High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
High-Order Central Schemes for Hyperbolic Systems of Conservation Laws
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DOI：
10.1137/s1064827597324998
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发表时间：
1999-08
期刊：
影响因子：
--
通讯作者：
Franca Bianco;G. Puppo;G. Russo
中科院分区：
文献类型：
--
作者：
Franca Bianco;G. Puppo;G. Russo
本文给出了一类求解双曲型守恒律方程组的激波捕获格式。该计划是基于一个修改的ENO重建逐点的值从细胞的平均值和近似计算的细胞边界上的通量。交错网格的使用避免了对黎曼解算器的需要。通量的积分由辛普森法则计算。在求积节点上的通量的近似是通过Runge-Kutta格式的自然连续扩展（NCE）的帮助下获得的。这种选择以低计算成本提供了极大的灵活性。对标量方程和系统进行了几次测试。数值结果证实了该格式的高精度和高分辨率特性。
A family of shock capturing schemes for the approximate solution of hyperbolic systems of conservation laws is presented. The schemes are based on a modified ENO reconstruction of pointwise values from cell averages and on approximate computation of the flux on cell boundaries. The use of a staggered grid avoids the need of a Riemann solver. The integral of the fluxes is computed by Simpson's rule. The approximation of the flux on the quadrature nodes is obtained by Runge--Kutta schemes with the aid of natural continuous extension (NCE). This choice gives great flexibility at low computational cost. Several tests are performed on the scalar equation and on systems. The numerical results confirm the expected accuracy and the high resolution properties of the schemes.