A Hierarchical Multiscale Method for Nonlocal Fine-scale Models via Merging Weak Galerkin and VMS Frameworks

Masud, Arif

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https://hdl.handle.net/2142/100367 Copy

Description

Title

A Hierarchical Multiscale Method for Nonlocal Fine-scale Models via Merging Weak Galerkin and VMS Frameworks

Author(s)

Masud, Arif

Issue Date

2017

Keyword(s)

• Hierarchical Multiscale Method
• Nonlocal fine-scale models
• Stabilized Interface Method
• Discontinuous Galerkin
• Multi-constituent materials
• Weak discontinuities
• Strong discontinuities

Abstract

Many problems in natural sciences and engineering involve phenomena that possess a wide spectrum of material, spatial and temporal scales. Most often these scales are nonlocal and therefore pose great challenge to current computational techniques. Of specific interest to the objectives of this proposal are advection dominated viscous flows leading to anisotropic turbulence where all the scales are nonlocal and they concurrently interact all across. Another class of problems from mathematical physics that we address involves propagating steep fronts wherein interacting discontinuities in the underlying physical fields challenge the stability of the numerical methods. Modeling such problems raises open mathematical questions: How should the information obtained from a model at one level be incorporated into a model at a different level? And secondly, how should these scales be made to communicate seamlessly if both coarse and fine scales are inherently non-local? Focus of the proposed research is a unifying mathematical framework for the development of robust numerical methods in two areas of Computational Fluid Dynamics (CFD): (i) Methods for anisotropic turbulence that are derived consistently from the Navier-Stokes equations via facilitating two-way coupling between global and local scales, and (i) Methods that have sound variational structures for the modeling of problems with steep gradients and propagating discontinuities. Emphasis is placed throughout on variationally consistent interscale coupling with rigorous treatment of the continuity conditions that are critical for the mathematical and algorithmic stability.

Series/Report Name or Number

NSF - DMS-16-20231, 2016-17

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/100367

Sponsor(s)/Grant Number(s)

NSF - DMS-16-20231, 2016-17

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