Implementation of Virtual Multiscale Method in COMSOL Multiphysics

Open Access
Author:
Mazza, Michael
Area of Honors:
Mechanical Engineering
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Francesco Costanzo, Thesis Supervisor
  • Stephanie Stockar, Honors Advisor
Keywords:
  • stabilized finite element methods
  • varaitional multi-scale method
  • COMSOL Multiphysics®
Abstract:
An overview of classical numerical stabilization techniques for advection-dominated problems is presented along with a more recent stabilization method called the Virtual Multiscale Method (VMM). The VMM has been implemented by various researchers using in-1house specilized codes. This thesis shows how the VMM can be implemented in commercial finite element software like COMSOL Multiphysics®, without requiring access to the software native code. The COMSOL Multiphysics® implementation of the VMM is demonstrated for two problems, the classical scalar advection-diffusion problem and the steady Navier-Stokes problem. The numerical stability of the VMM is presented as well as two studies to demonstrate the comparison between the VMM implemented in COMSOL Multiphysics® and other stabilization techniques employed for advection-dominanated problems.