-Dimensional Porous Medium
• An Optimal-Order Error Estimate for a Family of ELLAM-MFEM Approximations to Porous Medium Flow
• Some Improved Error Estimates for the Modified Method of Characteristics
• Coupling Discontinuous Galerkin and Mixed Finite Element Discretizations using Mortar Finite Elements
• Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures
• On the Optimality of the Discrete Karhunen--Loève Expansion
• An Approximation to Miscible Fluid Flows in Porous Media with Point Sources and Sinks by an Eulerian--Lagrangian Localized Adjoint Method and Mixed Finite Element Methods
• An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions
• A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems
• A Component-Based Eulerian--Lagrangian Formulation for Multicomponent Multiphase Compositional Flow and Transport in Porous Media
• High-Order Collocation Methods for Differential Equations with Random Inputs
• Similarity solutions for fluid injection into confined aquifers
• A fast marching method for reservoir simulation
• A multiscale Eulerian–Lagrangian localized adjoint method for transient advection–diffusion equations with oscillatory coefficients

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