Official Information  

Course Number:  Mathematics 9200.001 
Course Title:  Topics in Numerical Analysis I: Computational Methods for Flow Problems 
Times:  MW 1:002:40 
Places:  Wachman 527 
Instructor:  Benjamin Seibold 
Instructor Office:  518 Wachman Hall 
Instructor Email:  seibold(at)temple.edu 
Instructor Office Hours:  M 2:203:20, W 12:001:00 
Course Textbooks: 
There is no single textbook for this course. The materials come from a variety of books and other sources. Recommended resources:

Official:  Course Syllabus 
Prerequisites:  see Math Course Listings 
Topics Covered:  This course provides an overview of many important flow problems, ranging from incompressible fluids (NavierStokes equations), over shock problems (such as the compressible Euler equations) and front propagation problems, to kinetic equations (Boltzmann equation, radiative transfer) and network flows (traffic flow). One third of the course will be devoted to the modeling, derivation, and mathematical/physical properties of the equations and their solutions; and two thirds to the design of efficient and robust numerical approaches for their solution on compute infrastructures. The computational approaches include: finite volume methods, finite difference methods, particle methods, spectral methods, level set methods, moment methods. The purpose of this course is provide a broad perspective on these important types of flow problems, their connections, and how to tackle them computationally. Participants will be provided with sufficient familiarity with each topic to enable them to engage into further studies via literature. Course Grading: Homework problems sets and final examination. 
Course Goals:  Provide students knowledge and a solid big picture perspective about important flow problems that arise in many fields of science and engineering applications, and in particular effective computational methods to approximate their solutions. 
Attendance Policy:  Students are expected to attend every class. If a student cannot attend a class for some justifiable reason, he or she is expected to contact the instructor before class (if possible). 
Course Grading:  Homework problems sets and final examination. 
Exam Date:  04/30/2015 (oral exam schedule via email) 
Course Schedule  
01/12/2015 Lec 1  Fundamentals of flows: Examples of flows

01/14/2015 Lec 2  reference frames, transport equations, incompressibility, vorticity

01/21/2015 Lec 3  stream function, flow lines
Read:
stream function,
streamlines etc.

01/26/2015 Lec 4  potential flow
Read:
potential flow,
conformal map

01/28/2015 Lec 5  Particle methods

02/02/2015 Lec 6  Software development and best practices
Read:
software licenses

02/06/2015 Lec 7  SemiLagrangian methods: fundamentals
Read:
semiLagrangian scheme

02/09/2015 Lec 8  Highorder semiLagrangian methods
Read:
jet schemes

02/11/2015 Lec 9  Finite difference methods: Consistency, stability, convergence, truncation errors

02/16/2015 Lec 10  Von Neumann stability, semidiscretization

02/18/2015 Lec 11  Upwind, LaxWendroff, LaxFriedrichs methods

02/23/2015 Lec 12  Advectionreactiondiffusion problems

02/25/2015 Lec 13  Operator splitting

02/27/2015 Lec 14  Hyperbolic conservation laws: Examples, characteristics (scalar 1d)

03/09/2015 Lec 15  weak solutions, Riemann problem, entropy
Read:
weak solution,
Riemann problem

03/11/2015 Lec 16  Finite volume methods: Godunov's method

03/23/2015 Lec 17  Highorder methods, limiters

03/25/2015 Lec 18  Semidiscrete methods, MUSCL, SSP time stepping

03/27/2015 Lec 19  ENO/WENO, hyperbolic systems
Read:
shallow water equations

03/30/2015 Lec 20  Incompressible viscous flows: Calculus of variations
Read:
calculus of variations

04/01/2015 Lec 21  Stokes problem, saddlepoint structure
Read:
Stokes flow

04/06/2015 Lec 22  Finite elements for Stokes problem [guest lecture by Scott Ladenheim]

04/08/2015 Lec 23  Implementation in deal.II [guest lecture by Scott Ladenheim]

04/13/2015 Lec 24  Orders of convergence for advection with discontinous solutions
Read:
modified equation

04/15/2015 Lec 25  Staggered grid finite differences and NavierStokes equations

04/20/2015 Lec 26  Pseudospectral methods for NavierStokes

04/22/2015 Lec 27  Kinetic equations: Vlasov and Boltzmann equation

04/27/2015 Lec 28  Moment methods for radiative transfer
Read:
radiative transfer

04/30/2015  Final Examination 
Matlab Programs  
 
Software Used in the Course  
 
Homework Problem Sets  
