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MAT 799, Dissertation Study in the
Concentration of Computational Mathematics
Modeling Study and Numerical Methodology for
Unsteady Interface Problems and Fluid-Structure Interaction (FSI) Problems
Spring 2026
(01/20/2026-05/09/2026)
COURSE DESCRIPTION:
This dissertation study topic aims at the modeling and advanced
numerical methodology studies for fluid-structure interaction (FSI) problems.
Incompressible fluid flow modeled by the dynamic Navier-Stokes equations
in Eulerian description, and compressible elastic structure modeled by the
dynamic mechanical equation in Lagrangian
description together with the structural constitutive laws are coupled through
some appropriately proposed boundary conditions on the moving interfaces of
fluid and structure, forming a monolithic model system of FSI. In terms of mesh
conformity through the fluid-structure interfaces, numerical methodologies to tackle FSI
model comprise the arbitrary Lagrangian-Eulerian (ALE) method (conforming mesh), fictitious domain method
(nonconforming mesh), and full Eulerian method with
phase field model, level set model (single mesh), and etc. Mixed finite
element method, upwind-finite volume method, Galerkin-least-square method and
streamline diffusion method are the main numerical techniques for discretizing and stabilizing the
induced saddle-point type weak formulations of FSI problems. The other
classification of numerical methodology for FSI simulation is based upon
the solution strategy for the derived discretization scheme, termed as
partitioned method if fluid and structure equation are separately computed
within an alternating iteration cycle and communicate with each other through
the interface transmission condition, and as monolithic method if both fluid and
structure equations are computed together within a saddle-point system where the
interface conditions are built into the discretization spaces. Depending on the
academic progress and practical situation of the graduate students, some of the
above numerical methods will be appropriately chosen to investigate for their
dissertation studies.
Reference
materials and lecture notes will be distributed in
the class.
COURSE
PROJECT:
The graduate students will complete an intensive study of the FSI problems on
the aspects of both modeling and numerical methodology, where, modeling study
includes Navier-Stokes equations, constitutive relations for
the linear elasticity problem, and conservation laws. Numerical study
comprises certain types of numerical techniques in terms of different
classification, such as arbitrary Lagrangian-Eulerian method and fictitious domain method,
or monolithic method and partitioned method. Graduate students will
critically examine these advanced numerical methods and their applications to a
general FSI model. Special attention will be given to the algorithm design and
analysis of the efficient and robust numerical technique in order to
overcome some particular but significant situations existing in FSI
applications, e.g., when the structure is deforming, rotating and translating,
at the same time, interacting with the surrounding fluid flow.
COURSE OBJECTIVES:
Upon completion of this course, the
graduate student will:
- Develop and pursue a unique study
question through substantial, legitimate research that fosters focus and
flexibility.
- Maintain a research note
documenting work and sources.
- Gain a thorough understanding of
the topic through investigation and discussion of modeling and numerical
studies, such as conservation laws, monolithic FSI model and the associated scientific
and engineering computing.
- Contribute original scholarship of
the topic, including developing a source code and summary of previous work.
- Prepare an article based on work
for submission to a conference or journal.
INSTRUCTIONAL METHODS AND LEARNING:
This is the dissertation study
utilizing extensive readings, intensive research, and experiential learning.
Questions, observations and computer programming are strongly required.
COURSE PARTICIPATION AND ATTENDANCE:
Expect to meet weekly with
the advisor for discussion, advising, and constructive criticism. However, the
graduate student is personally responsible for the development and progress of
the project. Meetings can be held semiweekly if necessary or desired. Contact
via email and phone is encouraged.
GRADE DETERMINATION:
Regular attendance and
participation in meetings is required and essential for success. If
special circumstances arise, the graduate student must contact the
advisor as soon as possible.
The final grade is
determined by the graduate student's adherence and development of a
research note, a paper of the findings and analysis (10-15 pages),
and attendance and participation including regular progress of the
project. Grades are ultimately at the discretion of the advisor.
Paper = 50%
Research note = 30%
Attendance and participation = 20%
ACADEMIC INTEGRITY:
Academic integrity is the pursuit of scholarly
activity in an open, honest and responsible manner. Academic integrity is a
basic guiding principle for all academic activity at
University of Nevada, Las Vegas, and all members of the University community are expected to act in
accordance with this principle. Consistent with this expectation, the
University's Code of Conduct states that all students should act with personal
integrity, respect other students' dignity, rights and property, and help create
and maintain an environment in which all can succeed through the fruits of their
efforts.
Academic integrity includes a commitment not to engage in or
tolerate acts of falsification, misrepresentation or deception. Such acts of
dishonesty violate the fundamental ethical principles of the University
community and compromise the worth of work completed by others.
Based on the University's
Student
Academic Misconduct Policy, a range of academic sanctions may be
taken against a student who engages in academic dishonesty.
DISCLAIMER:
The advisor reserves the right to make verbal or written changes to the
syllabus at any time. All changes and exceptions are at the advisor’s
discretion.
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