提出了一种用于求解一维标量方程和无粘Euler方程组的高阶有限体积格式.其中时间离散采用Simpson数值积分公式从而实现时间上的高阶.利用特征线理论得到网格节点在各个时间层沿着特征线的位置,而积分公式中的节点值通过三阶和五阶的中心加权本质无震荡重构得到.最后,给出了几个数值算例验证此方法的高精度和收敛性以及捕获激波的能力.
A high-order finite-volume scheme was presented for the one-dimensional scalar and inviscid Euler conservation laws. The Simpson' s quadrature rule was used to achieve high-order accuracy. To get the point value of the Simpson's quadrature, the characteristic theory was used to obtain the positions of the grid points at each sub-time stages along the characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory (CWENO) reconstruction was adopted to estimate the cell point values. Several standard one-dimensional examples were used to verify high-order accuracy, convergence and capability of capturing shock.