Dr.
Will
Miles
Assistant
Professor of
Office:
214-7, Elizabeth Hall
email: wmiles@stetson.edu
phone: 386-822-7555
Stetson University
Math and CS
Department
FaceBook Google
Sources for Math Help
Your Professor's Office Hours (free)
The Math Clinic (free): Elizabeth Hall, Room 209
Mon-Thu: 2:30 pm - 4:30 pm, 7:00 pm - 10:00 pm
Sun: 8:00 pm - 10:00 pm
Private Tutoring (cost varies depending on tutor): A list of private tutors is available in the Math/CS Department office.
Online Support (cost varies): There are now several websites dedicated to helping students with math.
Recent Publications
Ervin, V.J., and Miles, W.W., Approximation of Time-Dependent, Multi-Component, Viscoelastic Fluid Flow, Comput. Methods Appl. Mech. Engrg., Vol. 194, pp 2229-2255, (2005).
Abstract: In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling equations for the individual fluids are combined into a single system of equations using a continuum surface model. The numerical approximation is stabilized by using a SUPG approximation for the constitutive equation. Under a small data assumption on the true solution, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of the mesh parameter $h$, the time discretization parameter $\Delta t$, and the SUPG coefficient $\nu$ are also derived. Numerical simulations of viscoelastic fluid flow involving two immiscible fluids are also presented.(paper in pdf format)
Miles, W.W., Approximation of Multicomponent Fluid Flows with a Varying Coefficient of Interfacial Tension, Computational Methods in Multiphase Flow II/, edited by A.A. Mammoli and C.A. Brebbia, WIT Press, 2004.
Abstract: This work investigates the modeling of multicomponent, viscoelastic fluid flows. The governing equations are presented as well as results pertaining to the existence and accuracy of the solution to the approximating system of equations. The set of governing equations includes the imposition of a ``jump'' condition which exists at a fluid-fluid interface. The interfacial tension forces which act along the interface are transformed into volumetric forces via a method similar to the \emph{continuous surface force} model of Brackbill, et. al. \cite{bra921}. In multicomponent fluid flows, the interfacial tension forces may play a significant role in morphological development. Higher values of the \emph{coefficient of interfacial tension} $\sigma$ allow for less deformation of the minor phase while lower values of $\sigma$ allow the minor phase to udergo large deformation under appropriate mixing conditions. To date, most numerical implementations assume that $\sigma$ is constant. In the implementations which allow $\sigma$ to vary, the surface gradient of $\sigma$, denoted $\nabla_s\sigma$, is neglected. The model implemented in this work allows $\sigma$ to vary spatially and
incorporates the $\nabla_s\sigma$ term into the interfacial tension forces.(paper in pdf format)
Ervin, V.J., and Miles, W.W., Approximation of Time-Dependent, Viscoelastic Fluid Flow: SUPG Approximation,
Abstract: In this article we consider the numerical approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a SUPG approximation for the constitutive equation. We analyse both the semi-discrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the numerical approximations.(paper in pdf format)
Undergraduate
Research
Fowks, Gary Thomas, Mathematics of the Gridiron: ACCUV College Football Ranking Model, Stetson University, (2008).(paper)
Hagerman, Keri, Optimization of Work Schedules Based on Circadian Rhythms, Stetson University, (2008).(paper)
Deyo-Svendsen, Matthew, The Evolution of Solutions to Boundary-Valued Problems Using Finite Elements and Genetic Algorithms}, Stetson University, (2007).(paper)
Litsch, Anthony, An Analysis of TL Wimpout: A Probability Study and Examination of Game-Playing Strategies, Stetson University, (2006).(paper)
Coates, April, A Statistical Analysis of Student Athletes at Stetson University, Stetson University, (December 2005).(paper)
Reott, Veronica, Hurricanes and Disaster Declarations: A Statistical Analysis, Stetson University, (May 2005).(paper)
Swango, Carolyn,
An Analysis of
the
Advanced Placement Calculus
Exam as a Measure of Preparedness for Calculus II and a Regression
Analysis of Precalculus Grades,
Stetson University, (May 2005).(paper)