Domain decomposition methods for flow in heterogeneous porous media

Espedal, Magne S.; Hersvik, Karl J.; Ersland, Brit G.

doi:10.1090/conm/218/03005

Cited by 5 publications

(1 citation statement)

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“…As a result, a-priori knowledge of where these nonlinear regions lie should help improve accuracy without significant computational cost. Indeed, if a domain partition can be devised subdividing the medium into a slow region and a fast region, then a domain-decomposition algorithm [2,10,27] can be run over this partition where Darcy's law is solved in the slow region and a nonlinear law, such as the Darcy-Forchheimer law, is solved in the fast region. We expect this approach to be more precise than solving Darcy's law globally and faster than solving the nonlinear law globally.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

Fumagalli

Patacchini

2023

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

Fumagalli

Patacchini

2023

Journal of Computational Physics

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Numerical solution of reservoir flow models based on large time step operator splitting algorithms

Espedal¹,

Karlsen²

2000

Lecture Notes in Mathematics

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During recent years the authors and collaborators have been involved in an activity related to the constmction and analysis of large time step operator sphtting algorithms for the numerical simulation of multi-phase fiow in heterogeneous porous media. The purpose of these lecture notes is to review some of this activity. We illustrate the main ideas behind these novel operator sphtting algorithms for a basic two-phase flow model. Special focus is posed on the numerical solution algorithms for the saturation equation, which is a convection dominated, degenerate convection-diffusion equation. Both theory and applications are discussed. The gen eral background for the reservoir flow model is reviewed, and the main features of the numerical algorithms are presented. The basic mathematical results supporting the numerical algorithms are also given. In addition, we present some results from the BV solution theory for quasilinear degenerate parabolic equations, which provides the correct mathematical framework in which to analyse our nmnerical algorithms. Two-and three-dimensional munerical test cases are pre sented and discussed. The main conclusion drawn from the numerical experiments is that the operator sphtting algorithms indeed exhibit the property of resolving accurately internal layers with steep gradients, give very little numerical diffusion, and, at the same time, permit the use of large time steps. In addition, these algorithms seem to capture all potential combinations of convection and diffusion forces, ranging from convection dominated problems (including the pure hyperbolic case) to more diffusion dominated problems. CONTENTS 1.

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Numerical validation of an adaptive model for the determination of nonlinear-flow regions in highly heterogeneous porous media

Fumagalli,

Patacchini

2025

Mathematics and Computers in Simulation

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Domain decomposition methods for flow in heterogeneous porous media

Abstract: Here, u is the total Darcy velocity, which is the sum of the Darcy velocities of the oil and water phases:1991 Mathematics Subject Classification. Primary 76T05; Secondary 35M20, 65M55, 65M25.

Cited by 5 publications

References 19 publications

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

Well-posedness and variational numerical scheme for an adaptive model in highly heterogeneous porous media

Numerical solution of reservoir flow models based on large time step operator splitting algorithms

Numerical validation of an adaptive model for the determination of nonlinear-flow regions in highly heterogeneous porous media

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