An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications

Stephen Lin, Jacob Smith, Wing Kam Liu, Gregory J. Wagner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A concurrent multiscale method is developed to model time-dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved. Ensuring this energetic consistency among scales enables the implementation of high fidelity physics-based models at critical locations within the coarse-scale to temporally and spatially resolve highly complex and localized phenomena. To achieve this, only Neumann boundary conditions are applied over the fine scale domain, ensuring a conservative formulation. The coarse-scale solution is used to reconstruct these Neumann boundary conditions on the fine scale, which are then used to evolve a separate system of governing equations. The results on the fine scale are then sent back to the coarse scale through an energy-based homogenization scheme. Transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness, including the coupling of a phase field model at the fine scale to a coarse-scale heat equation.

Original languageEnglish (US)
Pages (from-to)100-120
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Volume315
DOIs
StatePublished - Mar 1 2017

Keywords

  • Concurrent multiscale method
  • Heat equation
  • Multilevel finite elements
  • Phase field models

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'An energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications'. Together they form a unique fingerprint.

Cite this