Outline and schedule

There is a lot of material to cover (see Course information for an overview of topics and goals). It will not be possible to cover everything in detail in lectures.

The textbook [FVMHP] covers many details that will be omitted from lectures. You should read the relevant sections before lecture and come with any questions you have about the material.

See the class Canvas page for videos to watch before lectures. Note that many of the slides indicate in the bottom right corner what section of the book is most relevant. The slides can be found in the slides directory of the Class GitHub Repository.

See Homework and midterm for Homework schedule and assignments.

Schedule (tentative)

  • Week 1: Overview of course, advection and acoustics equations

    • Overview, introduction to hyperbolic PDEs and conservation laws

    • Chapters 1 and 2 of [FVMHP].

    • See also Chapter 1 and 2 of [ETH].

  • Week 2:

    • Linear hyperbolic systems and Riemann problems

    • Chapters 2 and 3 of [FVMHP].

    • See also Chapters 10 and 11 of [ETH].

  • Week 3:

    • Monday, January 16: Martin Luther King Day – no class.

    • Finite volume methods and Godunov for linear systems

    • CFL condition, first and second order methods, modified equations

    • Chapter 4 of [FVMHP].

  • Week 4:

    • High resolution methods, TVD, limiters

    • Chapter 6 of [FVMHP].

  • Week 5:

    • Nonlinear scalar conservation laws

    • Chapters 11-12 of [FVMHP].

  • Week 6:

    • Nonlinear scalar methods, entropy, convergence

    • Chapters 11-12 of [FVMHP].

  • Week 7:

    • Wednesday, February 15: Midterm in class

    • Nonlinear systems, Hugoniot locus and integral curves

    • Chapter 13 of [FVMHP].

  • Week 8:

    • Monday, February 20: Presidents’ Day – No class

    • Gas dynamics

    • FV methods for nonlinear systems

    • Chapters 14-15 of [FVMHP].

  • Week 9:

    • FV methods for nonlinear systems, approximate Riemann solvers

    • Hyperbolic problems in two space dimensions

    • Chapters 15,19 of [FVMHP].

  • Week 10:

    • Hyperbolic problems in two space dimensions

    • Other applications

    • Chapters 20-21 of [FVMHP].