Official Information  

Course Number:  Mathematics 9200.001 
Course Title:  Topics in Numerical Analysis I: Computational Methods for Flow Problems 
Time:  TR 2:003:20 
Place:  617 Wachman Hall 
Instructor:  Benjamin Seibold 
Instructor Office:  518 Wachman Hall 
Instructor Email:  seibold(at)temple.edu 
Office Hours:  TR 3:304:30pm 
Official:  Course Syllabus 
Course Textbooks: 
There is no single textbook for this course. The materials come from a variety of books and other sources. Recommended resources:

Grading Policy  
The final grade consists of two parts, each counting 50%: homework problem sets and final examination.  
Outline  
This course provides an overview of numerical methods for many important types of flow problems, ranging from passive convection, over incompressible fluids (NavierStokes equations), shock problems (such as the compressible Euler equations), kinetic equations (Boltzmann equation, radiative transfer), to network flows (such as traffic on roads).
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 methods for their solution. The computational approaches include: finite volume methods, finite difference methods, meshfree and particle methods, moment methods. The goal of this course is provide a broad perspective on these important types of flow problems, their connections, and how to tackle them computationally. This course provides the needed familiarity with each topic to enable the participants to engage into further studies via literature.  
Course Schedule  
08/23/2022 Lec 1  I. Fundamentals of Flows: Different types of flow problems

08/25/2022 Lec 2  reference frames, transport equations, incompressibility, vorticity

08/30/2022 Lec 3  stream function, field lines
Read:
stream function,
streamlines etc.

09/01/2022 Lec 4  potential flow
Read:
potential flow,
conformal map

09/06/2022 Lec 5  II. Passive Convection: Particle methods

09/08/2022 Lec 6  SemiLagrangian methods: fundamentals
Read:
semiLagrangian scheme

09/13/2022 Lec 7  SemiLagrangian methods: high order
Read:
jet schemes

09/15/2022 Lec 8  Eulerian finite difference methods: convergence, truncation errors, stability

09/20/2022 Lec 9  Method of lines, upwind, LaxWendroff, LaxFriedrichs

09/22/2022 Lec 10  Advectiondiffusionreaction problems

09/27/2022 Lec 11  III. Hyperbolic conservation laws: Examples, characteristics, weak solution, Riemann problem, entropy

09/29/2022 Lec 12  Finite volume methods: Godunov's method

10/04/2022 Lec 13  Celltransmission model
Read:
celltransmission model

10/06/2022 Lec 14  Network flows, theory and numerics
Read:
Braess's paradox

10/11/2022 Lec 15  Particle methods for conservation laws
Read:
particleclaw

10/13/2022 Lec 16  Linear hyperbolic systems

10/18/2022 Lec 17  Nonlinear hyperbolic systems

10/25/2022 Lec 18  Approximate Riemann solvers, higher dimensions
Read:
Riemann solver,
Roe solver

10/26/2022 Lec 19  IV. Incompressible viscous flows: Calculus of variations, Stokes problem

10/27/2022 Lec 20  Saddlepoint problems, infsup condition, staggered grids

11/01/2022 Lec 21  Finite element methods for the Stokes problem (guest lecture by Kiera Kean)
Read:
finite element method

11/03/2022 Lec 22  NavierStokes equations, derivation, Reynolds number

11/07/2022 Lec 23  Finite differences for the NavierStokes equations
Read:
staggered grids

11/08/2022 Lec 24  Pseudospectral methods for NavierStokes

11/10/2022 Lec 25  Turbulence and turbulence models (guest lecture by Kiera Kean)
Read:
turbulence,
turbulence model

11/28/2022 Lec 26  V. Kinetic equations: Vlasov and Boltzmann equation

11/29/2022 Lec 27  Moment methods for radiative transfer, StaRMAP (guest lecture by Rujeko Chinomona)
Read:
radiative transfer,
StaRMAP

12/01/2022 Lec 28  Moment methods, asymptotic preserving methods

12/12/2022  Final Examination 
Matlab Programs  
 
Software Used in the Course  
 
Homework Problem Sets  
