Computational hyperbolic PDE (Jan-Apr 2024)
Class : Tuesday at 11 AM, Wednesday at 2 PM, Friday at 9 AM
Place : Auditorium
Grading : Homework (30), midterm (30), final (40)
First class: 3 Jan 2024
Students
- Aadi Bhure (C)
- Kousik Samanta (C)
- Aniket Pal (C)
- Keshav Sharma (C)
- Nanda Raghunathan (C)
- Arpit Babbar
- Jalil Khan
- Sandeep Kumar
- Venkatesh Parasuram
Syllabus
Linear equations: Conservation laws and differential equations, characteristics and Riemann problem for hyperbolic systems, finite volume methods, high resolution methods, boundary conditions, convergence, accuracy and stability, variable coefficient linear equations
MUSCL-Hancock, ENO-WENO schemes, time stepping, Central schemes
Nonlinear equations: Scalar problems and finite volume method, nonlinear systems, gas dynamics and Euler equations, FVM for nonlinear systems, approximate Riemann solvers, nonclassical hyperbolic problems, source terms
Multidimensional problems: Some PDE models, fully discrete and semi-discrete methods, methods for scalar and systems of pde
Parallel programming using MPI and PETSc (Fortran/C/C++)
Codes
References
- Randall J. LeVeque: Finite volume methods for hyperbolic problems, Cambridge Univ. Press.
- D. I. Ketcheson, R. J. LeVeque and Mauricio J. del Razo, Riemann problems and Jupyter solutions, SIAM. html, code
- E. F. Toro, Riemann solvers and numerical methods for fluid dynamics, Springer.
- E. Godlewski and P-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Springer.