报告题目：An Modified WENO Schemes for Hyperbolic Conservation Laws
报告人：Jianxian Qiu，

School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University
报告时间：7月17日周一下午4:30-6:30

报告地点：理科楼407

Abstract：
In this presentation, a class of modified weighted essentially non-oscillatory (MWENO) schemes is presented in the finite difference framework for solving the hyperbolic conservation laws. These schemes adapt between the linear upwind scheme and the WENO scheme automatically by the usage of a new simple switching principle. The methodology to reconstruct numerical fluxes for the MWENO schemes is split into two parts: if all extreme points of the
reconstruction polynomial for numerical flux in the big spatial stencil are located outside of the stencil, the the numerical flux is approximated directly by the reconstruction polynomial, and the approximation is a linear and high order accuracy; otherwise the WENO procedure in fG.-S. Jiang and C.-W. Shu, J. Comput. Phys., 126 (1996), 202-228g is applied to reconstruct the numerical flux. The main advantage of these new MWENO schemes is their robustness and efficiency comparing with the classical WENO schemes specified in fG.-S. Jiang and C.-W. Shu,. Comput. Phys., 126 (1996), 202-228g. The MWENO schemes can be applied to compute some extreme test cases such as the Sedov blast wave, the Leblanc and the high Mach number astrophysical jet problems et al. by using a normal CFL number without any further positivity preserving procedure for the purpose of controlling the concurrence of the negative density and pressure. Extensive numerical results are provided to illustrate the good performance of the MWENO schemes.

报告人简介：

邱建贤教授，厦门大学数学科学学院教授，博士生导师 ，Journal of Computational Physics编委。研究方向为：

1. 双曲守恒律及对流占优问题的数值解法研究，主要方法:

（1）本质无振荡(ENO）及加权本质无振荡(WENO)的差分方法和有限体积方法；

（2）间断Galerkin有限元(DG)；

2.  Hamilton-Jacobi 类型方程的数值解法；

3.    计算流体力学；

4.     WENO及DG方法在多相流问题数值模拟的应用。