Moving mesh finite difference solution of non-equilibrium radiation diffusion equations

A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves nonlinear diffusion coefficients and its solutions stay positive for all time when they are positive initially. Nonlinear diffusion and preservation of solution positivity pose challenges in the numerical solution of the model. A coefficient-freezing predictor-corrector method is used for nonlinear diffusion while a cutoff strategy with a positive threshold is used to keep the solutions positive. Furthermore, a two-level moving mesh strategy and a sparse matrix solver are used to improve the efficiency of the computation. Numerical results for a selection of examples of multi-material non-equilibrium radiation diffusion show that the method is capable of capturing the profiles and local structures of Marshak waves with adequate mesh concentration. The obtained numerical solutions are in good agreement with those in the existing literature. Comparison studies are also made between uniform and adaptive moving meshes and between one-level and two-level moving meshes.Comment: 29 page

Developing EFL Reading Fluency in Upper Elementary Schools in China

This project aims to help EFL educators and EFL teachers realize the importance of developing EFL students’ reading fluency, and more importantly, to provide specific curriculum for upper elementary school EFL students to improve their reading fluency. The most important intervention being used in this curriculum is extensive reading which appears in every class. Besides extensive reading, using rapid word recognition, repeated reading, paced reading, cloze reading, echo reading and choral reading are also discussed in this project. Teachers are suggested to rotate the interventions during the whole semester and they can adapt the materials and the curriculum in this project according to their needs