Domain Decomposition in Computational Fluid Dynamics for Pipe-like Domains Pubblico

Wenda Zheng (Spring 2018)

Permanent URL: https://etd.library.emory.edu/concern/etds/mc87pq30p?locale=it
Published

Abstract

Nowadays, as the result of progress of numerical methods for solving complex problems, simulations of patient-specific cardiovascular districts are possible and used in medicine. Nevertheless, when covering large portion of the circulation, simulations on regular computers can be not affordable. In this thesis, starting from the evidence that the circulatory network is made of pipes and junctions, we test the efficacy of ``domain decomposition” techniques on our constructed 2D models. Using FreeFem++ as the simulation tool, we evaluates the Domain Decomposition techniques on 2D problems and try to find the possibilities to extend our work into 3D realistic cases. 

Table of Contents

1 Introduction  1.1  Motivation 1.2  Contribution 1.3  Outline 2 The Mathematical Problems  2.1  IntrotoHilbertSpaces 2.2  A simple 2D diffusion-reaction problem 2.3  Navier-Stokes Equations for Incompressible Fluids .

3 Domain Decomposition Techniques and Finite Element Method

3.1  Domain Decomposition Techniques

3.1.1  Test Cases Using 2D Elliptic Equation 

3.1.2  TheOverlappingMethod 

3.1.3  The Non-overlapping Method 

3.2  IntroductiontoFiniteElements 

              3.2.1 Finite Elements Using Galerkin Method               3.2.2 FreeFem++ 

4 Numerical Results 

       4.1 Results of a Single Model with Bifurcation

       4.2 Results of Modified Model with Child Bifurcation 

5 Conclusion  A FreeFem++ Code  Bibliography 

About this Honors Thesis

Rights statement
  • Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
School
Department
Degree
Submission
Language
  • English
Research Field
Parola chiave
Committee Chair / Thesis Advisor
Committee Members
Ultima modifica

Primary PDF

Thumbnail Title Date Uploaded Actions
Domain Decomposition in Computational Fluid Dynamics for Pipe-like Domains () 2018-04-09 20:53:10 -0400

Supplemental Files

Thumbnail Title Date Uploaded Actions
FreeFem++ Code (Codes corresponds to Appendix) 2018-04-09 20:53:01 -0400