MTL793: Numerical Methods for Hyperbolic PDEs

3 Credits (3-0-0)

Scalar conservation laws: Method of characteristics, Shocks, Rarefactions, weak and entropy solutions, existence and uniqueness results, Finite volume schemes, Riemann solvers, Convergence of first order schemes. Higher-order schemes: Lax-Wendroff, TVD schemes, Limiters, ENO schemes, Higher order Runge-Kutta methods. Linear systems: Exact solutions, First- and higher-order finite volume schemes. Non-linear Systems: Solutions of Riemann problems, FirstOrder finite volume schemes for systems. Higher-order schemes for systems: TVD Limiters. Finite-volume schemes on unstructured meshes. Hyperbolic systems with source term.