Dissertation/Thesis Abstract

Numerical Investigation on the Projection Method for the Incompressible Navier-Stokes Equations on MAC Grid
by Yek, Vorleak, M.S., California State University, Long Beach, 2018, 82; 10825591
Abstract (Summary)

The motion of a viscous fluid flow is described by the well-known Navier-Stokes equations. The Navier-Stokes equations contain the conservation laws of mass and momentum, and describe the spatial-temporal change of the fluid velocity field. This thesis aims to investigate numerical solvers for the incompressible Navier-Stokes equations in two and three space dimensions. In particular, we focus on the second-order projection method introduced by Kim and Moin, which was extended from Chorin’s first-order projection method. We apply Fourier-Spectral methods for the periodic boundary condition. Numerically, we discretize the system using central differences scheme on Marker and Cell (MAC) grid spatially and the Crank-Nicolson scheme temporally. We then apply the fast Fourier transform to solve the resulting Poisson equations as sub-steps in the projection method. We will verify numerical accuracy and provide the stability analysis using von Neumann. In addition, we will simulate the particles' motion in the 2D and 3D fluid flow.

Indexing (document details)
Advisor: Sun, Hui
Commitee: Chaderjian, Bruce, Lee, Chung-Min
School: California State University, Long Beach
Department: Mathematics and Statistics
School Location: United States -- California
Source: MAI 58/01M(E), Masters Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Fourier-Spectral method, Incompressible Navier-Stokes equations, Navier-Stokes equations derivation, Particles simulation, Projection method on MAC grid, Stability analysis
Publication Number: 10825591
ISBN: 978-0-438-25862-4
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