Computational hyperbolic PDE
Elective course with 5 credits
Pre-requisities: Basic PDE course, knowledge of atleast one of Python/Fortran/C/C++, instructors approval
Audience: Students in 4’th semester of Int-PhD, 3’rd year of Int-PhD and PhD
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.