High Order Accurate Algorithms for Shocks, Rapidly Changing Solutions and Multiscale Problems.

摘要

Research has been performed on weighted essentially non-oscillatory schemes and discontinuous Galerkin methods, and other related numerical methods, which are high order accurate numerical methods for solving problems with shocks and other complicated solution structures. New algorithm aspects include subcell resolution for non-conservative systems, high order well balanced schemes, stable Lagrangian schemes, schemes for front propagation with obstacles, and homotopy method for steady states. Applications include high order simulations for 3D gaseous detonations, sound generation study via vortex interactions, turbulence simulations, simulations of resonant photons, and dynamic continuum models for traffic flows in urban cities with efficient and stable numerical simulations.