Publicado 6 números por año
ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352
Indexed in
Multiscale Discontinuous Galerkin and Operator-Splitting Methods for Modeling Subsurface Flow and Transport
SINOPSIS
Multiscale algorithms are considered for solving flow and transport problems in geological media. Challenges of multiscale permeability variation in subsurface flow problems are addressed by using multiscale discontinuous Galerkin (DG) methods, where we construct local DG basis functions at a coarse scale while capturing local properties of Darcy flow at a fine scale, and then solve the DG formulation using the newly constructed local basis functions on the coarse-scale elements. Challenges of transport problems include the coupling of multiple processes, such advection, diffusion, dispersion, and reaction across different scales, which is treated here by using two splitting approaches based on operator decomposition. The methods decompose the coupled system into various individual operators with respect to their scales and physics, so that each subproblem can be solved with its own most efficient algorithm. These subproblems are coupled adaptively with iterative steps. Error estimates for the decomposition methods are derived. Numerical examples are provided to demonstrate the properties and effectiveness of both multiscale DG and operator-splitting methods.
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Kou Jisheng, Sun Shuyu, Yu Bo, Multiscale Time-Splitting Strategy for Multiscale Multiphysics Processes of Two-Phase Flow in Fractured Media, Journal of Applied Mathematics, 2011, 2011. Crossref
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Fan Xiaolin, Sun Shuyu, Wei Wei, Kou Jisheng, Numerical Simulation of Pollutant Transport in Fractured Vuggy Porous Karstic Aquifers, Journal of Applied Mathematics, 2011, 2011. Crossref
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Sun Shuyu, Salama Amgad, El-Amin M.F., An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media, Procedia Computer Science, 9, 2012. Crossref
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Sun Shuyu, Salama Amgad, El Amin M.F., Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media, Computers & Fluids, 68, 2012. Crossref
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Sun Shuyu, Firoozabadi Abbas, Kou Jisheng, Numerical modeling of two-phase binary fluid mixing using mixed finite elements, Computational Geosciences, 16, 4, 2012. Crossref
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Kou Jisheng, Sun Shuyu, Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media, Mathematical Methods in the Applied Sciences, 37, 7, 2014. Crossref
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Qiao Zhonghua, Sun Shuyu, Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State, SIAM Journal on Scientific Computing, 36, 4, 2014. Crossref
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Kou Jisheng, Sun Shuyu, Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility, Journal of Computational Physics, 318, 2016. Crossref
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El-Amin Mohamed F., Kou Jisheng , Sun Shuyu , Multiscale Adapted Time-Splitting Technique for Nonisothermal Two-Phase Flow and Nanoparticles Transport in Heterogenous Porous Media, Day 2 Tue, May 09, 2017, 2017. Crossref
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Geiser Jürgen, Einleitung und Überblick zum vorliegenden Buch, in Computational Engineering, 2018. Crossref
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Jiang Lijian, Mishev Ilya D., Mixed Multiscale Finite Volume Methods for Elliptic Problems in Two-Phase Flow Simulations, Communications in Computational Physics, 11, 1, 2012. Crossref
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Sun Shuyu, Darcy-scale phase equilibrium modeling with gravity and capillarity, Journal of Computational Physics, 399, 2019. Crossref
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Moortgat Joachim , Li Zhidong , Firoozabadi Abbas , Three-Phase Compositional Modeling of CO2 Injection by Higher-Order Finite Element Methods with CPA Equation of State, All Days, 2011. Crossref
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Geiser Jürgen, Einleitung und Überblick, in Computational Engineering 2, 2022. Crossref
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El-Amin Mohamed F., Kou Jisheng, Sun Shuyu, Discrete-fracture-model of multi-scale time-splitting two-phase flow including nanoparticles transport in fractured porous media, Journal of Computational and Applied Mathematics, 333, 2018. Crossref
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Sun Shuyu, Firoozabadi Abbas, Compositional Modeling in Three-Phase Flow for CO2 and Other Fluid Injections Using Higher-Order Finite Element Methods, All Days, 2009. Crossref