非结构网格上求解二维H-J方程的一种WENO格式

A weighted ENO scheme for 2D H-J equations on unstructured meshes

基于WENO(Weighted Essentially Non-Oscillatory)的思想,提出了一种在非结构网格上求解二维Hamilton-Jacobi(简称H-J)方程的数值方法.该方法利用Abgrall提出的数值通量,在每个三角形单元上构造三次加权插值多项式,得到了一个求解H-J方程的高阶精度格式.数值实验结果表明,该方法计算速度较快,具有较高的精度,而且对导数间断有较高的分辨率.

A numerical method for Hamilton-Jacobi equations was developed on unstructured meshes with the WENO（Weighted Essentially Non-Oscillatory） idea.A scheme was gotten with high-order accuracy by constructing cubic weighted interpolation polynomial on every triangular mesh and using the numerical flux Abgrall proposed.Numerical experimental results show that the method costs efficiently,with higher accuracy and higher resolution for the derivative discontinuities.