二维浅水波方程的非结构网格ENO型有限体积法

ENO-Style Finite Volume Method on Unstructured Meshes for the Two-Dimensional Shallow Water Equations

考虑二维浅水波方程及其离散方法,对二维非结构三角形网格给出了ENO型有限体积法,主要思想是在每一个单元上对各物理量构造线性插值多项式,再选择不同的数值流函数,得到两种复合型有限体积格式,时间离散采用二阶Runge-Kutta方法.对二维溃坝问题进行数值模拟,结果表明,这两种格式精度高且稳定.

Two-dimensional shallow water equations and its discretization are presented. Combining with ENO scheme, some composite finite volum methods are put forward on two dimensional unstructured meshes. The composite FVM is formed by constructing a linear interpolation on every triangular mesh and choosing different flux functions. Two order TVD Runge-Kutta method is used for time discretization. Then,by using such methods,the numerical solutions of two-dimensional partial dam break problem are made on unstructured triangular meshes. The numerical results show that the proposed schemes are accurate and stable.