The University of Houston System Houston United States
AccomplishmentsNew Findings. The PI, together with her group members, have been involved in the following research activities in the development, analysis and applications of efficient, robust and high order numerical approaches for kinetic and fluid simulations. In particular, the following topics are being pursued. 1. Development of highly accurate and efficient numerical methods for the Vlasov equation, see our publications 6, 7, 9, 10, 12,13, 14, 17, 18. 2. Error analysis of integral deferred correction method for solving stiff problems, such as singular perturbation problems. Specific schemes we consider are implicit Runge-Kutta RK methods for stiff problems and implicit-explicit RK methods for temporal multi-scale problems, see our publications 1, 16. 3. Development and analysis of high order asymptotic preserving schemes for kinetic equations in the hyperbolic limit, see our publications 11. 4. Development and analysis of high order maximum principle preserving and positivity preserving methods for convection-diffusion equations and for the Euler system, see our publications 2, 3. 5. Development of high order DG scheme for hyperbolic net and network problems, see our publications 4, 8.