Cristin-resultat-ID: 1371136
Sist endret: 16. februar 2017 12:42
NVI-rapporteringsår: 2016
Resultat
Vitenskapelig artikkel
2016

Stochastic Galerkin framework with locally reduced bases for nonlinear two-phase transport in heterogeneous formations

Bidragsytere:
  • Per Pettersson og
  • Hamdi Tchelepi

Tidsskrift

Computer Methods in Applied Mechanics and Engineering
ISSN 0045-7825
e-ISSN 1879-2138
NVI-nivå 2

Om resultatet

Vitenskapelig artikkel
Publiseringsår: 2016
Volum: 310
Sider: 367 - 387

Importkilder

Scopus-ID: 2-s2.0-84982844531

Beskrivelse Beskrivelse

Tittel

Stochastic Galerkin framework with locally reduced bases for nonlinear two-phase transport in heterogeneous formations

Sammendrag

The generalized polynomial chaos method with multiwavelet basis functions is applied to the Buckley–Leverett equation. We consider a spatially homogeneous domain modeled as a random field. The problem is projected onto stochastic basis functions which yields an extended system of partial differential equations. Analysis and numerical methods leading to reduced computational cost are presented for the extended system of equations. The accurate representation of the evolution of a discontinuous stochastic solution over time requires a large number of stochastic basis functions. Adaptivity of the stochastic basis to reduce computational cost is challenging in the stochastic Galerkin setting since the change of basis affects the system matrix itself. To achieve adaptivity without adding overhead by rewriting the entire system of equations for every grid cell, we devise a basis reduction method that distinguishes between locally significant and insignificant modes without changing the actual system matrices. Results are presented for problems in one and two spatial dimensions, with varying number of stochastic dimensions. We show how to obtain stochastic velocity fields from realistic permeability fields and demonstrate the performance of the stochastic Galerkin method with local basis reduction. The system of conservation laws is discretized with a finite volume method and we demonstrate numerical convergence to the reference solution obtained through Monte Carlo sampling.

Bidragsytere

Per Pettersson

  • Tilknyttet:
    Forfatter
    ved NORCE Energi ved NORCE Norwegian Research Centre AS

Hamdi Tchelepi

  • Tilknyttet:
    Forfatter
    ved Stanford University
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