Special Topics in Astrophysics - Numerical Hydrodynamics (PHYS*7900)

Code and section: PHYS*7900*01

Term: Fall 2020

Instructor: Daniel Siegel


1: Course Information 

1.1: Instructor:

Daniel Siegel, MacN 435C, Extension 53983

1.2: Time and Location:

Online synchronous lectures via zoom
To be updated: day & time

2: Learning Resources 

2.1: Primary Course References:

The primary textbook recommendations for this course are:

  • E. Toro: Riemann Solvers and Numerical Methods for Fluid Dynamics (Springer, 3rd edition, 2009)
  • R. Leveque: Finite Volume Methods for Hyperbolic Problems (Cambridge Univ. Press, Cambridge Texts in Applied Mathematics, 2002)

Please note: Both textbooks are available as e-books via the UoG Library. The UoG Bookstore will not order Toro’s book by default due to pricing. Should students be interested in the recommended title, they are welcome to contact the University Bookstore and they can “Special Order” it.

2.2: Additional Textbook References:

  • A. Anile: Relativistic fluids and magneto-fluids (Cambridge Univ. Press, 1990)
  • P. Bodenheimer, G. Laughlin, M. Rozyczka, H. Yorke: Numerical Methods in Astrophysics (Taylor & Francis, 2007)
  • R. Leveque: Finite Difference Methods for Ordinary and Partial Differential Equations (SIAM, 2007)

More mathematically inclined literature includes:

  • D. Kröner: Numerical Schemes for Conservation Laws (Wiley, 1997)
  • L. Evans: Partial Differential Equations (Graduate Studies in Mathematics, American Mathematical Society, 2nd edition, 2010)

3: Evaluation

30% Assignments
70% Final Exam

Assignments for this course will be posted and submitted online. Assignments will not be accepted after the corresponding deadline. Submitted assignment solutions must show calculation details, be legible, and written with a logical flow. Code submitted as part of the hands-on assignments must be well documented and execute without errors. Marks on assignments will rapidly approach zero if not presented well.

4: Course Aims and Objectives 

4.1: Course Prerequisites 

Standard undergraduate knowledge of mathematical methods, basic hydrodynamics, and electrodynamics is an expected prerequisite. Previous familiarity with numerical methods and basic programming skills (e.g., in python) are not strictly necessary, but certainly beneficial.

4.2: Course Description 

This course provides a graduate-level introduction to computational fluid dynamics, covering the theoretical concepts and numerical methods that form the foundation of much of modern theoretical astrophysics and cosmology. Beyond applications in astrophysics and cosmology the concepts introduced here are of relevance in many other fields of physics and engineering. Assignments will include both analytical problems and hands-on programming problems. The latter will be python-based and are designed to provide a deeper understanding of the numerical concepts through practical implementation. A brief introduction to python and jupyter notebooks will be given.   

4.3: Course Topics 

Topics include:

  • Basic notions of partial differential equations
  • The equations of Newtonian and relativistic hydrodynamics, magnetohydrodynamics, and radiation transport
  • Finite differencing methods for PDEs
  • Properties of conservation laws: Riemann problem, weak solutions, Sobolev spaces
  • Finite volume methods and Riemann solvers
  • Multi-dimensional problems and higher-order schemes
  • Outlook: Galerkin methods

5. Assignments and collaboration:

Discussion between students regarding assignments is encouraged. All work submitted for grading in this course, however, must be each individual student’s own work. It is not acceptable to share assignment solutions in any way; the assignments are not group projects.

6. Course Policies

6.1 Accessibility

The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community's shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identified, ongoing disability or a short-term disability should contact the Student Accessibility Services as soon as possible. For more information, contact SAS at 519-824-4120 ext. 56208 or email accessibility@uoguelph.ca  

6.2 Academic Misconduct

The University of Guelph takes a serious view of academic misconduct and will severely penalize students, faculty and staff who are found guilty of offenses associated with misappropriation of others' work, misrepresentation of personal performance and fraud, improper access to scholarly resources, and obstructing others in pursuit of their academic endeavours. Each student is assumed to be familiar with the regulations surrounding academic misconducts, as spelled out in the Undergraduate Calendar.

6.3 Course and Instructor evaluation

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and possible areas of improvement. In addition, annual student assessment of teaching provides part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member's contribution in the area of teaching. 

The Department's teaching evaluation questionnaire invites student response both through numerically quantifiable data, and written student comments. In conformity with University of Guelph Faculty Policy, the Department Tenure and Promotions Committee only considers comments signed by students or by choosing \I agree" in question 14 (online process). Your instructor will see all signed and unsigned comments after final grades are submitted. Written student comments may also be used in support of a nomination for internal and external teaching awards. 

NOTE: No information will be passed on to the instructor until after the final grades have been submitted.

6.4 Disclaimer

Please note that the ongoing COVID-19 pandemic may necessitate a revision of the format of course offerings and academic schedules. Any such changes will be announced via CourseLink and/or class email. All University-wide decisions will be posted on the COVID-19 website and circulated by email.  

6.5 Illness

The University will not require verification of illness (doctor's notes) for the fall 2020 or winter 2021 semesters.