Engineering Commons^™

A Monolithic Arbitrary Lagrangian-Eulerian Finite Element Method For An Unsteady Stokes/Parabolic Interface Problem, Ian Kesler

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, a non-conservative arbitrary Lagrangian-Eulerian (ALE) method is developed

and analyzed for a type of linearized Fluid-Structure Interaction (FSI) problem in a

time dependent domain with a moving interface - an unsteady Stokes/parabolic interface

problem with jump coefficients. The corresponding mixed finite element approximation is

analyzed for both semi- and full discretization based upon the so-called non-conservative

ALE scheme. The stability and optimal convergence properties in the energy norm are

obtained for both schemes.

Numerical Analysis And Fluid Flow Modeling Of Incompressible Navier-Stokes Equations, Tahj Hill

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Navier-Stokes equations (NSE) are an essential set of partial differential equations for governing the motion of fluids. In this paper, we will study the NSE for an incompressible flow, one which density ρ = ρ0 is constant.

First, we will present the derivation of the NSE and discuss solutions and boundary conditions for the equations. We will then discuss the Reynolds number, a dimensionless number that is important in the observations of fluid flow patterns. We will study the NSE at various Reynolds numbers, and use the Reynolds number to write the NSE in a nondimensional form.

We will …