求解双曲型守恒律的半离散三阶中心迎风格式

给出了求解一维双曲型守恒律的一种半离散三阶中心迎风格式，并利用逐维进行计算的方法将格式推广到二维守恒律。构造格式时利用了波传播的单侧局部速度，三阶重构方法的引入保证了格式的精度。时间方向的离散采用三阶TVD Runge—Kutta方法。本文格式保持了中心差分格式简单的优点，即不需用Riemann解算器，避免了进行特征分解过程。用该格式对一维和二维守恒律进行了大量的数值试验，结果表明本文格式是高精度、高分辨率的。

Third-order semi-discrete central-upwind scheme for hyperbolic conservation laws

A third-order semi-discrete central-upwind scheme for one-dimensional system of conservation laws was presented.The scheme is extended to two-dimensional hyperbolic conservation law by the dimension-by-dimension approach.The presented scheme is based on the one-sided local speed of wave propagation.In order to guarantee the accuracy of spatial discretizaiton,a third-order reconstruction is introduced in this paper.The time integration is implemented by using the third-order TVD Runge-Kutta method.The resulting scheme retains the main advantage of the central-schemes simplicity,namely no Riemann solvers are involved and hence characteristic decompositions can be avoided.A variety of numerical experiments in both one and two dimensions are computed.The results show the high accuracy and high resolution of the scheme.