A characteristic-based shock-capturing scheme for hyperbolic problems
A characteristic-based shock-capturing scheme for hyperbolic problems
复制标题
DOI：
10.1016/j.jcp.2007.03.007
复制
发表时间：
2007-08
期刊：
影响因子：
--
通讯作者：
Guohua Tu;Xiang-jiang Yuan
中科院分区：
文献类型：
--
作者：
Guohua Tu;Xiang-jiang Yuan
为了抑制线性紧致格式在间断处的数值振荡，本文引入了一种基于特征线的通量分裂限制方法来代替ENO/韦诺等激波捕捉算法。该方法从迎风格式和通量矢量分裂开始。迎风格式沿沿着特征方向以不同的方式投影，并通过一个特殊的限制器来控制格式的振幅，以满足熵条件并防止非物理振荡。用这种方法对一个五阶线性紧致迎风格式进行了改进，使其能用于求解含间断问题。在一维、二维和三维空间中的一些基准问题上检验了数值算法的性能。数值结果表明，该方法具有高阶精度、高分辨率和无振荡等优点。
In order to suppress numerical oscillations of linear compact schemes around discontinuities, a characteristic-based flux splitting limited method is introduced instead of ENO/WENO or other shock-capturing algorithms. This method begins with upwind schemes and flux vector splittings. The upwind schemes are projected along characteristic directions in a different way, and their amplitudes are carefully controlled by a special limiter in order to meet entropy condition and to prevent non-physical oscillations. A fifth-order linear compact upwind scheme is modified by this method for solving problems involving discontinuities. The properties of the numerical algorithm are checked on some benchmark problems in one, two and three space dimensions. Numerical results show that it is high-order accurate with high resolution and oscillation-free.