MTH-219.4 Computational hyperbolic PDE
Couse Code | MTH-219.4 |
|---|---|
No. of credits | 5 |
Subject Board | Mathematics |
Course Type | Elective course for students in 4th semester of Int-PHd, 3rd year of Int-PhD and PhD |
Prerequisites | Basic PDE course, knowledge of atleast one of Python/Fortran/C/C++, instructors approval |
Class schedule | Two classes and one tutorial per week |
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++)
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.
- 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.