报告人： Prof. Etan Tadmor
High Resolution Central Schemes: A Black-Box Solvers for Quasilinear PDEs
Nonlinear conservation laws and related quasilinear problems admit shocks, kinks, and other large scale features of non-smoothness. The multiscale aspect of these gradients poses a main computational challenge for their numerical solution. We discuss the solution of such problems by central schemes. Central schemes avoid the intricate and time-consuming details of the eigen-structure of the underlying PDEs, and in particular, the use of (approximate) Riemann solvers, dimensional splitting, etc. Instead, .the main ingredients here are the propagation speeds of the underlying PDE, detection of spurious edges and non-oscillatory reconstruction in the directions of smoothness. Quadrature rules replace Riemann solvers. The resulting family of central schemes offers high-resolution ``black-box-solvers'' to an impressive range of such nonlinear problems. We shall discuss a host of examples, including recent results of one- and two-dimensional MHD equations.
报告时间： 2006年6月16日(周五) 上午10:15--11:15