Multiscale Materials Science - A Mathematical Approach to the Role of Defects and Uncertainty

Abstract

The bottom line of our work is to develop affordable numerical methods in the context of heterogeneous,possibly random, materials. In thisreport, we first consider a multiscale advection-diffusion problem on a perforated domain, in the convection-dominated regime. We showhow to adapt two classical methods, MsFEM type approaches and stabilized type techniques (e.g. the Streamline Upwind Petrov-Galerkin[SUPG] method), in a unified single approach to efficiently solve these multiscale advection-diffusion problems. Numerical results are shown,and a comparison amongst the MsFEM approaches is given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Oct 28, 2016
Accession Number
AD1020861

Entities

People

  • Claude Le Bris
  • F. Madiot
  • Frederic Legoll
  • S. Lemaire

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Air Force Research Laboratories
  • Algorithms
  • Boundaries
  • Boundary Layer
  • Coefficients
  • Computational Science
  • Construction
  • Convection
  • Differential Equations
  • Diffusion Coefficient
  • Equations
  • Linear Systems
  • Materials
  • Materials Science
  • Numerical Analysis

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)