An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method

Open Access
Author:
Kauffman, Justin A
Graduate Program:
Engineering Science and Mechanics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
January 08, 2018
Committee Members:
  • Jonathan S Pitt, Dissertation Advisor
  • Jonathan S Pitt, Committee Chair
  • Francesco Costanzo, Committee Member
  • Corina Stefania Drapaca, Committee Member
  • James Joseph Brannick, Outside Member
  • Scott Miller, Special Member
Keywords:
  • Overset Mesh Methods
  • Hybridizable discontinuous Galerkin
  • HDG
  • Finite Element Method
  • Pseudo-compressibility
  • Arbitrary Lagrangian-Eulerian
  • Navier-Stokes
  • Elasticity
Abstract:
Computational simulations contain discretizations of both a physical domain and a mathematical model. In this dissertation, an overset mesh framework is used to discretize the physical domain, and the hybridizable discontinuous Galerkin (HDG) finite element method is used to discretize the mathematical model. It is proposed that using an overset mesh framework for the HDG method enables stable solutions to be computed for complex geometries and dynamic meshes. Overset mesh methods are chosen because they are efficient at decomposing geometrically complex domains. The HDG method was chosen because it provides solutions that are arbitrarily high-order accurate, reduces the size of the global discrete problem, and has the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. An overset mesh method can utilize an inherent property of the HDG method, the decomposition of the solution into global (face) and local (volume) parts. The global solution exists only on the cell boundaries; while, the local solution exists in the interior of each cell and is decoupled between neighboring cells. This decomposition introduces face-volume coupling in the weak form for degrees of freedom on cell boundaries, which is used as the foundation for the overset communication between subdomains. Ultimately, the goal of this work is to simulate full-scale hydrodynamic and fluid-structure interaction (FSI) problems. To achieve these simulations, the necessary building blocks must first be verified and validated in the overset-HDG framework. The building blocks demonstrated in this dissertation are steady convection-diffusion, linear elasticostatics, and pseudo-compressible Navier-Stokes in both Eulerian and arbitrary Lagrangian-Eulerian frames. Computational simulations are performed to demonstrate the applicability and accuracy of the overset-HDG algorithm.