求解双曲型守恒律的半离散中心差分格式

Semi-Discrete Central Scheme for Hyperbolic Conservation Laws

给出了一种求解双曲型守恒律的三阶半离散中心差分格式。该格式以一种推广的三阶重构为基础,同时考虑了波传播的局部速度。格式的构造方法是利用重构,先计算非一致交错网格上的均值,再将该网格均值投影回原来的非交错网格,得到新的全离散中心差分格式,该格式有半离散形式。本文半离散格式保持了中心差分格式简单的优点,即不需用R iemann解算器,避免了进行特征解耦。它具有守恒形式,数值通量满足相容性条件。数值试验结果表明该格式是高精度、高分辨率的。

A third-order semi-discrete central scheme for approximate solution of the hyperbolic conservation laws was presented based on a new reconstruction, where local wave propagation velocity was taken into account. The cell averages over the nonuniform, staggered grid were computed, which then were projected back onto the original grid of the uniform, non-staggered cells to obtain the fully discrete third-order central scheme with a semi-discrete formulation. This scheme retains the main advantage of the central scheme-simplicity, hence Riemann solvers were unnecessary for characteristic decompositions. The numerical results confirm the desired accuracy and high resolution of the scheme with a conservative form and a consistent numerical flux.